From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 09:31:18 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1BTl8l029807 for ; Sat, 1 Dec 2007 09:29:47 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB1BTlXi029805 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 09:29:47 -0200 Received: from smtpi01s.infolink.com.br (smtpi01s.infolink.com.br [200.187.64.121]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1BTk8l029802 for ; Sat, 1 Dec 2007 09:29:46 -0200 Received: from smtpi01s.infolink.com.br (localhost [127.0.0.1]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 794CB1A7812 for ; Sat, 1 Dec 2007 10:31:06 -0200 (EDT) Received: from [127.0.0.1] (c9113d25.rjo.virtua.com.br [201.17.61.37]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 601EE1B006E for ; Sat, 1 Dec 2007 10:31:06 -0200 (EDT) Message-ID: <475153E5.4070309@infolink.com.br> Date: Sat, 01 Dec 2007 10:30:29 -0200 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] Re: [obm-l] esfera no cone References: <4750585F.9060901@infolink.com.br> In-Reply-To: Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 071130-0, 30/11/2007), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,CTYPE_JUST_HTML,HTML_FONT_COLOR_BLUE,IN_REP_TO, JAVASCRIPT_UNSAFE,MAILTO_LINK,RCVD_IN_DSBL, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 37.61.17.201.list.dsbl.org] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 37.61.17.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: CTYPE_JUST_HTML (0.4 points) HTML-only mail, with no text version SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Oi, Ney,

Equilátero não poderia ser pelos dados e a solução postada realmente só vale se ele for reto...

Abraços,
Nehab

Ney Falcao escreveu:
Olá Nehab,
 
suponho que seja um cone reto, embora o problema não mencione, como também não menciona se é equilátero ou não. Talvez o certo fosse mencionar, mas  a solução dos amigos bateu com a resposta.
 
Obrigado
Ney


 
Em 30/11/07, Carlos Nehab <nehab@infolink.com.br> escreveu:
Oi, Ney,

O cone é reto?

Nehab

Ney Falcao escreveu:
Como seria possivel calcular a área pedida no problema abaixo sem conhecer o raio da esfera?
 
Calcule o volume exterior a uma esfera e interior a um cone de raio da base igual a 6 e altura 8, sendo a esfera inscrita no cone.
 
Obrigado
Ney
========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html =========================================================================

========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 11:27:39 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1DPo8l005210 for ; Sat, 1 Dec 2007 11:25:50 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB1DPn3C005207 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 11:25:49 -0200 Received: from sc2.he.tucows.com (smtpout2012.sc2.he.tucows.com [64.97.155.12]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1DPh8l005115 for ; Sat, 1 Dec 2007 11:25:44 -0200 Received: from esquadrao (201.51.240.86) by sc2.he.tucows.com (7.3.127) (authenticated as marcusaurelio80) id 4747D5A6000E044F for obm-l@mat.puc-rio.br; Sat, 1 Dec 2007 14:27:00 +0000 From: "Marcus" To: Subject: [SPAM] ENC: [obm-l] Probabilidade Date: Sat, 1 Dec 2007 12:26:55 -0200 Message-ID: <002101c83426$3a53c830$aefb5890$@com> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: Acgzdb5XjsmSpah9Svi8KxneLzQ2eAAsHPZw Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcus" X-Spam-Status: Yes, hits=7.0 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_50_70,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0022_01C83415.76CAF830" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 12.155.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 12.155.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_0022_01C83415.76CAF830 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Marcus Enviada em: sexta-feira, 30 de novembro de 2007 15:24 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Probabilidade =20 Boa Tarde pessoal da lista, a minha d=FAvida e a seguinte eu fiz esse exerc=EDcio usando arranjo nos c=E1lculos de probabilidade, porem o meu professor me deu errado na prova, mas as respostas finas foram as mesma. = Eu queria saber se ta errado o que fiz.. =20 Meus c=E1lculos: =20 P(3 mulheres)=3D A(4,3) / A(10,3) =3D 1/30 =20 P(2 ao menos sendo mulheres) =3D A(4,2)*A(6,1)/ A(10,3) =3D 1/10 + 1/30 = =3D 1/15 =20 =20 Resposta do gabarito=20 P(3 mulheres)=3D C(4,3) / C(10,3) =3D 1/30 =20 P(2 ao menos sendo mulheres) =3D C(4,3) / C(10,3) + {C(4,2) / C(10,3)} = * 6 =3D 1/10 + 1/30 =3D 1/15 =20 =20 =20 Um grupo e constitu=EDdo de seis homens e quatro mulheres. Tr=EAs = pessoas s=E3o selecionadas ao acaso, neste grupo, sem reposi=E7=E3o, e os seguintes = eventos s=E3o considerados: as tr=EAs pessoas s=E3o mulheres; ao menos duas = pessoas s=E3o mulheres. =20 Calcule a probabilidade de cada um dos eventos definidos ocorrerem. ------=_NextPart_000_0022_01C83415.76CAF830 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

 

 

De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Marcus
Enviada em: sexta-feira, 30 de novembro de 2007 15:24
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] Probabilidade

 

Boa Tarde pessoal da lista, a minha d=FAvida e a = seguinte eu fiz esse exerc=EDcio usando arranjo nos c=E1lculos de probabilidade, = porem o meu  professor me deu errado na prova, mas as respostas finas foram = as mesma. Eu queria saber se ta errado o que fiz..

 

Meus c=E1lculos:

 

P(3 mulheres)=3D A(4,3) / A(10,3) =3D = 1/30

 

P(2 ao menos sendo mulheres) =3D A(4,2)*A(6,1)/ = A(10,3) =3D 1/10 + 1/30 =3D 1/15

 

 

Resposta do gabarito

P(3 mulheres)=3D C(4,3) / C(10,3) =3D = 1/30

 

P(2 ao menos sendo mulheres) =3D C(4,3) / C(10,3) +  {C(4,2) / C(10,3)} * 6  =3D 1/10 + 1/30 =3D = 1/15

 

 

 

Um grupo e constitu=EDdo de seis homens e quatro = mulheres. Tr=EAs pessoas s=E3o selecionadas ao acaso, neste grupo, sem = reposi=E7=E3o, e os seguintes eventos s=E3o considerados: as tr=EAs pessoas s=E3o mulheres; = ao menos duas pessoas s=E3o mulheres.

 

Calcule a probabilidade de cada um dos eventos = definidos ocorrerem.

------=_NextPart_000_0022_01C83415.76CAF830-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 12:39:48 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1Ebr8l009644 for ; Sat, 1 Dec 2007 12:37:53 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB1EboPP009641 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 12:37:50 -0200 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.239]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1EbY8l009632 for ; Sat, 1 Dec 2007 12:37:35 -0200 Received: by wr-out-0506.google.com with SMTP id c8so374275wra for ; Sat, 01 Dec 2007 07:38:54 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=Q/a07hWBUr1qpVpEpXegaRDbEgK1MehH9vLRTX9j5R4=; b=YF61erkiSBbYiUttTyzMFeVS0a6YhdffsBsTNxlQqUVL6wJozZTArYww1QQgohpsM1tv9Ijc7EMkqGfW9V9SupwPXxefbDIUAJIKczALkhxpEosYZZlG8TNb0bhSvnVIvu+GHrNXSRV0ML0heTTCGvvJ8mDobs2jvhNnj/qxIkA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:mime-version:content-type; b=gAu71ORYbGTOa3tOLBu5osYeVqma3ikgt8O5obCCwGbkgWSw8tS8OvjLXFpHQeFJrB92gyh2G3SWVnpsdXPKgfcB0ZxuMpDhMZxa3qPEOzQnG08VK3o+y8wSQZqFx0oya/bEcM5epvSumdeHUmJ5maw/WkQ9r4vY8lqvujQaO+I= Received: by 10.150.205.13 with SMTP id c13mr2272805ybg.1196523534582; Sat, 01 Dec 2007 07:38:54 -0800 (PST) Received: by 10.150.50.2 with HTTP; Sat, 1 Dec 2007 07:38:54 -0800 (PST) Message-ID: Date: Sat, 1 Dec 2007 13:38:54 -0200 From: "Ney Falcao" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] complexos_valores distintos MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ney Falcao" X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,HTML_70_90,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_636_4463444.1196523534555" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 239.184.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 239.184.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_636_4463444.1196523534555 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 amigos da lista, gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos: Determine, para k =CE N, o n=FAmero de valores distintos da express=E3o: y =3D i2k + 1 ik Obrigado, Ney ------=_Part_636_4463444.1196523534555 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Ol=E1 amigos da lista,
 
gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos:
 

Determine, para k =CE N, o n=FAmero de valores distin= tos da express=E3o:

=

y =3D

i 2k=  + 1

i k

Obrigado,

Ney

------=_Part_636_4463444.1196523534555-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 13:00:14 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1Ex98l010204 for ; Sat, 1 Dec 2007 12:59:09 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB1Ex89Z010199 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 12:59:08 -0200 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.237]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1Ex68l010195 for ; Sat, 1 Dec 2007 12:59:07 -0200 Received: by wr-out-0506.google.com with SMTP id c8so378307wra for ; Sat, 01 Dec 2007 08:00:26 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=sbkLPdQBe+QBF7b+Uvintjhgg8pu8s9l+kcGuNX6hOk=; b=U49Oc1wzB29izbiQGmiKCmlCqZse5RNgN+VXD5L/lGpvAMXKCXa35uJxciHUxWhD21cPecPgxQ3fJL3clMXi5YlJzN4N+ZLWClXJA0Gq37p14JqugSbRIiq+ZyCJL97frteJfd6r2tK9A5AVx/rhhN8myVz4OaPrm8hq/hziXek= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=QCkW6WAUQqyTJtNGyoPn2MHID0OA1LOzLmk6ulWqA6lukutwqmO67oSapkIBpa+wcWm+xxUXAIk43QGknx594IBwm5zDezXT82FyNNtcTXKCi1ZqyXTMfdjYk9c5mlptbIVKJqkbMeEELGUW+SxtaiJMae7LIAHU9IWJYQPauGg= Received: by 10.150.156.9 with SMTP id d9mr469955ybe.1196524826019; Sat, 01 Dec 2007 08:00:26 -0800 (PST) Received: by 10.150.50.2 with HTTP; Sat, 1 Dec 2007 08:00:25 -0800 (PST) Message-ID: Date: Sat, 1 Dec 2007 14:00:25 -0200 From: "Ney Falcao" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Re: complexos_valores distintos In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ney Falcao" X-Spam-Status: Yes, hits=5.3 required=5.0 tests=AWL,HTML_50_70,HTML_FONT_COLOR_BLUE,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_646_1434538.1196524825988" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 237.184.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 237.184.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_646_1434538.1196524825988 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Desculpem, a express=E3o =E9: y =3D (i^(2k) + 1) / 1^(k) ou seja, *2k* e *k* s=E3o expoentes de *i * Ney Em 01/12/07, Ney Falcao escreveu: > > Ol=E1 amigos da lista, > > gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos: > > > Determine, para k =CE N, o n=FAmero de valores distintos da express=E3o: > > y =3D > > i 2k + 1 > > i k > > Obrigado, > > Ney > ------=_Part_646_1434538.1196524825988 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Desculpem, a express=E3o =E9:
 
y =3D (i^(2k) + 1) / 1^(k)
 
ou seja, 2k e k s=E3o expoentes de <= strong>i

Ney


Em 01/12/07, Ney Falcao <neyfalcao@gmail.= com> escreveu:
Ol=E1 amigos da lista,
 
gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos:
 

Determine, para k <= span>=CE N, o n=FAmero de valo= res distintos da express=E3o:

y =3D

i 2k  + 1

i k

Obrigado,

Ney<= /p>


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saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lAS0fZTH018572 for ; Tue, 27 Nov 2007 22:41:41 -0200 Received: from www.urisan.tche.br (localhost [127.0.0.1]) by gama-rt.urisan.tche.br (Postfix) with ESMTP id E088E174442 for ; Tue, 27 Nov 2007 23:45:07 -0200 (BRST) Received: from 10.1.1.148 by www.urisan.tche.br with HTTP; Tue, 27 Nov 2007 23:45:07 -0200 (BRST) Message-ID: <1105.10.1.1.148.1196214307.squirrel@www.urisan.tche.br> In-Reply-To: <826521.76751.qm@web50611.mail.re2.yahoo.com> References: <826521.76751.qm@web50611.mail.re2.yahoo.com> Date: Tue, 27 Nov 2007 23:45:07 -0200 (BRST) Subject: [SPAM] Re: [obm-l] Res: [obm-l] =?iso-8859-1?Q?demonstra=E7=E3o:_pequeno_teorema_de_FERMAT?= From: rbdantas@urisan.tche.br To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.4.6 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: rbdantas@urisan.tche.br X-Spam-Status: Yes, hits=5.5 required=5.0 tests=IN_REP_TO,NO_REAL_NAME,PRIORITY_NO_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 150.104.203.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 150.104.203.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- > Certa vez vi uma prova da convergencia na revista professor de matematica mas não lembro qual foi o numero. Abs. Rivaldo pensei ter escrito n^p == n+ 1 mod p, desculpe............. > > aproveitando, vc sabe de alguma prova de convergência da sequência de > fibonacci? ou sequências com a mesma regra de formação (a de lucas, por > exemplo: 1,3,4,7,11,18...) > > Dei uma prova de convergência "feia" a partir da sequência de lucas (mas > o mesmo argumento vale para a sequência de fibonacci e qualquer outra) > > Repare que achar a razão áurea (pelo menos pelo método tradicional***) não > prova a convergência da sequência > > seja an = an-1 + an-2 a regra de formação; SE a sequência das razões > an/an-1converge para um limite L, então quando n--> infinito, an/an-1 --> > L > > na verdade, no limite an/an-1 = L, como an+1 = an + an-1, an/an-1 = (an + > an-1)/an = 1+an-1/an, oq implica L = 1 + 1/L ==> L^2 - L - 1 = 0 ==> L = > (1 +ou- 5^1/2)/2, desprezando-se o caso do sinal negativo (pois an é > sempre maior que an-1 e no caso negativo L seria < 1) > > Mas tudo isso baseado na suposição, gostaria de ver uma prova da > convergência > > ----- Mensagem original ---- > De: Maurício Collares > Para: obm-l@mat.puc-rio.br > Enviadas: Terça-feira, 27 de Novembro de 2007 19:10:51 > Assunto: Re: [obm-l] Res: [obm-l] Res: [obm-l] RES: [obm-l] Res: [obm-l] > demonstração: pequeno teorema de FERMAT > > On Nov 27, 2007 12:11 PM, Rodrigo Cientista > wrote: >> >> Só uma pequena correção, na útima passagem eu coloquei (n+1)^p == n + 1 >> mod >> p mas foi por acidente que o 1 ficou ali, esqueci de apagá-lo. > > Não vejo nenhum "1" extra na prova... De qual "1" você está falando? > > -- > Abraços, > Maurício > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 15:43:34 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1HgK8l019906 for ; Sat, 1 Dec 2007 15:42:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB1HgK1d019904 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 15:42:20 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB1HgI8l019901 for ; Sat, 1 Dec 2007 15:42:18 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4092952wag for ; Sat, 01 Dec 2007 10:43:37 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Gqu7vLw4556iKKqA6vcijPQgKEQg4kWo/6ATlouDPLI=; b=beMDEHMfqM3MgkdVlnhmSFYJgSIWk6vPzCoquRXhKjaikYvlUJZygrpUZkqML8AgVx1/PQpFxVM1WpgeJwTIb/zoIi1xx4rcj4ghLo/VnzyHOhwdYRrtBVcAdfocBnq9LWScxV2wb0BaAVTWrFM/0h63q6thnaOTsjCbbWVuwLs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=ui3kvkyoJAb2UZsvV3Fn6TfpZBZll8ZeLGY17YoOw+YzITbGqyKSOoO730ixfiYAwh5NfXBYKmPD1F3yZ4uWA+m6JX6Kkp8B8sEb2MSMN5VRNUxehGUK+EXW0UqQcQlFusjE5Hqxfq7ZRYYWRJpmzby8nVPJ3ewzp+1hKqx1L34= Received: by 10.114.126.1 with SMTP id y1mr1198680wac.1196534617179; Sat, 01 Dec 2007 10:43:37 -0800 (PST) Received: by 10.114.135.9 with HTTP; Sat, 1 Dec 2007 10:43:37 -0800 (PST) Message-ID: <3bd00efc0712011043w6fc62d7ao9861ce29458153ac@mail.gmail.com> Date: Sat, 1 Dec 2007 16:43:37 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: complexos_valores distintos In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4134_19500808.1196534617170" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=2.8 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,HTML_50_70,HTML_FONT_COLOR_BLUE, IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_4134_19500808.1196534617170 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Ney, i^(2k) =3D (i^2)^k =3D (-1)^k deste modo: y =3D [ 1 + (-1)^k ] / i^k se k for impar, o numerador =E9 0, logo: y =3D 0 se k for par, coloquemos k =3D 2a, o numerador =E9 2, e teremos: y =3D 2/i^= (2a) =3D 2/(-1)^a se a for par, y=3D2 se a for impar, y =3D -2 logo, os possiveis valores sao: -2, 0, 2 abracos, Salhab On Dec 1, 2007 2:00 PM, Ney Falcao wrote: > Desculpem, a express=E3o =E9: > > y =3D (i^(2k) + 1) / 1^(k) > > ou seja, *2k* e *k* s=E3o expoentes de *i > * > Ney > > > Em 01/12/07, Ney Falcao escreveu: > > > Ol=E1 amigos da lista, > > > > gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos: > > > > > > Determine, para k =CE N, o n=FAmero de valores distintos da express=E3o= : > > > > y =3D > > > > i 2k + 1 > > > > i k > > > > Obrigado, > > > > Ney > > > > ------=_Part_4134_19500808.1196534617170 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Ney,

i^(2k) =3D (i^2)^k =3D (-1)^k
deste modo:

y =3D= [ 1 + (-1)^k ] / i^k

se k for impar, o numerador =E9 0, logo: y =3D= 0
se k for par, coloquemos k =3D 2a, o numerador =E9 2, e teremos: y = =3D 2/i^(2a) =3D 2/(-1)^a
se a for par, y=3D2
se a for impar, y =3D -2

logo, os possive= is valores sao: -2, 0, 2

abracos,
Salhab


On Dec 1, 2007 2:00 PM, Ney Falcao < neyfalcao@gmail.com> wrote:
Desculpem, a express=E3o =E9:
 
y =3D (i^(2k) + 1) / 1^(k)
 
ou seja, 2k e k s=E3o expoentes de i

Ney

Em 01/12/07, Ney Falcao <neyfalcao@gmail.com> escreveu:
Ol=E1 amigos da lista,
 
gostaria de entender a solu=E7=E3o para essa quest=E3o de complexos:
 

Determine, para k =CE N, o n=FAmero de va= lores distintos da express=E3o:

y =3D

i 2k  + 1

i k

Obrigado,<= /font>

Ney=



------=_Part_4134_19500808.1196534617170-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 1 22:48:14 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB20kO8l027461 for ; Sat, 1 Dec 2007 22:46:24 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB20kO1B027459 for obm-l-MllGbsmmN; Sat, 1 Dec 2007 22:46:24 -0200 Received: from web33809.mail.mud.yahoo.com (web33809.mail.mud.yahoo.com [209.191.69.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB20kM8l027448 for ; Sat, 1 Dec 2007 22:46:23 -0200 Received: (qmail 92113 invoked by uid 60001); 2 Dec 2007 01:47:41 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=v2p4ba47haJW4uO3OX3v6B/WcOv06urDuj4H6fuillAjiiffUc9AybAguyguIHmPnN5VSC4if6qcpfvMUz/8hJIWMCg9bYpJsytSi1EhHeb7qJdB/+URG+hOKXBVnZotPj0v8A8m2WDIhc5OZjN2/Nmia1ZoJdQNJZN8XX4TAkk=; X-YMail-OSG: _b_1Re4VM1mUrNEBcOvaPZEBYV7xV5jkjzxGelwGAzxLsRj6jmQwDFuYTswuf7ZUgQ-- Received: from [201.51.122.141] by web33809.mail.mud.yahoo.com via HTTP; Sat, 01 Dec 2007 17:47:41 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.157 Date: Sat, 1 Dec 2007 17:47:41 -0800 (PST) From: Klaus Ferraz Subject: [SPAM] [obm-l] integral simples To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <821122.90334.qm@web33809.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Klaus Ferraz X-Spam-Status: Yes, hits=7.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1755719053-1196560061=:90334" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 172.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 172.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1755719053-1196560061=:90334 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Ol=C3=A1 alguem sabe como que resolvo a seguinte integral:=0A$e^x / x.=0A= =0A=0A Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa= =C3=A7o para armazenamento!=0Ahttp://br.mail.yahoo.com/ --0-1755719053-1196560061=:90334 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Ol=C3=A1 alguem sabe como que resolvo a seguinte integ= ral:
=0A
$e^x / x.

=0A=0A=0A
Abr= a sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7= o para armazenamento! =0A --0-1755719053-1196560061=:90334-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 2 13:38:26 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Fah8l007128 for ; Sun, 2 Dec 2007 13:36:43 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB2Fahad007126 for obm-l-MllGbsmmN; Sun, 2 Dec 2007 13:36:43 -0200 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.181]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Faf8l007123 for ; Sun, 2 Dec 2007 13:36:41 -0200 Received: by py-out-1112.google.com with SMTP id a29so7208506pyi for ; Sun, 02 Dec 2007 08:38:01 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=U2eBnJ4VcqDGsP5lFQTsrDTlgotcZGnrrnwmQ8KPCc4=; b=TjQAlwddA/rsdK3HU1lYFJpIgiQyePiO9wYr99YlrDAD2gg9SyWaxKoEbwRjfdsv8SZ23OiWkoOevE4yF/I1hziGMlgnBrc4WbohWNwpjNj6AY9WTjtmPQYJeanwAVUQ70yDvaxteqhKw2VwvJHzpPIOPuY0d/bYQWj8Ybh9mUc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:mime-version:content-type; b=ol0KeRI3B+xTrVkt7aUIWB2QDna62DANdhh3WHNrtt5fmpzZ5lhLNsq3ZK/UIz4tKJ6msIToLztAxRo4qcdATCEI5fsrsKQVzc0NKTvaXytnHvZChtGKTn4mePiBOE9WANtXWvh/cLXd9WquGBs8AlGOZeyS4GSqErUHa72faIE= Received: by 10.150.153.19 with SMTP id a19mr2484514ybe.1196613480211; Sun, 02 Dec 2007 08:38:00 -0800 (PST) Received: by 10.150.50.2 with HTTP; Sun, 2 Dec 2007 08:37:59 -0800 (PST) Message-ID: Date: Sun, 2 Dec 2007 14:37:59 -0200 From: "Ney Falcao" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] +complexos MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ney Falcao" X-Spam-Status: Yes, hits=6.7 required=5.0 tests=AWL,HTML_70_90,RCVD_IN_MULTIHOP_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_737_8683015.1196613479656" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_MULTIHOP_DSBL (0.8 points) RBL: Received via a relay in multihop.dsbl.org SPAM: [RBL check: found 181.166.233.64.multihop.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 181.166.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 181.166.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_737_8683015.1196613479656 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 amigos, podem me ajudar com esta? Considere a express=E3o: Z =3D 1 + =D6 3 a + bi b + ai Sabendo que os reais *a** * e *b* s=E3o tais que *a=B2 + b=B2 =3D 1,* dete= rmine *a*e *b* de modo que *z* seja: 1=B0) um n=FAmero real; 2=B0) imagin=E1rio puro. Obrigado Ney ------=_Part_737_8683015.1196613479656 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Ol=E1 amigos,
 
podem me ajudar com esta?
 
 

Considere a express=E3o:

Z =3D=

1

+

=D6

3

a + b= i

b +

 ai

Sabendo que os reais a  e b  s=E3o tais que a=B2 + b=B2 =3D 1, determi= ne a e b de modo que z seja:

1=B0) um n=FAmero real;

2=B0) imagin=E1rio puro.

 

Obrigado
Ney
 
------=_Part_737_8683015.1196613479656-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 2 13:40:10 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Fd38l007387 for ; Sun, 2 Dec 2007 13:39:03 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB2Fd340007385 for obm-l-MllGbsmmN; Sun, 2 Dec 2007 13:39:03 -0200 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Fd08l007374 for ; Sun, 2 Dec 2007 13:39:01 -0200 Received: by py-out-1112.google.com with SMTP id a29so7210530pyi for ; Sun, 02 Dec 2007 08:40:21 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=wve1PgcKoJ9l6n/OLUpwOag+L8Sw8SBYerQFWFmdkGg=; b=pfhXH/ec0cKCVZSlmVz/mRmwDn1i8Pl7vBhxjHEIUh//7ngLTNoFDXMFgm8hcMov8u+F5s05HNE3bLB+frWCHpFZcy9zL+oawvXcXGprS7SrARYrpKHp9C13dZYn8IEbaxb81LavBZJMf6GD9ApG4EUk1I2SkLniA07XQqBHojM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:mime-version:content-type; b=oTb14rr6cYg+hnK+eG++2RU40wHQKVXSp7Upy3oNbab0qOSXcFHORxZM04mz8+cMon4//P+tbbFtQCDc2dqXNIGk+vNNWmhP3nHfTIQ8JBk1KI+L+C+1nmyn+Vd1RPTiVlmgHjgs+sosOwKuieexHj2XpLBWKse6oviqfVY6ack= Received: by 10.150.177.20 with SMTP id z20mr2484229ybe.1196613620509; Sun, 02 Dec 2007 08:40:20 -0800 (PST) Received: by 10.150.50.2 with HTTP; Sun, 2 Dec 2007 08:40:20 -0800 (PST) Message-ID: Date: Sun, 2 Dec 2007 14:40:20 -0200 From: "Ney Falcao" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] outra de complexos MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ney Falcao" X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,HTML_70_90,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_740_7676587.1196613620482" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.166.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.166.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_740_7676587.1196613620482 Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Gostaria de uma ajuda com esta tamb=E9m: Para que valores de *x*, *x **=CE R*, o n=FAmero *z* =E9 real? Z =3D 1 + i + 1 =96 i x =96 i x + i Obrigado Ney ------=_Part_740_7676587.1196613620482 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
 
Gostaria de uma ajuda com esta tamb=E9m:
 

Para que valores de x, x =CE R, o n=FAmero z =E9 real?

 

Z =3D

1 + i

+

1 =96 i

x =96 i

x + i

 

Obrigado

Ney

------=_Part_740_7676587.1196613620482-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 2 14:49:53 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2GmD8l013333 for ; Sun, 2 Dec 2007 14:48:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB2GmDLM013331 for obm-l-MllGbsmmN; Sun, 2 Dec 2007 14:48:13 -0200 Received: from web56310.mail.re3.yahoo.com (web56310.mail.re3.yahoo.com [216.252.110.234]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB2GmB8l013326 for ; Sun, 2 Dec 2007 14:48:12 -0200 Received: (qmail 97364 invoked by uid 60001); 2 Dec 2007 17:49:26 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=5KxRnH1hbKvmpbcTbcPaHR76NGiIorSn+P9NmMEUVPxwdD+ia23PLhS3x6GDuc7guNGNnEccvKCXra/VkkAa4KdHCGP5Xn555JnmDZCL2Gnv2mpBaJoqE1i6IR4gO9YyAH4AhUIOzKBe6e0VRBDCeugRftL/Tt29m2TypavtTiA=; X-YMail-OSG: Q6F0XJgVM1lzpLz87GthY4Ib.ZREO8mlqDJIezGuhLVfafo0ILLxGgMCXhsFc0oUewdka_WH2ZplyohpxJ2Wr34SLZSahm9jQcSCGfDlVZDBhwvxGWm4j5ibhu3q4A-- Received: from [201.69.154.96] by web56310.mail.re3.yahoo.com via HTTP; Sun, 02 Dec 2007 14:49:26 ART Date: Sun, 2 Dec 2007 14:49:26 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] [obm-l] =?iso-8859-1?q?Resolu=E7=E3o?= To: =?iso-8859-1?q?Lista=20discuss=E3o=20obm?= MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <598895.96444.qm@web56310.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=7.2 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 234.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 234.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Gostaria que alguém me indicasse onde achar os exercicios resolvidos da obm2007, terceira fase , níveis 1,2 e 3. Preciso muito. Obrigado, Ruy Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 2 14:58:38 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Gve8l013586 for ; Sun, 2 Dec 2007 14:57:40 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB2GvevD013584 for obm-l-MllGbsmmN; Sun, 2 Dec 2007 14:57:40 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.191]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2Gvb8l013581 for ; Sun, 2 Dec 2007 14:57:39 -0200 Received: by rv-out-0910.google.com with SMTP id c27so2423265rvf for ; Sun, 02 Dec 2007 09:58:57 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=g3JvsQOfNCMXaAZx1U4/T/M+ct+rVICozRDb7Lt0knw=; b=RcJp+VXFpuyIKQIAkNtBE6zPtJpE2JFfElIMoKIeoNKfT1g+mqoMsJPCQFOnfDqCgrvWgOTY/NtCnLMI3oX5GA1nLsuxik3ywKzwRZ9rUxbVIK9gMtnNv04ymWCVfXEXihk+QvPT3Nb/lQIhcc+ZMqkY8wALXH/HJ9ODY5WPE+8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=S5x8XI3WJqLDgpFnHiSTB60aFki8NA76KSqE+JSMww07gKz7mLTWZhvnJX5CkLQYpdZkEoBR7lJx2Tuf0QpkfHPNxAwGu95JgAl+lMTT3HAPGpgK8ydc9GvZKO5lKH/0FIZUuC7hha2HRwbpR3ooDM8JQ84s3qU4UtvVvuTs88M= Received: by 10.141.116.16 with SMTP id t16mr5173637rvm.1196618337886; Sun, 02 Dec 2007 09:58:57 -0800 (PST) Received: from ?200.185.254.105? ( [200.185.254.105]) by mx.google.com with ESMTPS id m6sm6110697wrm.2007.12.02.09.58.55 (version=TLSv1/SSLv3 cipher=RC4-MD5); Sun, 02 Dec 2007 09:58:56 -0800 (PST) Message-ID: <4752F25C.1080706@gmail.com> Date: Sun, 02 Dec 2007 15:58:52 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] outra de complexos References: In-Reply-To: Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lB2Gvd8l013582 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=4.0 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ney Falcao escreveu: > > Gostaria de uma ajuda com esta também: > > > Para que valores de *x*, *x ** Î R*, o número *z* é real? > > > > Z = > > > > 1 + i > > > > + > > > > 1 – i > > x – i > > > > x + i > > > > Obrigado > > Ney > Olá Ney. Para resolver isso, primeiro é nescessario colocar z na forma z = a + i b Para isso é só fazer z = ( 1 + i )/( x - i ) + ( 1 - i )/( x + i ) = = [ ( x + i )( 1 + i ) + ( x - i )( 1 - i ) ]/[ ( x + i )( x - i ) ] = = [ x + ix + i - 1 + x - ix -i + 1 ]/[ x^2 + 1 ] = = [ 2x ]/[ x^2 + 1 ] = 2x/(x^2 + 1) e como se vê, z já é real para todo x real. Ok ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 2 15:19:15 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2HIG8l014634 for ; Sun, 2 Dec 2007 15:18:16 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB2HIFu6014632 for obm-l-MllGbsmmN; Sun, 2 Dec 2007 15:18:15 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB2HIB8l014608 for ; Sun, 2 Dec 2007 15:18:12 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4909199wag for ; Sun, 02 Dec 2007 10:19:32 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=pZLMXKAxMRfq6QUhi7S7KlTomEHhC4MzVW5qnrQ1BHg=; b=oZ2/UWijTUOAB1zQCAmQ4yB5z3BTVnktuOquwQFUQr2NVfmBuT7VQoQf5dp1UDRN4VWd8HgyCgQuw4BdbN2sXHOSA4SL7fcFiwVGTuySAxG8+SvDaP+rpEwPcIdCy9fzqJrRJMyFYDSPGRSWfuXwIHNiXCWZUUbJmPiqYMruN60= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=W6nEtJDOHSfo/7dUECcKPKGQRKg/dDLumCIw1hxfHtr6OTwu51cuy+8mbCzvW1mpO5bDGOAy4YOvcB+MgRfNH/JxvRFo2ErR9/o289kG6pqZSV/jA5HeOGaQLjmY+FzhGD2NuV1P+vEzmHJGUkiRw3K5IYXo85upVVtgvelchaU= Received: by 10.142.201.3 with SMTP id y3mr400678wff.1196619572294; Sun, 02 Dec 2007 10:19:32 -0800 (PST) Received: by 10.142.110.9 with HTTP; Sun, 2 Dec 2007 10:19:32 -0800 (PST) Message-ID: <789aac5a0712021019i6950fdd3i52c097be500ddb5f@mail.gmail.com> Date: Sun, 2 Dec 2007 16:19:32 -0200 From: Iuri To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] outra de complexos In-Reply-To: <4752F25C.1080706@gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=WINDOWS-1252 Content-Disposition: inline References: <4752F25C.1080706@gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lB2HIF8l014627 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Iuri X-Spam-Status: No, hits=3.6 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** (1-i)/(x+i) é o conjugado de (1+i)/(x-i) (prova-se usando só propriedades básicas de complexos), e portanto z=2.Re((1+i)/(x-i)), ou seja, é sempre real. Iuri On Dec 2, 2007 3:58 PM, albert richerd carnier guedes wrote: > Ney Falcao escreveu: > > > > > Gostaria de uma ajuda com esta também: > > > > > > Para que valores de *x*, *x ** Î R*, o número *z* é real? > > > > > > > > Z = > > > > > > > > 1 + i > > > > > > > > + > > > > > > > > 1 – i > > > > x – i > > > > > > > > x + i > > > > > > > > Obrigado > > > > Ney > > > Olá Ney. > > Para resolver isso, primeiro é nescessario colocar z na forma > > z = a + i b > > Para isso é só fazer > > z = ( 1 + i )/( x - i ) + ( 1 - i )/( x + i ) = > = [ ( x + i )( 1 + i ) + ( x - i )( 1 - i ) ]/[ ( x + i )( x - i ) ] = > = [ x + ix + i - 1 + x - ix -i + 1 ]/[ x^2 + 1 ] = > = [ 2x ]/[ x^2 + 1 ] = 2x/(x^2 + 1) > > e como se vê, z já é real para todo x real. > Ok ? > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 11:07:47 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3D5n8l021875 for ; Mon, 3 Dec 2007 11:05:49 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3D5neG021873 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 11:05:49 -0200 Received: from bay0-omc2-s29.bay0.hotmail.com (bay0-omc2-s29.bay0.hotmail.com [65.54.246.165]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3D5k8l021859 for ; Mon, 3 Dec 2007 11:05:47 -0200 Received: from BAY123-W15 ([207.46.11.50]) by bay0-omc2-s29.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Mon, 3 Dec 2007 06:07:07 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_bdec6ef0-fd45-4135-b841-9e1ce0c2a1dc_" X-Originating-IP: [201.22.126.178] From: =?iso-8859-1?Q?Lu=EDs_Lopes?= To: Subject: RE: [obm-l] mais uma de trigonometria Date: Mon, 3 Dec 2007 14:07:07 +0000 Importance: Normal In-Reply-To: <186963.44277.qm@web37404.mail.mud.yahoo.com> References: <186963.44277.qm@web37404.mail.mud.yahoo.com> MIME-Version: 1.0 X-OriginalArrivalTime: 03 Dec 2007 14:07:07.0974 (UTC) FILETIME=[CA515660:01C835B5] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Lu=EDs_Lopes?= X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** --_bdec6ef0-fd45-4135-b841-9e1ce0c2a1dc_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sauda,c~oes,=20 =20 Oi Graciliano,=20 D=E1 pra construir o tri=E2ngulo (T) com R&C.=20 E a=ED obter seus =E2ngulos, lados etc.=20 =20 Seja (B,C) a base do T. A reta (A,C) =E9 a reflex=E3o da reta=20 (A,B) em torno da bissetriz interna de A. Se B' =E9 a imagem=20 de B, ent=E3o AB'=3DAB=3Dc e CB'=3Db-c. Considere agora o T BCB'.=20 Deste T conhecemos BC=3Da, CB'=3Db-c e =E2ngulo CBB'=3D(B-C)/2.=20 E o =E2ngulo BB'C?=20 =20 O T BCB' =E9 f=E1cil de construir. Prolongue a reta (C,B') e ache=20 o ponto A. Sabe como?=20 =20 Outro problema: construir o T ABC dados .=20 =20 []'s=20 Lu=EDs=20 =20 Date: Fri, 30 Nov 2007 09:35:32 -0300From: bissa_damazo@yahoo.com.brSubject= : [obm-l] mais uma de trigonometriaTo: obm-l@mat.puc-rio.br1) em um triangu= lo qualquer ABC, temos como dado o lado "a", a diferen=E7a dos lados "b-c",= a diferen=E7a dos angulos "B-C" e pede-se calcular cos(A/2). =20 gostaria da colabora=E7=E3o dos amigos da lista =20 Graciliano=20 _________________________________________________________________ Encontre o que procura com mais efici=EAncia! Instale j=E1 a Barra de Ferra= mentas com Windows Desktop Search GR=C1TIS! http://desktop.msn.com.br/= --_bdec6ef0-fd45-4135-b841-9e1ce0c2a1dc_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sauda,c~oes,
 
Oi Graciliano,

D=E1 pra construir o tri=E2ngulo (T) com R&C.
E a=ED obter seus =E2ngulos, lados etc.
 
Seja (B,C) a base do T. A reta (A,C) =E9 a reflex=E3o da reta
(A,B) em torno da bissetriz interna de A. Se B' =E9 a imagem
de B, ent=E3o AB'=3DAB=3Dc e CB'=3Db-c. Considere agora o T BCB'.
Deste T conhecemos BC=3Da, CB'=3Db-c e =E2ngulo CBB'=3D(B-C)/2.
E o =E2ngulo BB'C?
 
O T BCB' =E9 f=E1cil de construir. Prolongue a reta (C,B') e ache
o ponto A. Sabe como?
 
Outro problema: construir o T ABC dados <a,b+c,B-C>.
 
[]'s
Lu=EDs
 

Date: Fri, 30 Nov 2007 09:35:32 -0300
From: bissa_damazo@yahoo.com.brSubject: [obm-l] mais uma de trigonometria
To: obm-l@mat.puc-rio.br

1) em um triangulo qualquer= ABC, temos como dado o lado "a", a diferen=E7a dos lados "b-c", a dif= eren=E7a dos angulos "B-C" e pede-se calcular cos(A/2).
 
gostaria da colabora=E7=E3o dos amigos da lista
 
Graciliano 


Encontre o que voc=EA procura com mais efici= =EAncia! Instale j=E1 a Barra de Ferramentas com Windows Desktop Search! =C9 GR=C1TIS! = --_bdec6ef0-fd45-4135-b841-9e1ce0c2a1dc_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 13:27:37 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3FJ0Gb032765 for ; Mon, 3 Dec 2007 13:25:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3ELSPM029475 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 12:21:28 -0200 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3ELF8l029359 for ; Mon, 3 Dec 2007 12:21:16 -0200 Received: from esquadrao (201.51.225.6) by sc2.he.tucows.com (7.3.127) (authenticated as marcusaurelio80) id 4747D58D0011E777 for obm-l@mat.puc-rio.br; Mon, 3 Dec 2007 15:22:35 +0000 From: "Marcus" To: Subject: [SPAM] [obm-l] Ajuda Date: Mon, 3 Dec 2007 13:22:31 -0200 Message-ID: <000f01c835c0$535261c0$f9f72540$@com> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: Acg1wFIJwqP8dhYETWOfniOneVhCzA== Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcus" X-Spam-Status: Yes, hits=7.0 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_50_70,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0010_01C835AF.8FC991C0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 80.154.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 80.154.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_0010_01C835AF.8FC991C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Boa Tarde pessoal da lista, a minha d=FAvida e a seguinte eu fiz esse exerc=EDcio usando arranjo nos c=E1lculos de probabilidade, porem o meu professor me deu errado na prova, mas as respostas finas foram as mesma. = Eu queria saber se ta errado o que fiz.. =20 Meus c=E1lculos: =20 P(3 mulheres)=3D A(4,3) / A(10,3) =3D 1/30 =20 P(2 ao menos sendo mulheres) =3D A(4,2)*A(6,1)/ A(10,3) =3D 1/10 + 1/30 = =3D 1/15 =20 =20 Resposta do gabarito=20 P(3 mulheres)=3D C(4,3) / C(10,3) =3D 1/30 =20 P(2 ao menos sendo mulheres) =3D C(4,3) / C(10,3) + {C(4,2) / C(10,3)} = * 6 =3D 1/10 + 1/30 =3D 1/15 =20 =20 =20 Um grupo e constitu=EDdo de seis homens e quatro mulheres. Tr=EAs = pessoas s=E3o selecionadas ao acaso, neste grupo, sem reposi=E7=E3o, e os seguintes = eventos s=E3o considerados: as tr=EAs pessoas s=E3o mulheres; ao menos duas = pessoas s=E3o mulheres. =20 Calcule a probabilidade de cada um dos eventos definidos ocorrerem. =20 ------=_NextPart_000_0010_01C835AF.8FC991C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Boa Tarde pessoal da lista, a minha d=FAvida e a = seguinte eu fiz esse exerc=EDcio usando arranjo nos c=E1lculos de probabilidade, porem o = meu  professor me deu errado na prova, mas as respostas finas foram as mesma. Eu queria = saber se ta errado o que fiz..

 

Meus c=E1lculos:

 

P(3 mulheres)=3D A(4,3) / A(10,3) =3D = 1/30

 

P(2 ao menos sendo mulheres) =3D A(4,2)*A(6,1)/ = A(10,3) =3D 1/10 + 1/30 =3D 1/15

 

 

Resposta do gabarito

P(3 mulheres)=3D C(4,3) / C(10,3) =3D = 1/30

 

P(2 ao menos sendo mulheres) =3D C(4,3) / C(10,3) + =  {C(4,2) / C(10,3)} * 6  =3D 1/10 + 1/30 =3D 1/15

 

 

 

Um grupo e constitu=EDdo de seis homens e quatro = mulheres. Tr=EAs pessoas s=E3o selecionadas ao acaso, neste grupo, sem reposi=E7=E3o, e = os seguintes eventos s=E3o considerados: as tr=EAs pessoas s=E3o mulheres; ao menos = duas pessoas s=E3o mulheres.

 

Calcule a probabilidade de cada um dos eventos = definidos ocorrerem.

 

------=_NextPart_000_0010_01C835AF.8FC991C0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 15:06:33 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3H4S8l009886 for ; Mon, 3 Dec 2007 15:04:28 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3H4Rf2009884 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 15:04:27 -0200 Received: from bay0-omc2-s20.bay0.hotmail.com (bay0-omc2-s20.bay0.hotmail.com [65.54.246.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3H4P8l009873 for ; Mon, 3 Dec 2007 15:04:26 -0200 Received: from BAY109-W20 ([64.4.19.120]) by bay0-omc2-s20.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Mon, 3 Dec 2007 10:05:46 -0800 Message-ID: Content-Type: text/plain X-Originating-IP: [200.185.255.56] From: Francisco To: =?iso-8859-1?Q?Lista_de_discurs=E3o?= Subject: [SPAM] [obm-l] =?iso-8859-1?Q?limite_de_2_vari=E1veis?= Date: Mon, 3 Dec 2007 21:05:46 +0300 Importance: Normal MIME-Version: 1.0 X-OriginalArrivalTime: 03 Dec 2007 18:05:46.0683 (UTC) FILETIME=[20EEF0B0:01C835D7] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Francisco X-Spam-Status: Yes, hits=5.3 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="_69434d62-db17-4729-acb5-7fb88606a9b4_" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 120.19.4.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 120.19.4.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --_69434d62-db17-4729-acb5-7fb88606a9b4_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable _________________________________________________________________ Conhe=E7a o Windows Live Spaces, a rede de relacionamentos conectada ao Mes= senger! http://spaces.live.com/signup.aspx= --_69434d62-db17-4729-acb5-7fb88606a9b4_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Conhe=E7a o Windows Live Spaces, o site de relacionamentos do M= essenger! Cr= ie j=E1 o seu! = --_69434d62-db17-4729-acb5-7fb88606a9b4_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 15:39:16 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3Hc38l018493 for ; Mon, 3 Dec 2007 15:38:03 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3Hc2U4018491 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 15:38:02 -0200 Received: from web56306.mail.re3.yahoo.com (web56306.mail.re3.yahoo.com [216.252.110.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB3Hbt8l018443 for ; Mon, 3 Dec 2007 15:37:56 -0200 Received: (qmail 47934 invoked by uid 60001); 3 Dec 2007 18:39:16 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=Q99VK7pvnidZyBAeSYqQitiEUN36/kvL9Pi5TqR8HIBCDks5PcF2gwtqwTg60O0Fx9JZgLS+3qa+eWDZcr04qfQ7eTgqpA2Ya7DNqkLXH4N8evfaOvOohTg1KVgPkKz1l0ripASSk+dTpQPN7tupWH1rLSnC8qYVl3mjnB0s52Y=; X-YMail-OSG: FzCYfHsVM1nxsG1zQ7SxutfrXFIDDmQLDN46oAyBYB7C9N6nUQMWFPMeKFYyi4maJTPXFrL_y0FBCbOFxqo9JbHEeghOFFGAVwNJXlzmPW1bfgCF2KE- Received: from [201.69.154.114] by web56306.mail.re3.yahoo.com via HTTP; Mon, 03 Dec 2007 15:39:16 ART Date: Mon, 3 Dec 2007 15:39:16 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] [obm-l] Exercicio olimpico To: =?iso-8859-1?q?Lista=20discuss=E3o=20obm?= MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <367300.46052.qm@web56306.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=7.2 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 230.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 230.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Caiu na terceira fase...Qual o valor de a para que(a^29-1)/(a-1)tenha pelo menos 2007 fatores primos? Não sei se o enunciado perguntava qual o menor valor de a.... Se alguém puder me mandar a resolução agradeço antecipadamente. Ruy Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 17:09:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3J7x8l000972 for ; Mon, 3 Dec 2007 17:07:59 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3J7xPo000970 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 17:07:59 -0200 Received: from web50601.mail.re2.yahoo.com (web50601.mail.re2.yahoo.com [206.190.38.88]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB3J7v8l000962 for ; Mon, 3 Dec 2007 17:07:57 -0200 Received: (qmail 90048 invoked by uid 60001); 3 Dec 2007 20:09:17 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=3IrWfKCgmkH2JVjjiwf8NQBlNbx/NP88lzqxRAe6wZjckvhy9An0ykyamlf6ImeoP8+jc/If+0fBoO6v2hwM2z+UG85HTBHss1z+oIatO0FS/9KuzLpSRiLjizHytMzqyxURwcZNOHZRrVHFM/IIK38Vli0l0iSHEQA2f2C3kNw=; X-YMail-OSG: ttMLt1AVM1llbiXB6jgJkMS2EHL9_WpxUG2a0etHU1g4KjzaQE9dhy1ilE24ApPUyzce2iTuEbeQegacsU5a2Soz3YHGcbNBcNP3E43BDMnRMB_SszB0uEZwZQ1j7onO4PWjkKKaiPYzxuw- Received: from [161.148.223.53] by web50601.mail.re2.yahoo.com via HTTP; Mon, 03 Dec 2007 12:09:17 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.157 Date: Mon, 3 Dec 2007 12:09:17 -0800 (PST) From: Rodrigo Cientista Subject: [SPAM] Res: [obm-l] Exercicio olimpico To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <782792.89014.qm@web50601.mail.re2.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lB3J7w8l000968 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Rodrigo Cientista X-Spam-Status: Yes, hits=7.5 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.50 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 88.38.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 88.38.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- fala só em 2007 fatores primos? sem especificar se são distintos ou não, então? pode ser p^2007 se não houver essa restrição, digamos (a^29-1)/(a-1) = p^2007 ==> ==> a^29 - a*p^2007 + (p^2007 - 1) = 0 por fermat a^29 == a mod 29 a divide (p^2007 - 1) ==> p^2007 == 1 mod a continua com fi de a, acho q sai alguma coisa... ----- Mensagem original ---- De: Ruy Oliveira Para: Lista discussão obm Enviadas: Segunda-feira, 3 de Dezembro de 2007 16:39:16 Assunto: [obm-l] Exercicio olimpico Caiu na terceira fase...Qual o valor de a para que(a^29-1)/(a-1)tenha pelo menos 2007 fatores primos? Não sei se o enunciado perguntava qual o menor valor de a.... Se alguém puder me mandar a resolução agradeço antecipadamente. Ruy Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 21:57:30 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3NtK8l021815 for ; Mon, 3 Dec 2007 21:55:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB3NtJkH021811 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 21:55:19 -0200 Received: from bay0-omc3-s8.bay0.hotmail.com (bay0-omc3-s8.bay0.hotmail.com [65.54.246.208]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB3NtF8l021762 for ; Mon, 3 Dec 2007 21:55:17 -0200 Received: from hotmail.com ([65.54.161.50]) by bay0-omc3-s8.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Mon, 3 Dec 2007 13:48:53 -0800 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Mon, 3 Dec 2007 13:48:53 -0800 Message-ID: Received: from 65.54.161.200 by by106fd.bay106.hotmail.msn.com with HTTP; Mon, 03 Dec 2007 21:48:50 GMT X-Originating-IP: [144.226.230.36] X-Originating-Email: [leandrorecova@msn.com] X-Sender: leandrorecova@msn.com In-Reply-To: <821122.90334.qm@web33809.mail.mud.yahoo.com> From: "LEANDRO L RECOVA" To: obm-l@mat.puc-rio.br Subject: RE: [obm-l] integral simples Date: Mon, 03 Dec 2007 13:48:50 -0800 Mime-Version: 1.0 Content-Type: text/plain; format=flowed X-OriginalArrivalTime: 03 Dec 2007 21:48:53.0718 (UTC) FILETIME=[4C3A5F60:01C835F6] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "LEANDRO L RECOVA" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,MSG_ID_ADDED_BY_MTA_2,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Voce quer saber a primitiva ou e uma integral definida? Se for definida, quais sao os limites de integracao? >From: Klaus Ferraz >Reply-To: obm-l@mat.puc-rio.br >To: obm-l@mat.puc-rio.br >Subject: [obm-l] integral simples >Date: Sat, 1 Dec 2007 17:47:41 -0800 (PST) > >Olá alguem sabe como que resolvo a seguinte integral: >$e^x / x. > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para >armazenamento! >http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 3 22:01:43 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB400g8l023875 for ; Mon, 3 Dec 2007 22:00:42 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB400fKp023872 for obm-l-MllGbsmmN; Mon, 3 Dec 2007 22:00:41 -0200 Received: from smtp110.mail.mud.yahoo.com (smtp110.mail.mud.yahoo.com [209.191.85.220]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB400Z8l023798 for ; Mon, 3 Dec 2007 22:00:36 -0200 Received: (qmail 91229 invoked from network); 4 Dec 2007 00:01:56 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:Content-Transfer-Encoding:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=iKd4hNWNlLVTPL1DnxkaLwJToIkQ9dUU4ur/U36XgJ0D20Y4ImLOfYVRzUA9dXKF0xT8B1MhBbjLdbLv2BDYqIjXOZcfL0Q1869OinAz+nUO1CNWJu/JVs0KXqoYv+LlpMWCmYGFHotNtVeuimk710uQlBteH4ZC+DCVD/E7k1o= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp110.mail.mud.yahoo.com with SMTP; 4 Dec 2007 00:01:55 -0000 X-YMail-OSG: G98t2GgVM1kRip9xiP9y3yr5Fq7kbzhi9nbSsgzQpCjH8c9AUCToye1XwbMyKmUPMl4c7cSsu3.pd07Yy6qQSYe3A6ptHZik5oPGff4t_u0W6zhXR2A- Message-ID: <001301c83611$6723ea10$02270269@rodrigo7a25356> From: To: References: <782792.89014.qm@web50601.mail.re2.yahoo.com> Subject: [SPAM] Re: [obm-l] Exercicio olimpico Date: Mon, 3 Dec 2007 22:02:41 -0300 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,NO_REAL_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.30 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 220.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 220.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- O problema formulado corretamente é: Mostre que existe um inteiro positivo a tal que (a^29-1)/(a-1) tem pelo menos 2007 fatores primos distintos. (aliás, não se pode afirmar que a^29 == a mod 29, desconsidere meu email anterior) escreva-se (a^29-1)/(a-1) = p_1^a_1*p_2^a_2*...*p_n^a_r, com p_1, p_2,..., p_n totalizando 2007 fatores primos distintos ( particularmente, n = 2007) chamaremos N = p_1^a_1*p_2^a_2*...*p_n^a_n ==> ==> phi(N) = 2^2007*I*p_1^(a_1 - 1)*p_2(^a_2 - 1)*...*p_n^(a_n - 1), sendo I um ímpar qualquer (a^29-1)/(a-1) == 0 mod N ==> (a^29-1)/(a-1) + 1 == 1 mod N ==> a^29 - 1+ a - 1 == a - 1 mod N ==> a^29 == 1 mod N a^29 == 1 mod N como (a^29-1)/(a-1) = 1 + a + a^2 + a^3 + ... + a^28 ==> N == 1 mod a ==> N^phi(a) == 1^phi(a) mod a ==> N^phi(a) == 1 mod a assim a^29 == 1 mod N, e N^phi(a) == 1 mod a daqui eu não consegui sair........ ----- Original Message ----- From: "Rodrigo Cientista" To: Sent: Monday, December 03, 2007 5:09 PM Subject: Res: [obm-l] Exercicio olimpico > fala só em 2007 fatores primos? sem especificar se são distintos ou não, > então? pode ser p^2007 se não houver essa restrição, digamos > > (a^29-1)/(a-1) = p^2007 ==> > > ==> a^29 - a*p^2007 + (p^2007 - 1) = 0 > > por fermat a^29 == a mod 29 > > a divide (p^2007 - 1) ==> p^2007 == 1 mod a > > continua com fi de a, acho q sai alguma coisa... > > ----- Mensagem original ---- > De: Ruy Oliveira > Para: Lista discussão obm > Enviadas: Segunda-feira, 3 de Dezembro de 2007 16:39:16 > Assunto: [obm-l] Exercicio olimpico > > Caiu na terceira fase...Qual o valor de a para > que(a^29-1)/(a-1)tenha pelo menos 2007 fatores primos? > Não sei se o enunciado perguntava qual o menor valor > de a.... > Se alguém puder me mandar a resolução agradeço > antecipadamente. > Ruy > > > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > http://br.mail.yahoo.com/ > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 12:08:55 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4E6R8l000820 for ; Tue, 4 Dec 2007 12:06:27 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4E6RU4000818 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 12:06:27 -0200 Received: from nz-out-0506.google.com (nz-out-0506.google.com [64.233.162.236]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4E6P8l000812 for ; Tue, 4 Dec 2007 12:06:25 -0200 Received: by nz-out-0506.google.com with SMTP id z6so2158588nzd for ; Tue, 04 Dec 2007 07:07:47 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=HD/C2Y/uQGRcqMQE9Y4jb+ZhkXhkY3S4Qy/7EBz5CLE=; b=uWC7ssyCHJORAW0fTM+K+ChFvdclIHcX+M4AlUs3nLVGIIEyB/p+aNKlusqYg+Wv7R5PrwyYjtaxVJQXVUg2cpDKc1fpvwlGoTS3AViFZvEsPblQRHIeJlyY2tl1++HklvsmTG6I2xXmMRq3qNUQWX2MauctMppMjPOWiJ5Qx8M= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Mspgx4vnnYqi/IDxPIBpgxmu8Cr0qLSBCEhyg8vzfO54DLjUe4nYErpIJgor2Teck1HXEmyDFeFipWqynPjsPzm4U3mbsL3GPmO6kOXPfsYay3KDuHsJko8DjjIj1+ICE+RAN433gLwM4mxsg5PHRhP3HOFfKMp8Eg2O8FBuJA8= Received: by 10.142.213.9 with SMTP id l9mr232979wfg.1196780866208; Tue, 04 Dec 2007 07:07:46 -0800 (PST) Received: by 10.142.108.14 with HTTP; Tue, 4 Dec 2007 07:07:46 -0800 (PST) Message-ID: Date: Tue, 4 Dec 2007 12:07:46 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_De_volta_=E0s_rec?= =?ISO-8859-1?Q?urs=F5es_em_duas_vari=E1veis!!!?= In-Reply-To: <5713b60b0711301123u7cefeb44gb4818879de4e81c6@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_16389_29625943.1196780866172" References: <5713b60b0711301123u7cefeb44gb4818879de4e81c6@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,GAPPY_TEXT,IN_REP_TO, JAVASCRIPT_UNSAFE,MAILTO_LINK,PLING_PLING, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_16389_29625943.1196780866172 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline A(x,1)=3D(n-x)A(x+1,0)-(x+1)A(x,0)=3D(n-x)-x-1=3Dn-1-2x A(x,y+1)=3D(n-x)A(x+1,y) -(x+1)A(x,y) A(x,y+2)=3D(n-x)A(x+1,y+1)-(x+1)A(x,y+1) somatorioA(x,k)(1,n)=3D(n-x)somatorioA(x+1,k)(0,n-1)-(x+1)somatorioA(x,k)(0= ,n-1) A(x,0)+A(x,n)+(x+2)somatorioA(x,k)(1,n-1)=3D(n-x)somatorioA(x+1,k)(0,n-1) A(n,0)+A(n,n)+(n+2)somaA(n,k)(1,n-1)=3D0 somaA(n,k)(1,n-1)=3D-(A(n,0)+A(n,n))/(n+2) somaA(n,k)(0,n)=3D(A(n,0)+A(n,n))(n+1)/(n+2) falta achar o A(n,n) On 11/30/07, Lestat di Lioncourt wrote: > Oi pessoal...tenho o seguinte problema... > ... > > A: N=B2-->R > x,y e N > n e N (par=E2metro) > > > > A(x,y+1)=3D(n-x)A(x+1,y) -(x+1)A(x,y) > A(x,0)=3D1 > > > A(x,y)=3D??? > > A(x,0)+A(x,1)+...+A(x,n)=3DS(x,n)=3D??? > > Agradeceria bastante se algu=E9m me resolvesse este trambolho... > ali=E1s...para o felizardo tenho v=E1rias outras d=FAvidas...e tamb=E9m, = claro, > porqu=EA das mesmas... > > At=E9! :) > ------=_Part_16389_29625943.1196780866172 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
A(x,1)=3D(n-x)A(x+1,0)-(x+1)A(x,0)=3D(n-x)-x-1=3Dn-1-2x
A(x,y+1)=3D(n-x)A(x+1,y) -(x+1)A(x,y)
A(x,y+2)=3D(n-x)A(x+1,y+1)-(x+1)A(x,y+1)
somatorioA(x,k)(1,n)=3D(n-= x)somatorioA(x+1,k)(0,n-1)-(x+1)somatorioA(x,k)(0,n-1)
A(x,0)+A(x,n)+(x+2)somatorioA(x,k)(1,n-1)=3D(n-x)somatorioA(x+1,k)(0,n= -1)
A(n,0)+A(n,n)+(n+2)somaA(n,k)(1,n-1)=3D0
somaA(n,k)(1,n-1)=3D-(A(n,0)+A(n,n))/(n+2)
somaA(n,k)(0,n)=3D(A(n,0)+A(n,n))(n+1)/(n+2)
falta achar o A(n,n)
 On 11/30/07, Lestat di Lioncourt <lestat.gauss@gmail.com > wrote:
Oi pessoal...tenho o seguinte problema...
...
 
A: N=B2-->R
x,y e  N
n e N       &= nbsp;           &nbs= p;    (par=E2metro)

 
 
A(x,y+1)=3D(n-x)A(x+1,y) -(x+1)A(x,y)
A(x,0)=3D1
 
 
A(x,y)=3D???
 
A(x,0)+A(x,1)+...+A(x,n)=3DS(x,n)=3D???
 
Agradeceria bastante se algu=E9m me resolvesse este trambolho...
ali=E1s...para o felizardo tenho v=E1rias outras d=FAvidas...e tamb=E9= m, claro, porqu=EA das mesmas...
 
At=E9!   :)

------=_Part_16389_29625943.1196780866172-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 12:27:26 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4EQ18l003459 for ; Tue, 4 Dec 2007 12:26:02 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4EQ0Jw003456 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 12:26:00 -0200 Received: from claretianas.com.br (server8.claretianas.com.br [200.245.46.125]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4EPt8l003448 for ; Tue, 4 Dec 2007 12:25:55 -0200 Received: from server8.claretianas.com.br (localhost [127.0.0.1]) by claretianas.com.br (8.13.8/8.13.5) with ESMTP id lB4FRGaM015380 for ; Tue, 4 Dec 2007 13:27:16 -0200 Received: (from nobody@localhost) by server8.claretianas.com.br (8.13.8/8.13.5/Submit) id lB4FRGT2015375; Tue, 4 Dec 2007 13:27:16 -0200 X-Authentication-Warning: server8.claretianas.com.br: nobody set sender to crmoraes@claretianas.com.br using -f Received: from 200.232.239.58 (SquirrelMail authenticated user crmoraes) by mail.claretianas.com.br with HTTP; Tue, 4 Dec 2007 13:27:16 -0200 (BRST) Message-ID: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> Date: Tue, 4 Dec 2007 13:27:16 -0200 (BRST) Subject: [obm-l] probabilidades From: crmoraes@CLARETIANAS.COM.BR To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.5.1 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Claretianas-MailScanner-Information: Para maiores informações entre em contato com seu provedor. X-Claretianas-MailScanner: Found to be clean X-Claretianas-MailScanner-From: crmoraes@claretianas.com.br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: crmoraes@claretianas.com.br X-Spam-Status: No, hits=4.3 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SIGNATURE_SHORT_SPARSE,SPAM_PHRASE_00_01,USER_AGENT, X_AUTH_WARNING,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Podem me ajudar com esses problemas? I-)Tenho o mesmo número de bolinhas de gude verdes, amarelas, azuis e brancas. 1. Qual a probabilidade de, em 10 bolinhas, não ter as 4 cores? II-) Tenho o mesmo número de bolinhas de gude azuis, vermelhas e amarelas. 1. Qual a probabilidade de, em 18 bolinhas, todas serem da mesma cor? 2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores (quaisquer)? 3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos 1 de cada cor? -- Mensagem verificada contra virus. Provedor Claretianas. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 12:32:33 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4EVZ8l003764 for ; Tue, 4 Dec 2007 12:31:35 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4EVZBL003762 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 12:31:35 -0200 Received: from claretianas.com.br (server8.claretianas.com.br [200.245.46.125]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4EVX8l003755 for ; Tue, 4 Dec 2007 12:31:34 -0200 Received: from server8.claretianas.com.br (localhost [127.0.0.1]) by claretianas.com.br (8.13.8/8.13.5) with ESMTP id lB4FWrwZ017556 for ; Tue, 4 Dec 2007 13:32:54 -0200 Received: (from nobody@localhost) by server8.claretianas.com.br (8.13.8/8.13.5/Submit) id lB4FWrTr017555; Tue, 4 Dec 2007 13:32:53 -0200 X-Authentication-Warning: server8.claretianas.com.br: nobody set sender to crmoraes@claretianas.com.br using -f Received: from 200.232.239.58 (SquirrelMail authenticated user crmoraes) by mail.claretianas.com.br with HTTP; Tue, 4 Dec 2007 13:32:53 -0200 (BRST) Message-ID: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> Date: Tue, 4 Dec 2007 13:32:53 -0200 (BRST) Subject: [SPAM] [obm-l] probabilidade From: crmoraes@CLARETIANAS.COM.BR To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.5.1 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 1 (Highest) Importance: High X-Claretianas-MailScanner-Information: Para maiores informações entre em contato com seu provedor. X-Claretianas-MailScanner: Found to be clean X-Claretianas-MailScanner-From: crmoraes@claretianas.com.br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: crmoraes@claretianas.com.br X-Spam-Status: Yes, hits=5.0 required=5.0 tests=AWL,NO_REAL_NAME,PRIORITY_NO_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SIGNATURE_SHORT_SPARSE, SPAM_PHRASE_00_01,USER_AGENT,X_AUTH_WARNING,X_MAILING_LIST, X_OSIRU_OPEN_RELAY,X_PRIORITY_HIGH version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.00 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: X_AUTH_WARNING (-0.2 points) Found a X-Authentication-Warning header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: X_PRIORITY_HIGH (0.4 points) Sent with 'X-Priority' set to high SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: SIGNATURE_SHORT_SPARSE (-2.1 points) Short signature present (empty lines) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 125.46.245.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 125.46.245.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Alguem pode me ajudar com esses problemas? I-)Tenho o mesmo número de bolinhas de gude verdes, amarelas, azuis e brancas. 1. Qual a probabilidade de, em 10 bolinhas, não ter as 4 cores? II-) Tenho o mesmo número de bolinhas de gude azuis, vermelhas e amarelas. 1. Qual a probabilidade de, em 18 bolinhas, todas serem da mesma cor? 2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores (quaisquer)? 3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos 1 de cada cor? -- Mensagem verificada contra virus. Provedor Claretianas. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 14:02:33 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4G0q8l010479 for ; Tue, 4 Dec 2007 14:00:52 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4G0qMQ010477 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 14:00:52 -0200 Received: from bay0-omc2-s21.bay0.hotmail.com (bay0-omc2-s21.bay0.hotmail.com [65.54.246.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4G0o8l010457 for ; Tue, 4 Dec 2007 14:00:51 -0200 Received: from BAY112-W33 ([64.4.26.133]) by bay0-omc2-s21.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Tue, 4 Dec 2007 09:02:12 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_3cda77d6-a55b-43d6-9802-b0d4b934508d_" X-Originating-IP: [201.37.214.138] From: Pedro Cardoso To: Subject: RE: [obm-l] probabilidade Date: Tue, 4 Dec 2007 20:02:12 +0300 Importance: Normal In-Reply-To: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> MIME-Version: 1.0 X-OriginalArrivalTime: 04 Dec 2007 17:02:12.0259 (UTC) FILETIME=[69C5C730:01C83697] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=3.7 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** --_3cda77d6-a55b-43d6-9802-b0d4b934508d_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1... =20 De quantas maneiras eu posso escrever um n=FAmero N como a soma de fatores,= n=E3o importando a ordem deles? =20 Como a pergunta ficou mal formulada, eu dou exemplos:[2] =3D 1+1 =3D 2+0. [3] =3D 1+1+1 =3D 1+2 =3D 3+0 [4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 4+0 =3D 2+2 ... [N] =3D ??? _________________________________________________________________ Veja mapas e encontre as melhores rotas para fugir do tr=E2nsito com o Live= Search Maps! http://www.livemaps.com.br/index.aspx?tr=3Dtrue= --_3cda77d6-a55b-43d6-9802-b0d4b934508d_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Ol=E1...
 
De quantas maneiras eu posso escrever um n=FAmero N como a soma de fatores,= n=E3o importando a ordem deles?
 
Como a pergunta ficou mal formulada, eu dou exemplos:

[2] =3D 1= +1 =3D 2+0.
[3] =3D 1+1+1 =3D 1+2 =3D 3+0
[4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 4+0 =3D 2+2
...
[N] =3D ???

Veja mapas e encontre as melhores rotas para fug= ir do tr=E2nsito com o Live Search Maps! Experimente j=E1! = --_3cda77d6-a55b-43d6-9802-b0d4b934508d_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 14:30:20 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4GSb8l013738 for ; Tue, 4 Dec 2007 14:28:43 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4GSX0M013733 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 14:28:33 -0200 Received: from bay0-omc2-s36.bay0.hotmail.com (bay0-omc2-s36.bay0.hotmail.com [65.54.246.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4GS48l013704 for ; Tue, 4 Dec 2007 14:28:08 -0200 Received: from BAY112-W13 ([64.4.26.113]) by bay0-omc2-s36.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Tue, 4 Dec 2007 09:23:34 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_32a8d022-aee2-4b02-8c32-035ed9810594_" X-Originating-IP: [201.37.214.138] From: Pedro Cardoso To: Subject: RE: [obm-l] probabilidade Date: Tue, 4 Dec 2007 20:23:34 +0300 Importance: Normal In-Reply-To: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> MIME-Version: 1.0 X-OriginalArrivalTime: 04 Dec 2007 17:23:34.0789 (UTC) FILETIME=[66385350:01C8369A] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_32a8d022-aee2-4b02-8c32-035ed9810594_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Cmoraes, eu recomendo que voc=EA escreve no google "solu=E7=F5es inteiras n= =E3o-negativas". =20 I) Depende do n=FAmero de bolinhas. Se houver mais de 9 bolinhas de cada co= r, tudo bem. Caso contr=E1rio, fica mais complicado, eu acho. Supondo que s= ejam mais de 9 de cada cor... =20 Sejam x1 o n=FAmero de bolinhas verdes, x2 o n=FAmero de amarelas, x3 o de= azuis, x4 o de brancas.=20 P(A) =E9 a probabilidade de ocorrer o evento A.=20 Al=E9m disso, o sinal '>=3D" significa 'maior ou igual'. =20 x1+x2+x3+x4 =3D 10=20 =20 O n=FAmero de solu=E7=F5es inteiras n=E3o-negativas dessa equa=E7=E3o corre= sponde ao n=FAmero de casos poss=EDveis para os grupos de 10 bolinhas (desd= e que a ordem das bolinhas n=E3o importe). Casos poss=EDveis =3D 13!/(3!10!= ) =3D 260. =20 P(n=E3o haver quatro cores) =3D 1 - P(haver quatro cores) =20 Para que hajam quatro cores, devemos ter x1,x2,x3,x4>0. Considere y um inte= iro maior ou igual a 0. Assim, satisfazendo as condi=E7=F5es do problema, x1 =3D y1+1; x2 =3D y2+1;= x3 =3D y3+1; x4 =3D y4+1 =20 Como x1+x2+x3+x4 =3D 10, (y1+1)+(y2+1)+(y3+1)+(y4+1) =3D 10 .:. y1+y2+y3+y4= =3D 6 (y>=3D0) =20 Os casos favor=E1veis s=E3o as solu=E7=F5es dessa =FAltima equa=E7=E3o. N=FAmero de casos favor=E1veis =3D 9!/(3!6!) =3D 84. =20 P(haver quatro cores) =3D 84/260 =3D 21/65 P(n=E3o haver quatro cores) =3D 1 - 21/65 =3D 44/65. =20 O II =E9 parecido, ent=E3o, entendendo o I, acho que voc=EA consegue resolv= =EA-lo. =20 *Eu considerei x>=3D10 porque, caso contr=E1rio, na equa=E7=E3o x1+x2+x3+x4= =3D10, eu teria que trabalhar com v=E1rios casos. A solu=E7=E3o x1 =3D10, x2,x3,x4 =3D 0 n=E3o valeria, por exemplo.=20 =20 At=E9. Espero ter ajudado. _________________________________________________________________ Conhe=E7a o Windows Live Spaces, a rede de relacionamentos conectada ao Mes= senger! http://spaces.live.com/signup.aspx= --_32a8d022-aee2-4b02-8c32-035ed9810594_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Cmoraes, eu recomendo que voc=EA escreve no g= oogle "solu=E7=F5es inteiras n=E3o-negativas".
 
I) Depende do n=FAmero de bolinhas. Se houver mais de 9 bolinhas = de cada cor, tudo bem. Caso contr=E1rio, fica mais complicado, eu acho. Sup= ondo que sejam mais de 9 de cada cor...
 
Sejam x1 o n=FAmero de bolinhas verdes, x2  o n=FAmero de&nb= sp;amarelas, x3 o de azuis, x4 o de brancas.
P(A) =E9 a probabilidade de ocorrer o evento A.
Al=E9m disso, o sinal '>=3D" significa 'maior ou igual'.
 
x1+x2+x3+x4 =3D 10 
 
O n=FAmero de solu=E7=F5es inteiras n=E3o-negativas dessa equa=E7=E3o corre= sponde ao n=FAmero de casos poss=EDveis para os grupos de 10 bolinhas (desd= e que a ordem das bolinhas n=E3o importe). Casos poss=EDveis =3D 13!/(3!10!= ) =3D 260.
 
P(n=E3o haver quatro cores) =3D 1 - P(haver quatro cores)
 
Para que hajam quatro cores, devemos ter x1,x2,x3,x4>0. Considere y um i= nteiro maior ou igual a 0.
Assim, satisfazendo as condi=E7=F5es do problema, x1 =3D y1+1; x2 =3D = y2+1; x3 =3D y3+1; x4 =3D y4+1
 
Como x1+x2+x3+x4 =3D 10, (y1+1)+(y2+1)+(y3+1)+(y4+1) =3D 10 .:. y1+y2+y3+y4= =3D 6 (y>=3D0)
 
Os casos favor=E1veis s=E3o as solu=E7=F5es dessa =FAltima equa=E7=E3o.
N=FAmero de casos favor=E1veis =3D 9!/(3!6!) =3D 84.
 
P(haver quatro cores) =3D 84/260 =3D 21/65
P(n=E3o haver quatro cores) =3D 1 - 21/65 =3D 44/65.
 
O II =E9 parecido, ent=E3o, entendendo o I, acho que voc=EA consegue resolv= =EA-lo.
 
*Eu considerei x>=3D10 porque, caso contr=E1rio, na equa=E7=E3o x1+x2+x3= +x4 =3D10, eu teria que trabalhar com v=E1rios casos.
A solu=E7=E3o x1 =3D10, x2,x3,x4 =3D 0 n=E3o valeria, por exemplo.
 
At=E9. Espero ter ajudado.


Conhe=E7a o Windows Live Spac= es, o site de relacionamentos do Messenger! Crie j=E1 o seu! = --_32a8d022-aee2-4b02-8c32-035ed9810594_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 14:44:11 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4GgC8l015137 for ; Tue, 4 Dec 2007 14:42:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4Gfw3s015124 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 14:42:01 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.242]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4Get8l015069 for ; Tue, 4 Dec 2007 14:40:58 -0200 Received: by an-out-0708.google.com with SMTP id c31so846549ana for ; Tue, 04 Dec 2007 09:42:13 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=xCuq+NTqLChs58+vwOIo9Xt3NdZTsqVyJZuGyzK9Ehs=; b=vSqKKpZxNxcSHBlGKHLasvqVciUgFHVRWMvN/+ShHibzNd7ZrC2rB+SLd9SyE7mko/m+VEpwgcPb/wlan1Dtunc7dU2wTp2XhmjnQ1sD2Ltdm5IfkNf2r9WtLTHz1MI2nNeFhhYIpGetzHKca5SrV+uOM46on9TyOX7uM8K3wxw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=r2acf1eHVx/pVT9m3uwEZhI5vz8JGqACnLw/epZHrZwiBHesVfHHFhDYsCw7gVar4PxksO3jN5k2SD+QrM41AH/03cZQK0vl2ZbdSQjZsVLpCYsMIgxUo7pX+DujjCCMyAcCajuYyNNjOKemVZl5aS7/u1LmY5Jkj29sOXy7ZAM= Received: by 10.100.248.9 with SMTP id v9mr1870987anh.1196790133480; Tue, 04 Dec 2007 09:42:13 -0800 (PST) Received: by 10.90.49.13 with HTTP; Tue, 4 Dec 2007 09:42:13 -0800 (PST) Message-ID: <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> Date: Tue, 4 Dec 2007 14:42:13 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] probabilidades In-Reply-To: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_310_5344121.1196790133468" References: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_310_5344121.1196790133468 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline I) Tecnicamente, isto depende do n=FAmero de bolinhas que voc=EA tem. Se vo= c=EA tiver 3 bolinhas de cada cor, por exemplo, em 10 bolinhas sorteadas sem reposi=E7=E3o voc=EA tem 100% de probabilidade de ter as 4 cores! Vou interpretar de outro jeito (que =E9 equivalente a tomar o n=FAmero de bolinhas indo para infinito, ou supor que as bolinhas s=E3o sorteadas **com= ** reposi=E7=E3o): vou fazer 10 sorteios independentes; cada sorteio consiste em escolher uma de 4 cores, todas com a mesma probabilidade 1/4. A pergunta =E9: qual a chance de faltar alguma cor no decorrer dos 10 sorteios? Vou usar M (aMarelo), Z (aZul), V (verde) e B (branco) para denotar o n=FAm= ero de vezes que cada cor apareceu nos 10 sorteio. Note que M+Z+V+B=3D10. Quere= mos Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0). i) Pr(M=3D0)=3DPr(Z=3D0)=3DPr(V=3D0)=3DPr(B=3D0)=3D(3/4)^10 (3/4 de chance em cada sorteio daquela cor espec=EDfica n=E3o aparecer) ii) Pr(M=3DZ=3D0)=3DPr(M=3DV=3D0)=3D...=3DPr(B=3DV=3D0)=3D(2/4)^10 (2/4 de chance em cada sorteio de ambas aquelas cores n=E3o aparecerem) iii) Pr(M=3DZ=3DV=3D0)=3DPr(M=3DZ=3DB=3D0)=3D...=3D(1/4)^10 (basicamente, cada um destes significa "tudo de uma cor s=F3") Pelo princ=EDpio da inclus=E3o-exclus=E3o, queremos Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0) =3D =3D Pr(M=3D0)+Pr(Z=3D0)+...+Pr(B=3D0) -(Pr(M=3D0 e Z=3D0)+Pr(M=3D0 e V=3D0)+...Pr(B=3DV=3D0)) +Pr(M=3DZ=3DV=3D0)+Pr(M=3DZ=3DB=3D0)+... -Pr(M=3DZ=3DV=3DB=3D0) =3D =3D 4.(3/4)^10-6.(2/4)^10+4.(1/4)^10 - 0 =3D 230056/(2^20) =3D 21.94% II) De novo, s=F3 d=E1 para achar um n=FAmero se a gente supuser que as bol= inhas s=E3o sorteadas COM reposi=E7=E3o (que =E9 equivalente ao n=FAmero de bolin= has tender a infinito). O m=E9todo =E9 igual ao de ali em cima: usarei a mesma nota=E7= =E3o Z (# de aZuis), V (# de Vermelhas) e M (# de aMarelas). Note que Z+V+M=3D18. i) Pr(Z=3D18)=3DPr(V=3D18)=3DPr(M=3D18)=3D(1/3)^18 Ent=E3o Pr(todas da mesma cor) =3D 3.(1/3)^18 - 1/9(3^17) =3D 7.74(10^-9) ii) Pr(Z=3D0)=3DPr(V=3D0)=3DPr(M=3D0)=3D(2/3)^18 Ent=E3o Pr(Z=3D0 ou V=3D0 ou M=3D0) =3D =3D Pr(Z=3D0)+Pr(V=3D0)+Pr(M=3D0) -Pr(Z=3DV=3D0)-Pr(Z=3DM=3D0)-Pr(V=3DM=3D0) +Pr(Z=3DV=3DM=3D0) =3D =3D 3.(2/3)^18-3.(1/3)^18+0 =3D 0.203% iii) Queremos Pr(Z<>0 e V<>0 e M<>0) que =E9 exatamente o complementar do i= tem anterior. Ent=E3o a resposta =E9 1-(3.(2/3)^18-3.(1/3)^18) =3D 99.797% On 12/4/07, crmoraes@claretianas.com.br wrote= : > > Podem me ajudar com esses problemas? > > I-)Tenho o mesmo n=FAmero de bolinhas de gude verdes, amarelas, azuis e > brancas. > 1. Qual a probabilidade de, em 10 bolinhas, n=E3o ter as 4 cores? > > > II-) Tenho o mesmo n=FAmero de bolinhas de gude azuis, vermelhas e amarel= as. > 1. Qual a probabilidade de, em 18 bolinhas, todas serem da mesma cor? > 2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores > (quaisquer)? > 3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos 1 de cada cor? > > > -- > Mensagem verificada contra virus. > Provedor Claretianas. > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_310_5344121.1196790133468 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Sent: Thursday, December 20, = 2007 5:00=20 PM
Subject: Re: [obm-l]=20 Trigonometria...


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quem puder  ajuda  valeu

Abra sua conta no Yahoo!=20 Mail, o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_00C9_01C8433B.FEF7C000-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 18:34:01 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKKVu8l032120 for ; Thu, 20 Dec 2007 18:31:56 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKKVuw5032118 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 18:31:56 -0200 Received: from web63712.mail.re1.yahoo.com (web63712.mail.re1.yahoo.com [69.147.97.97]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBKKVs8l032110 for ; Thu, 20 Dec 2007 18:31:55 -0200 Received: (qmail 33933 invoked by uid 60001); 20 Dec 2007 21:26:46 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=uMmquZ4zQg1wKk52T53jj8kxZXazbOjbQmganfq6/+k7ebsSjvpcUufModrtS75KTxaI2UwVjsQXg/UNz3GCyu2fB9/EAoUfXkke2oZLLeiFAjuEFQbDisJ+cS8t8jFWz1RQhl2/hwRkRdMiVLhWZNsvH59ke/wZUPNwo8Q/JL0=; X-YMail-OSG: ixYTKWAVM1la7q5ProXKjOB8vEeNBHNG0e.hcpWyrIj3pbvA8XmVIrEN_fVHK.xBne_Eb9P3sd_wzMBmWihqMjP7eD3t4HEwBhO7OGFCKbNgMcTnHfcOLg-- Received: from [189.24.118.87] by web63712.mail.re1.yahoo.com via HTTP; Thu, 20 Dec 2007 18:26:46 ART Date: Thu, 20 Dec 2007 18:26:46 -0300 (ART) From: fagner almeida Subject: [SPAM] [obm-l] Geometria . To: obm-l@mat.puc-rio.br In-Reply-To: <36492.93572.qm@web63714.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <781326.33624.qm@web63712.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=9.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS, HTML_FONT_COLOR_CYAN,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MIME_BOUND_DIGITS_5,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-467198833-1198186006=:33624" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 97.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 97.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-467198833-1198186006=:33624 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit http://imagetoker.com/viewer.php?id=890318geometria.JPG http://imagetoker.com/viewer.php?id=541398geometria2.JPG Quem puder ajudar valeu --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-467198833-1198186006=:33624 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit

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Quem puder  ajudar  valeu
 
 


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-467198833-1198186006=:33624-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 19:29:59 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKLJbHT002385 for ; Thu, 20 Dec 2007 19:27:04 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKHP9gK018249 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 15:25:09 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKHOw8l018169 for ; Thu, 20 Dec 2007 15:25:02 -0200 Received: by rv-out-0910.google.com with SMTP id c27so2829492rvf.9 for ; Thu, 20 Dec 2007 10:26:34 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=4DxTbGaF2L1wi/p5U7Vvi0y1ME+4ugubU/c5eiCChds=; b=Au43d317wnQeTKHai9uAwUUpFE3oD47lU32tUdYuXAx7p/6rNUU9SVuP/PR4DAgV/umr/zDKkLl1JEm656VjIPl6qbOBfXdqkifSpJ/Hjmf5Nr/JuDQj5SdnW/Ushi5HJBYzERf5/wCdC5JsHo+CZq94GM9NxI8OpQe1u4rzME4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=a8vbZRA6bzI8+o9GL6+ibjnemliFP9BCsv51+VjL+kr3z6T7Rc2V6QbRHWSnPJRTby/1qkpnP6gEQqjzRR/CD6Vvy97oDHqpLmnrbUS2x5SlLSMbuXwrrFhhg0NzUVZ89gB9fKDvvdfbd6dVQ+ydxwAD04hjtkFYJJj/oxBpcJ0= Received: by 10.140.82.38 with SMTP id f38mr200207rvb.28.1198175194502; Thu, 20 Dec 2007 10:26:34 -0800 (PST) Received: by 10.141.99.13 with HTTP; Thu, 20 Dec 2007 10:26:34 -0800 (PST) Message-ID: <99886d920712201026i38004454m399211acaf2a8fb5@mail.gmail.com> Date: Thu, 20 Dec 2007 19:26:34 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] cossenos sucessivos In-Reply-To: <66F665E9F7124DD7AB1E1DB20965926D@PAVILION> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_22196_31826903.1198175194486" References: <369302.55965.qm@web33807.mail.mud.yahoo.com> <66F665E9F7124DD7AB1E1DB20965926D@PAVILION> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_22196_31826903.1198175194486 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ola. Este problema ja foi (bem) discutido pelo menos duas vezes aqui na lista. Uma delas foi, se n=E3o me engano, no segundo semestre de 2005. Nessa discuss=E3o, demonstrei que a sequencia a_n =3D f(a_(n-1)) converge para um ponto fixo de f. De uma olhada nos arquivos! Bruno 2007/12/20, Ojesed Mirror : > > Numa calculadora operando em radianos, submete-se qualquer n=FAmero a > opera=E7=F5es sucessivas de cosseno e observa-se que o n=FAmero converge = para um > mesmo valor, independente do valor inicial adotado. > O valor pode ser obtido numericamente de cos(x)=3Dx. > > Mostrar que esta opera=E7=E3o transforma qualquer real neste n=FAmero. > > Ojesed > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_22196_31826903.1198175194486 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ola.
Este problema ja foi (bem) discutido pelo menos duas vezes aqui na = lista. Uma delas foi, se n=E3o me engano, no segundo semestre de 2005. Ness= a discuss=E3o, demonstrei que a sequencia a_n =3D f(a_(n-1)) converge para = um ponto fixo de f.

De uma olhada nos arquivos!

Bruno

2007/12/20, Ojesed Mirror <ojesed@uol.com.br>:
Numa calculadora operando em= =20 radianos, submete-se qualquer n=FAmero a opera=E7=F5es sucessivas= de cosseno=20 e observa-se que o n=FAmero converge para um mesmo valor, indepen= dente=20 do valor inicial adotado.
O valor pode ser obtido numericamente = de=20 cos(x)=3Dx.
 
Mostrar que esta opera=E7=E3o&nbs= p;transforma=20 qualquer real neste n=FAmero.
 
Ojesed



--
Bruno FRAN=C7A DOS REIS=

msn: brunoreis666@hotma= il.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16

e^(pi= *i)+1=3D0 ------=_Part_22196_31826903.1198175194486-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 21:05:46 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKN3Q8l024740 for ; Thu, 20 Dec 2007 21:03:26 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKN3QQt024738 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 21:03:26 -0200 Received: from bay0-omc2-s14.bay0.hotmail.com (bay0-omc2-s14.bay0.hotmail.com [65.54.246.150]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKN3O8l024735 for ; Thu, 20 Dec 2007 21:03:25 -0200 Received: from hotmail.com ([65.54.161.41]) by bay0-omc2-s14.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Thu, 20 Dec 2007 16:05:00 -0800 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Thu, 20 Dec 2007 16:05:00 -0800 Message-ID: Received: from 65.54.161.200 by by106fd.bay106.hotmail.msn.com with HTTP; Fri, 21 Dec 2007 00:04:56 GMT X-Originating-IP: [144.226.230.36] X-Originating-Email: [leandrorecova@msn.com] X-Sender: leandrorecova@msn.com In-Reply-To: <99886d920712201026i38004454m399211acaf2a8fb5@mail.gmail.com> From: "LEANDRO L RECOVA" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] cossenos sucessivos Date: Thu, 20 Dec 2007 16:04:56 -0800 Mime-Version: 1.0 Content-Type: text/plain; format=flowed X-OriginalArrivalTime: 21 Dec 2007 00:05:00.0410 (UTC) FILETIME=[20FA6DA0:01C84365] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "LEANDRO L RECOVA" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,MSG_ID_ADDED_BY_MTA_2, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** O livro do Rudin "Principles of Mathematical Analysis" apresenta o principio da contracao e o teorema do ponto fixo no capitulo 9. Inclusive, a demonstracao e uma maneira de construir tal ponto. De uma olhada, e bem interessante. Leandro. >From: "Bruno França dos Reis" >Reply-To: obm-l@mat.puc-rio.br >To: obm-l@mat.puc-rio.br >Subject: Re: [obm-l] cossenos sucessivos >Date: Thu, 20 Dec 2007 19:26:34 +0100 > >Ola. >Este problema ja foi (bem) discutido pelo menos duas vezes aqui na lista. >Uma delas foi, se não me engano, no segundo semestre de 2005. Nessa >discussão, demonstrei que a sequencia a_n = f(a_(n-1)) converge para um >ponto fixo de f. > >De uma olhada nos arquivos! > >Bruno > >2007/12/20, Ojesed Mirror : > > > > Numa calculadora operando em radianos, submete-se qualquer número a > > operações sucessivas de cosseno e observa-se que o número converge para >um > > mesmo valor, independente do valor inicial adotado. > > O valor pode ser obtido numericamente de cos(x)=x. > > > > Mostrar que esta operação transforma qualquer real neste número. > > > > Ojesed > > > > > >-- >Bruno FRANÇA DOS REIS > >msn: brunoreis666@hotmail.com >skype: brunoreis666 >tel: +33 (0)6 28 43 42 16 > >e^(pi*i)+1=0 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 21 01:28:24 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBL3JcHP022670 for ; Fri, 21 Dec 2007 01:26:43 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBL2Q3Mp020017 for obm-l-MllGbsmmN; Fri, 21 Dec 2007 00:26:03 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.243]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBL2Pr8l019933 for ; Fri, 21 Dec 2007 00:25:54 -0200 Received: by an-out-0708.google.com with SMTP id c31so34130ana.120 for ; Thu, 20 Dec 2007 19:27:29 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; bh=hsx/XggXoHYLfoLNyNot1E8MHgMhxKatvByWdn8O+cA=; b=hB3/wiroGvJgeCBkwHFlDvb9PHZjRV3O1cspZ/QBKZXUPxV+dzq3oLCr5CMd/JZ3K/kxxR1JAGuglJbzJGQXF5IE190y/dPwv5W037efJzKaiMLMoclo5uml0Acd3+361D6UWO3L7MHb6lU2faqBqCKNpbA6M0f1lK+WF5RIJec= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; b=eKOl+KFnzxhQ8DUe7ogm8R6YvZRKe0C4DGWUY0ybWWQuGvpwzhrPtPPQxpobXQeCLhxwXlbtbd02gybCtfoeiBMah6p8CxyOtDnGvwSJCZOEZ+eZ62GDX+dE1Yiof2PjltJ4c3jNj0z10TCQ5cXAiltVLr/B8afmBchgvAkFkjs= Received: by 10.101.71.16 with SMTP id y16mr1545972ank.79.1198207649607; Thu, 20 Dec 2007 19:27:29 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.249.106]) by mx.google.com with ESMTPS id 1sm888481agb.16.2007.12.20.19.27.26 (version=TLSv1/SSLv3 cipher=RC4-MD5); Thu, 20 Dec 2007 19:27:27 -0800 (PST) Message-ID: <476B1674.9010805@gmail.com> Date: Thu, 20 Dec 2007 23:27:16 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Produto finito (2) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBL2Px8l019992 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: Yes, hits=5.3 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 243.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 243.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Se eu tenho duas séries numéricas {a_n} e {b_n} tais que prod^N_{n=r} a_n = prod^N_{n=r} b_n onde r é um inteiro menor ou igua a N, então a_n é nescessáriamente igual a b_n ? Se não for , então qual a condicao para que isso aconteça ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 21 11:47:48 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLDiw8l026469 for ; Fri, 21 Dec 2007 11:44:58 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBLDiw60026467 for obm-l-MllGbsmmN; Fri, 21 Dec 2007 11:44:58 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLDit8l026461 for ; Fri, 21 Dec 2007 11:44:56 -0200 Received: by wa-out-1112.google.com with SMTP id m28so551444wag.13 for ; Fri, 21 Dec 2007 06:46:32 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=DZVZsNx8RoL9bpVs0eFDEcLyR21Y//AFvyiEScrH2+Q=; b=iN5FG9GN5vE9Gk80gXn5gl27G1e4fCFH2pYOibhdKp2lIzf7kYIJeFk9rQxQFv33qxiN1oFBqzhbWqcIYlhjCYLt2neWtqzQp3L9stPnvCtDS9QUscwcBjBzDIGeHeOdjz9P3I8uGPCYY1EWLJm1vVVq0vRyTSv3GC9GpfaUpmc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=H80zzEaIHc68oYqgIQmTcB24WIkxddEqVqPpsmSM8pV/k4Glh+3OyOxuKpu7uqlgLJSZIyYsHGm1jqDWhIrxv5ifLRp4MghCI+UCnr9lJsSgZxupVey90YAzObegRoxsaHxzUPGwezbJ2LzTs2D8IBpDMn/q+kRpt6n6mamA0bs= Received: by 10.114.73.1 with SMTP id v1mr1506943waa.16.1198248392058; Fri, 21 Dec 2007 06:46:32 -0800 (PST) Received: by 10.114.136.9 with HTTP; Fri, 21 Dec 2007 06:46:32 -0800 (PST) Message-ID: <3bd00efc0712210646m34339298ted8044b09bcbcbb8@mail.gmail.com> Date: Fri, 21 Dec 2007 12:46:32 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Produto finito (2) In-Reply-To: <476B1674.9010805@gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_16_17824426.1198248392045" References: <476B1674.9010805@gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=3.0 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_16_17824426.1198248392045 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Albert, acredito que n=E3o... se a_r =3D 0 e b_r =3D 0, os produt=F3rios ser=E3o se= mpre iguais. Mas a_n n=E3o =E9 igor a b_n. Um outro modo deste fato acontecer, =E9, a_r, a_(r+1),..., a_N ser uma permuta=E7=E3o de b_r, b_(r+1), ..., b_N. talvez uma condi=E7=E3o que fa=E7a com que isso aconte=E7a at=E9 o N-=E9sim= o elemento =E9: para todo r inteiro menor ou igual a N. abra=E7os, Salhab On Dec 20, 2007 11:27 PM, albert richerd carnier guedes wrote: > Se eu tenho duas s=E9ries num=E9ricas {a_n} e {b_n} tais que > > prod^N_{n=3Dr} a_n =3D prod^N_{n=3Dr} b_n > > onde r =E9 um inteiro menor ou igua a N, ent=E3o a_n =E9 nescess=E1riamen= te > igual a b_n ? > Se n=E3o for , ent=E3o qual a condicao para que isso aconte=E7a ? > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_16_17824426.1198248392045 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Albert,

acredito que n=E3o... se a_r =3D 0 e b_r =3D 0, os pro= dut=F3rios ser=E3o sempre iguais. Mas a_n n=E3o =E9 igor a b_n.
Um outro= modo deste fato acontecer, =E9, a_r, a_(r+1),..., a_N ser uma permuta=E7= =E3o de b_r, b_(r+1), ..., b_N.

talvez uma condi=E7=E3o que fa=E7a com que isso aconte=E7a at=E9 o = N-=E9simo elemento =E9: para todo r inteiro menor ou igual a N.

abra= =E7os,
Salhab


On Dec 20, 2007 11:2= 7 PM, albert richerd carnier guedes < arcguede@gmail.com> wrote:
=
Se eu tenho duas = s=E9ries num=E9ricas {a_n} e {b_n} tais que

prod^N_{n=3Dr} a_n =3D prod^N_{n=3Dr} b_n

onde r =E9 um inte= iro menor ou igua a N, ent=E3o a_n =E9 nescess=E1riamente
igual a b_n ?<= br>Se n=E3o for , ent=E3o qual a condicao para que isso aconte=E7a ?



=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista emhttp://www.mat.puc-rio.br/~obmlistas/obm-l.html
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------=_Part_16_17824426.1198248392045-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 21 13:09:02 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLF6w8l001183 for ; Fri, 21 Dec 2007 13:06:58 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBLF6wvN001181 for obm-l-MllGbsmmN; Fri, 21 Dec 2007 13:06:58 -0200 Received: from nz-out-0506.google.com (nz-out-0506.google.com [64.233.162.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLF6t8l001163 for ; Fri, 21 Dec 2007 13:06:56 -0200 Received: by nz-out-0506.google.com with SMTP id z6so184720nzd.9 for ; Fri, 21 Dec 2007 08:08:32 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; bh=KOxBMCXXQPgGY+h9Vi5HP1OkMqKL0voevByFdrWstmw=; b=tTU8TcAlyaGAgraxOMkh+M20iPatpgkpc/pN7SfO8MCBxtiNBTSdWOelgWUexT1AGp44WWhLEdJFarMTUmIUai6Wk8BqgmnH3syVwarcRe1ud9gpLMZkAipQhEK+ZYMgfItVLnw4bKtLKmIQepnnrCSxkd8z+PjffVS1OHotcaQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; b=B6LkiSEDjCOuNuKdzOXnTK3udnqJiXvAIPt1mV+zKlOlfxQi/Zn4R8YALNkJdlmOLJGQlMLyznP0lENONNxVtcykhT+sO0qpOdhrjjsdejzVrAk4zeyqYwYT9TbRveGf1jauKqvbm3W+dPuctXD1m3P/EXdrsr8Bws+a7bkdfoU= Received: by 10.142.135.9 with SMTP id i9mr693419wfd.211.1198253312131; Fri, 21 Dec 2007 08:08:32 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.250.167]) by mx.google.com with ESMTPS id 18sm1831854wry.17.2007.12.21.08.08.29 (version=SSLv3 cipher=RC4-MD5); Fri, 21 Dec 2007 08:08:30 -0800 (PST) Message-ID: <476BE4F8.10107@gmail.com> Date: Fri, 21 Dec 2007 14:08:24 -0200 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Produto finito (2) References: <476B1674.9010805@gmail.com> <3bd00efc0712210646m34339298ted8044b09bcbcbb8@mail.gmail.com> In-Reply-To: <3bd00efc0712210646m34339298ted8044b09bcbcbb8@mail.gmail.com> Content-Type: multipart/alternative; boundary="------------060201060605050802010704" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: No, hits=3.4 required=5.0 tests=IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** This is a multi-part message in MIME format. --------------060201060605050802010704 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Era o que eu pensava, mas como não sou muito bom em formalizar provas matemáticas (mal de físico) , acreditava que talvez tenha escapado alguma coisa. Mas começar com um r menor que N me deu uma nova perspectiva. Valeu pela ajuda. Marcelo Salhab Brogliato escreveu: > Olá Albert, > > acredito que não... se a_r = 0 e b_r = 0, os produtórios serão sempre > iguais. Mas a_n não é igor a b_n. > Um outro modo deste fato acontecer, é, a_r, a_(r+1),..., a_N ser uma > permutação de b_r, b_(r+1), ..., b_N. > > talvez uma condição que faça com que isso aconteça até o N-ésimo > elemento é: para todo r inteiro menor ou igual a N. > > abraços, > Salhab > > > On Dec 20, 2007 11:27 PM, albert richerd carnier guedes < > arcguede@gmail.com > wrote: > > Se eu tenho duas séries numéricas {a_n} e {b_n} tais que > > prod^N_{n=r} a_n = prod^N_{n=r} b_n > > onde r é um inteiro menor ou igua a N, então a_n é nescessáriamente > igual a b_n ? > Se não for , então qual a condicao para que isso aconteça ? > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > --------------060201060605050802010704 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Era o que eu pensava, mas como não sou muito bom em formalizar provas matemáticas (mal de físico) , acreditava que talvez tenha escapado alguma coisa.
Mas começar com um r menor que N me deu uma nova perspectiva.
Valeu pela ajuda.

Marcelo Salhab Brogliato escreveu:
Olá Albert,

acredito que não... se a_r = 0 e b_r = 0, os produtórios serão sempre iguais. Mas a_n não é igor a b_n.
Um outro modo deste fato acontecer, é, a_r, a_(r+1),..., a_N ser uma permutação de b_r, b_(r+1), ..., b_N.

talvez uma condição que faça com que isso aconteça até o N-ésimo elemento é: para todo r inteiro menor ou igual a N.

abraços,
Salhab


On Dec 20, 2007 11:27 PM, albert richerd carnier guedes < arcguede@gmail.com> wrote:
Se eu tenho duas séries numéricas {a_n} e {b_n} tais que

prod^N_{n=r} a_n = prod^N_{n=r} b_n

onde r é um inteiro menor ou igua a N, então a_n é nescessáriamente
igual a b_n ?
Se não for , então qual a condicao para que isso aconteça ?




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--------------060201060605050802010704-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 21 14:42:05 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLGdM8l009961 for ; Fri, 21 Dec 2007 14:39:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBLGdL8G009959 for obm-l-MllGbsmmN; Fri, 21 Dec 2007 14:39:21 -0200 Received: from bay0-omc2-s37.bay0.hotmail.com (bay0-omc2-s37.bay0.hotmail.com [65.54.246.173]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLGdJ8l009951 for ; Fri, 21 Dec 2007 14:39:20 -0200 Received: from BAY113-W5 ([65.54.168.105]) by bay0-omc2-s37.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Fri, 21 Dec 2007 09:40:56 -0800 Message-ID: Content-Type: text/plain X-Originating-IP: [201.42.154.163] From: Tales Prates Correia To: Subject: [SPAM] RE: [obm-l] Geometria . Date: Fri, 21 Dec 2007 20:40:56 +0300 Importance: Normal In-Reply-To: <781326.33624.qm@web63712.mail.re1.yahoo.com> References: <36492.93572.qm@web63714.mail.re1.yahoo.com> <781326.33624.qm@web63712.mail.re1.yahoo.com> MIME-Version: 1.0 X-OriginalArrivalTime: 21 Dec 2007 17:40:56.0508 (UTC) FILETIME=[A427C7C0:01C843F8] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Tales Prates Correia X-Spam-Status: Yes, hits=5.9 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_FONT_COLOR_CYAN, HTML_FONT_COLOR_UNSAFE,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="_6e774222-98af-4c6f-b60e-886a533902bf_" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.90 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 105.168.54.65.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 105.168.54.65.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --_6e774222-98af-4c6f-b60e-886a533902bf_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable 4 - A afirma=E7=E3o prop=F5e um novo caso de congru=EAncia, a sab= er, o caso "lado-lado-=E2ngulo". Usando a figura fornecida, =E9 poss=EDvel = mostrar porque esse crit=E9rio n=E3o =E9 v=E1lido: segundo esse novo caso, os tr= i=E2ngulos ROP e QOP deveriam ser congruentes, por=E9m isto =E9 uma inverda= de, uma vez que o teorema do angulo externo aplicado ao tri=E2ngulo QOR nos p= ermite afirmar que o =E2ngulo PQO =E9 maior do que PRO. 5 - Por defini=E7=E3o, uma corda de uma circunfer=EAncia =E9 um s= egmento de reta cujas extremidades pertencem a essa circunfer=EAncia. A med= iatriz de um segmento de reta =E9 o lugar geom=E9trico dos pontos eq=FCidis= tantes das extremidades desse segmento. Ora, uma vez que as extremidades da corda pertencem =E0 circunfer=EAncia, as dist=E2ncias desses pont= os ao centro desta s=E3o iguais e congruentes ao raio. Por conseguinte, a m= ediatriz "passar=E1" pelo centro da circunfer=EAncia. = = Q.E.D. 6 - Todas as afirma=E7=F5es s=E3o verdadeiras. Item a: Propriedade fundamental dos paralelogramos que decorre do= teorema angular de Tales. Item b: Por defini=E7=E3o, um losango =E9 um quadril=E1tero plano= convexo cujos quatro lados s=E3o congruentes entre si. Usando essa defini= =E7=E3o e a propriedade caracter=EDstica dos paralelogramos referida no item = anterior, pode-se demonstrar essa afirma=E7=E3o. Item c: Propriedade dos ret=E2ngulos que pode ser demonstrada usa= ndo a defini=E7=E3o dessa figura geom=E9trica e as propriedade dos paralelo= gramos, uma vez que todo ret=E2ngulo =E9 um paralelogramo (fato tamb=E9m = justific=E1vel). Item d: Propriedade decorrente da defini=E7=E3o de losango e das = propriedades do paralelogramo, j=E1 que esta figura geom=E9trica tamb=E9m u= m=20 paralelogramo. Item e: A veracidade dessa afirma=E7=E3o decorre da defini=E7=E3o= de losango e do seguinte teorema: Todo losango =E9 um paralelogramo. Date: Thu, 20 Dec 2007 18:26:46 -0300 From: fagner_mat23@yahoo.com.br Subject: [obm-l] Geometria . To: obm-l@mat.puc-rio.br http://imagetoker.com/viewer.php?id=3D890318geometria.JPG http://imagetoker.com/viewer.php?id=3D541398geometria2.JPG Quem puder = ajudar valeu =20 =20 Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento!=20 _________________________________________________________________ Cansado de espa=E7o para s=F3 50 fotos? Conhe=E7a o Spaces, o site de relac= ionamentos com at=E9 6,000 fotos! http://www.amigosdomessenger.com.br= --_6e774222-98af-4c6f-b60e-886a533902bf_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
          4 - A afirma=E7= =E3o prop=F5e um novo caso de congru=EAncia, a saber, o caso "lado-lado-=E2= ngulo". Usando a figura fornecida, =E9 poss=EDvel mostrar porque

&nb= sp;         esse crit=E9rio n=E3o = =E9 v=E1lido: segundo esse novo caso, os tri=E2ngulos ROP e QOP deveriam se= r congruentes, por=E9m isto =E9 uma inverdade, uma vez

  &= nbsp;       que o teorema do angulo externo a= plicado ao tri=E2ngulo QOR nos permite afirmar que o =E2ngulo PQO =E9 maior= do que PRO.

          = 5 - Por defini=E7=E3o, uma corda de uma circunfer=EAncia =E9 um segmento de= reta cujas extremidades pertencem a essa circunfer=EAncia. A mediatriz de<= br>
          um segmento d= e reta =E9 o lugar geom=E9trico dos pontos eq=FCidistantes das extremidades= desse segmento. Ora, uma vez que as extremidades da

  &nb= sp;       corda pertencem =E0 circunfer=EAnci= a, as dist=E2ncias desses pontos ao centro desta s=E3o iguais e congruentes= ao raio. Por conseguinte, a mediatriz

     = ;     "passar=E1" pelo centro da circunfer=EAncia. = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;           Q.E.D.
          6 - Todas as afirma= =E7=F5es s=E3o verdadeiras.

      &nbs= p;   Item a: Propriedade fundamental dos paralelogramos que decor= re do teorema angular de Tales.

      =     Item b: Por defini=E7=E3o, um losango =E9 um quadril=E1t= ero plano convexo cujos quatro lados s=E3o congruentes entre si. Usando ess= a defini=E7=E3o e a

        =   propriedade caracter=EDstica dos paralelogramos referida no item ant= erior, pode-se demonstrar essa afirma=E7=E3o.

   &nbs= p;      Item c: Propriedade dos ret=E2ngulos que p= ode ser demonstrada usando a defini=E7=E3o dessa figura geom=E9trica e as p= ropriedade dos paralelogramos,

      &= nbsp;   uma vez que todo ret=E2ngulo =E9 um paralelogramo (fato t= amb=E9m justific=E1vel).

       &= nbsp;  Item d: Propriedade decorrente da defini=E7=E3o de losango e da= s propriedades do paralelogramo, j=E1 que esta figura geom=E9trica tamb=E9m= um

          paralelo= gramo.

          Item e= : A veracidade dessa afirma=E7=E3o decorre da defini=E7=E3o de losango e do= seguinte teorema: Todo losango =E9 um paralelogramo.


Date: Thu, 20 Dec 2007 18:26:46 -0300
From: fagner_mat23@yahoo.com= .br
Subject: [obm-l] Geometria .
To: obm-l@mat.puc-rio.br


=
http://im= agetoker.com/viewer.php?id=3D890318geometria.JPG

http://imagetoker.com/viewer.php?id=3D5= 41398geometria2.JPG
 
Quem puder  ajudar  valeu
 
 

=20
Abra sua conta no Yahoo! M= ail, o =FAnico sem limite de espa=E7o para armazenamento!=20
Encontre o que voc=EA procura com mais efici=EAnci= a! Instale j=E1 a Barra de Ferramentas com Windows Desktop Search! =C9 GR=C1TIS! = --_6e774222-98af-4c6f-b60e-886a533902bf_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 21 20:33:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBLMUP8l018714 for ; Fri, 21 Dec 2007 20:30:25 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBLMUPec018712 for obm-l-MllGbsmmN; Fri, 21 Dec 2007 20:30:25 -0200 Received: from web63706.mail.re1.yahoo.com (web63706.mail.re1.yahoo.com [69.147.97.91]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBLMUN8l018709 for ; Fri, 21 Dec 2007 20:30:23 -0200 Received: (qmail 3311 invoked by uid 60001); 21 Dec 2007 23:31:59 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=JVD285GO0JAix1z88vp+zkKjN+S8R5jgwSPr0wkY/kZ5voQ0KheZ6T2+B4p9qIWKXY+wCBJ44LAruAWVrXHQZkM50WxBMzS8lVHdp7enq7LaHTXrEmyFdGOHk/d/ComW/Nwp5Drjatcq7QscrnMX3uJ+UMuuNHbfmST3HrWteuc=; X-YMail-OSG: dmGOIt8VM1lzB.NSy3nS.Sj0J97aje7vBS5llK2JGub.YDzEB.TEwFHUmjdkY6dunc_mIxQB8y_ZMmO_T2srC_JXSStHWN4O2.x7EqJnD88.lJmDsPj05Q-- Received: from [189.24.133.180] by web63706.mail.re1.yahoo.com via HTTP; Fri, 21 Dec 2007 20:31:59 ART Date: Fri, 21 Dec 2007 20:31:59 -0300 (ART) From: fagner almeida Subject: [SPAM] RE: [obm-l] Geometria . To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <671196.2238.qm@web63706.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=9.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS, HTML_FONT_COLOR_CYAN,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-209529714-1198279919=:2238" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 91.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 91.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-209529714-1198279919=:2238 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit obrigado ,Muito boa suas soluções. Na 5 o Iezzi da a seguinte dica : Usando o caso de congruencia LLL pode se provar a propriedade como seria essa prova ? Tales Prates Correia escreveu: .hmmessage P { margin:0px; padding:0px } body.hmmessage { FONT-SIZE: 10pt; FONT-FAMILY:Tahoma } 4 - A afirmação propõe um novo caso de congruência, a saber, o caso "lado-lado-ângulo". Usando a figura fornecida, é possível mostrar porque esse critério não é válido: segundo esse novo caso, os triângulos ROP e QOP deveriam ser congruentes, porém isto é uma inverdade, uma vez que o teorema do angulo externo aplicado ao triângulo QOR nos permite afirmar que o ângulo PQO é maior do que PRO. 5 - Por definição, uma corda de uma circunferência é um segmento de reta cujas extremidades pertencem a essa circunferência. A mediatriz de um segmento de reta é o lugar geométrico dos pontos eqüidistantes das extremidades desse segmento. Ora, uma vez que as extremidades da corda pertencem à circunferência, as distâncias desses pontos ao centro desta são iguais e congruentes ao raio. Por conseguinte, a mediatriz "passará" pelo centro da circunferência. Q.E.D. 6 - Todas as afirmações são verdadeiras. Item a: Propriedade fundamental dos paralelogramos que decorre do teorema angular de Tales. Item b: Por definição, um losango é um quadrilátero plano convexo cujos quatro lados são congruentes entre si. Usando essa definição e a propriedade característica dos paralelogramos referida no item anterior, pode-se demonstrar essa afirmação. Item c: Propriedade dos retângulos que pode ser demonstrada usando a definição dessa figura geométrica e as propriedade dos paralelogramos, uma vez que todo retângulo é um paralelogramo (fato também justificável). Item d: Propriedade decorrente da definição de losango e das propriedades do paralelogramo, já que esta figura geométrica também um paralelogramo. Item e: A veracidade dessa afirmação decorre da definição de losango e do seguinte teorema: Todo losango é um paralelogramo. --------------------------------- Date: Thu, 20 Dec 2007 18:26:46 -0300 From: fagner_mat23@yahoo.com.br Subject: [obm-l] Geometria . To: obm-l@mat.puc-rio.br http://imagetoker.com/viewer.php?id=890318geometria.JPG http://imagetoker.com/viewer.php?id=541398geometria2.JPG Quem puder ajudar valeu --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Encontre o que você procura com mais eficiência! Instale já a Barra de Ferramentas com Windows Desktop Search! É GRÁTIS! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-209529714-1198279919=:2238 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
obrigado ,Muito boa  suas  soluções.
 
Na  5  o    Iezzi  da  a seguinte dica :
Usando o caso de congruencia  LLL pode se  provar a propriedade
como  seria  essa  prova ?

Tales Prates Correia <tales1337@hotmail.com> escreveu:

          4 - A afirmação propõe um novo caso de congruência, a saber, o caso "lado-lado-ângulo". Usando a figura fornecida, é possível mostrar porque

          esse critério não é válido: segundo esse novo caso, os triângulos ROP e QOP deveriam ser congruentes, porém isto é uma inverdade, uma vez

          que o teorema do angulo externo aplicado ao triângulo QOR nos permite afirmar que o ângulo PQO é maior do que PRO.

          5 - Por definição, uma corda de uma circunferência é um segmento de reta cujas extremidades pertencem a essa circunferência. A mediatriz de

          um segmento de reta é o lugar geométrico dos pontos eqüidistantes das extremidades desse segmento. Ora, uma vez que as extremidades da

          corda pertencem à circunferência, as distâncias desses pontos ao centro desta são iguais e congruentes ao raio. Por conseguinte, a mediatriz

          "passará" pelo centro da circunferência.                                                                                                                                         Q.E.D.

          6 - Todas as afirmações são verdadeiras.

          Item a: Propriedade fundamental dos paralelogramos que decorre do teorema angular de Tales.

          Item b: Por definição, um losango é um quadrilátero plano convexo cujos quatro lados são congruentes entre si. Usando essa definição e a

          propriedade característica dos paralelogramos referida no item anterior, pode-se demonstrar essa afirmação.

          Item c: Propriedade dos retângulos que pode ser demonstrada usando a definição dessa figura geométrica e as propriedade dos paralelogramos,

          uma vez que todo retângulo é um paralelogramo (fato também justificável).

          Item d: Propriedade decorrente da definição de losango e das propriedades do paralelogramo, já que esta figura geométrica também um

          paralelogramo.

          Item e: A veracidade dessa afirmação decorre da definição de losango e do seguinte teorema: Todo losango é um paralelogramo.


Date: Thu, 20 Dec 2007 18:26:46 -0300
From: fagner_mat23@yahoo.com.br
Subject: [obm-l] Geometria .
To: obm-l@mat.puc-rio.br



http://imagetoker.com/viewer.php?id=890318geometria.JPG

http://imagetoker.com/viewer.php?id=541398geometria2.JPG
 
Quem puder  ajudar  valeu
 
 



Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Encontre o que você procura com mais eficiência! Instale já a Barra de Ferramentas com Windows Desktop Search! É GRÁTIS!



Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-209529714-1198279919=:2238-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 22 01:45:30 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM3gp8l008916 for ; Sat, 22 Dec 2007 01:42:51 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBM3gpql008914 for obm-l-MllGbsmmN; Sat, 22 Dec 2007 01:42:51 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM3gm8l008884 for ; Sat, 22 Dec 2007 01:42:48 -0200 Received: from localhost (localhost [127.0.0.1]) by socom2.uol.com.br (Postfix) with ESMTP id 06E26FC3 for ; Sat, 22 Dec 2007 02:44:26 -0200 (BRST) Received: from microcf7b75528 (unknown [201.9.208.175]) by socom2.uol.com.br (Postfix) with SMTP id 6639D153F for ; Sat, 22 Dec 2007 02:44:24 -0200 (BRST) Message-ID: <004a01c84455$52a54190$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Raz=E3o_M=E1xima_entre_os_lados_de_um_Tri=E2ngulo?= Date: Sat, 22 Dec 2007 01:44:22 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: 6289ffb131212c9474ebf4fa73f74a8a Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.2 required=5.0 tests=HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0047_01C8443C.2CEF0E90" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 175.208.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 175.208.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0047_01C8443C.2CEF0E90 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos! Segue o problema extra=EDdo do livro Geometria II de A.C. Morgado, E. = Wagner e M. Jorge=20 Em um tri=E2ngulo ABC, BC =3D 16 e h_a =3D 8, calcule a raz=E3o AB/AC, = sabendo que ela =E9 m=E1xima. Nota: h_a denota a altura relativa ao lado BC. O uso de derivada n=E3o = =E9 permitido. Com o aux=EDlio do Geogebra, verifiquei que a raz=E3o =E9 m=E1xima = quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio do c=EDrculo de = Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo = coincidindo com o p=E9 de h_a.=20 Pergunta: Como provar que a raz=E3o entre os lados AB e AC =E9 m=E1xima = quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, sem o uso de = c=E1lculo? Abra=E7os. Ulysses Coelho de Souza. ------=_NextPart_000_0047_01C8443C.2CEF0E90 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 a todos!
 
 
Segue o problema extra=EDdo do livro = Geometria II de=20 A.C. Morgado, E. Wagner e M. Jorge
 
Em um tri=E2ngulo ABC, BC =3D 16 e h_a = =3D 8, calcule a=20 raz=E3o AB/AC, sabendo que ela =E9 m=E1xima.
 
Nota: h_a denota a altura relativa ao lado = BC.=20 O uso de derivada n=E3o =E9 = permitido.
 
 
Com o aux=EDlio do Geogebra, = verifiquei que a raz=E3o=20 =E9 m=E1xima quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio = do c=EDrculo de=20 Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo = coincidindo com o=20 p=E9 de h_a. 
 
Pergunta: Como provar que a raz=E3o entre os = lados AB e=20 AC =E9 m=E1xima quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, = sem o uso de=20 c=E1lculo?
 
Abra=E7os.
 
Ulysses Coelho de=20  Souza. 
------=_NextPart_000_0047_01C8443C.2CEF0E90-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 22 02:04:03 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM42D8l010071 for ; Sat, 22 Dec 2007 02:02:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBM42DrP010069 for obm-l-MllGbsmmN; Sat, 22 Dec 2007 02:02:13 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM42C8l010062 for ; Sat, 22 Dec 2007 02:02:12 -0200 Received: from localhost (localhost [127.0.0.1]) by socom4.uol.com.br (Postfix) with ESMTP id AABE2E0009B4 for ; Sat, 22 Dec 2007 03:03:49 -0200 (BRST) Received: from microcf7b75528 (unknown [201.9.208.175]) by socom4.uol.com.br (Postfix) with SMTP id F3B23E000982 for ; Sat, 22 Dec 2007 03:03:48 -0200 (BRST) Message-ID: <009701c84458$08c9c1b0$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] =?Windows-1252?Q?Raz=E3o_M=E1xima_entre_os_lados_de_um_Tri=E2ngulo?= Date: Sat, 22 Dec 2007 02:03:46 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: c0e63b037987824b38ce54d0e008401c Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0094_01C8443E.E31ABAA0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 175.208.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 175.208.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0094_01C8443E.E31ABAA0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos! Segue o problema extra=EDdo do livro Geometria II de A.C. Morgado, E. = Wagner e M. Jorge=20 Em um tri=E2ngulo ABC, BC =3D 16 e h_a =3D 8, calcule a raz=E3o AB/AC, = sabendo que ela =E9 m=E1xima. Nota: h_a denota a altura relativa ao lado BC. O uso de derivada n=E3o = =E9 permitido. Com o aux=EDlio do Geogebra, verifiquei que a raz=E3o =E9 m=E1xima = quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio do c=EDrculo de = Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo = coincidindo com o p=E9 de h_a.=20 Pergunta: Como provar que a raz=E3o entre os lados AB e AC =E9 m=E1xima = quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, sem o uso de = c=E1lculo? Abra=E7os. Ulysses Coelho de Souza. ------=_NextPart_000_0094_01C8443E.E31ABAA0 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable
Ol=E1 a todos!
 
 
Segue o problema extra=EDdo do livro = Geometria II de=20 A.C. Morgado, E. Wagner e M. Jorge
 
Em um tri=E2ngulo ABC, BC =3D 16 e h_a = =3D 8, calcule a=20 raz=E3o AB/AC, sabendo que ela =E9 m=E1xima.
 
Nota: h_a denota a altura relativa ao lado = BC.=20 O uso de derivada n=E3o =E9 = permitido.
 
 
Com o aux=EDlio do Geogebra, = verifiquei que a raz=E3o=20 =E9 m=E1xima quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio = do c=EDrculo de=20 Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo = coincidindo com o=20 p=E9 de h_a. 
 
Pergunta: Como provar que a raz=E3o entre os = lados AB e=20 AC =E9 m=E1xima quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, = sem o uso de=20 c=E1lculo?
 
Abra=E7os.
 
Ulysses Coelho de=20  Souza. 
------=_NextPart_000_0094_01C8443E.E31ABAA0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 22 02:12:25 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM4Af8l010598 for ; Sat, 22 Dec 2007 02:10:41 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBM4AffE010596 for obm-l-MllGbsmmN; Sat, 22 Dec 2007 02:10:41 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM4Ae8l010588 for ; Sat, 22 Dec 2007 02:10:40 -0200 Received: from localhost (localhost [127.0.0.1]) by socom6.uol.com.br (Postfix) with ESMTP id E63F9E0003B2 for ; Sat, 22 Dec 2007 03:12:17 -0200 (BRST) Received: from microcf7b75528 (unknown [201.9.208.175]) by socom6.uol.com.br (Postfix) with SMTP id 5BD45E0002E6 for ; Sat, 22 Dec 2007 03:12:15 -0200 (BRST) Message-ID: <000801c84459$373509a0$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] =?Windows-1252?Q?N=FAmero_de_Pol=EDgonos_Regulares_=28estrelados_inclus?= =?Windows-1252?Q?ive=29_n=E3o_Semelhantes?= Date: Sat, 22 Dec 2007 02:12:13 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: 5c0db683e0bddc7fbe314669a0ab736f Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0005_01C84440.111D2EA0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 175.208.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 175.208.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0005_01C84440.111D2EA0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Ol=E1, Quantos pol=EDgonos regulares n=E3o semelhantes existem com 48 lados? Abra=E7os. Ulysses Coelho de Souza. ------=_NextPart_000_0005_01C84440.111D2EA0 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable
Ol=E1,
 
Quantos pol=EDgonos regulares n=E3o = semelhantes=20 existem com 48 lados?
 
 
 
Abra=E7os.
 
 
Ulysses Coelho de=20 Souza.
------=_NextPart_000_0005_01C84440.111D2EA0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 22 02:17:23 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM4FQ8l010792 for ; Sat, 22 Dec 2007 02:15:26 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBM4FQ7A010790 for obm-l-MllGbsmmN; Sat, 22 Dec 2007 02:15:26 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBM4FP8l010787 for ; Sat, 22 Dec 2007 02:15:25 -0200 Received: from localhost (localhost [127.0.0.1]) by socom3.uol.com.br (Postfix) with ESMTP id 4E3C2322 for ; Sat, 22 Dec 2007 03:17:03 -0200 (BRST) Received: from microcf7b75528 (unknown [201.9.208.175]) by socom3.uol.com.br (Postfix) with SMTP id 95B2526C for ; Sat, 22 Dec 2007 03:17:02 -0200 (BRST) Message-ID: <001401c84459$e1d0e140$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] =?Windows-1252?Q?N=FAmero_de_Pol=EDgonos_Regulares_=28estrelados_inclus?= =?Windows-1252?Q?ive=29_n=E3o_Semelhantes?= Date: Sat, 22 Dec 2007 02:17:00 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: 6ea2e34adf4800b6ebd486d88a548c88 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0011_01C84440.BC1F9040" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 175.208.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 175.208.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0011_01C84440.BC1F9040 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Ol=E1, Quantos pol=EDgonos regulares n=E3o semelhantes existem com 48 lados? Abra=E7os. Ulysses Coelho de Souza. ------=_NextPart_000_0011_01C84440.BC1F9040 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable
 
Ol=E1,
 
Quantos pol=EDgonos regulares n=E3o = semelhantes=20 existem com 48 lados?
 
 
 
Abra=E7os.
 
 
Ulysses Coelho de=20 Souza.
------=_NextPart_000_0011_01C84440.BC1F9040-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 22 19:14:04 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBMLBi8l001868 for ; Sat, 22 Dec 2007 19:11:44 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBMLBiGV001866 for obm-l-MllGbsmmN; Sat, 22 Dec 2007 19:11:44 -0200 Received: from bay0-omc2-s18.bay0.hotmail.com (bay0-omc2-s18.bay0.hotmail.com [65.54.246.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBMLBf8l001862 for ; Sat, 22 Dec 2007 19:11:41 -0200 Received: from BAY113-W5 ([65.54.168.105]) by bay0-omc2-s18.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sat, 22 Dec 2007 14:13:18 -0800 Message-ID: Content-Type: text/plain X-Originating-IP: [201.42.159.198] From: Tales Prates Correia To: Subject: [SPAM] RE: [obm-l] Geometria . Date: Sun, 23 Dec 2007 01:13:18 +0300 Importance: Normal In-Reply-To: <671196.2238.qm@web63706.mail.re1.yahoo.com> References: <671196.2238.qm@web63706.mail.re1.yahoo.com> MIME-Version: 1.0 X-OriginalArrivalTime: 22 Dec 2007 22:13:18.0985 (UTC) FILETIME=[DB719F90:01C844E7] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Tales Prates Correia X-Spam-Status: Yes, hits=6.3 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_FONT_COLOR_CYAN, HTML_FONT_COLOR_UNSAFE,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="_77ba98cb-bc00-41de-bd65-c3c7a204871f_" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 105.168.54.65.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 105.168.54.65.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --_77ba98cb-bc00-41de-bd65-c3c7a204871f_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable A fim de mostrar a validade de tal afirma=E7=E3o, simbolizaremos= pela letra C a circunfer=EAncia, pela letra O o seu centro e pela letra R = o seu raio. 1=BA caso: a corda passa pelo centro Sejam A e B as extremidades da corda. J=E1 que os segmentos AO e = BO s=E3o congruentes (pois possuem o mesmo comprimento R) e os pontos=20 A, O e B s=E3o colineares, O =E9 o ponto m=E9dio da corda (di=E2m= etro) AB. Consecutivamente, a reta perpendicular ao segmento AB conduzida p= or seu ponto m=E9dio passa pelo centro O de C. 2=B0 caso: a corda n=E3o passa pelo centro Nesse caso, a reuni=E3o dos segmentos determinados pelos pontos A= , O e B corresponde a um tri=E2ngulo. Haja visto que AO =3D OB, AM =3D MB e= OM =E9 comum aos dois tri=E2ngulos AOM e BOM, em que M =E9 o ponto m= =E9dio da corda AB, conclui-se pelo crit=E9rio de congru=EAncia de tri=E2ng= ulos LLL que o pol=EDgono AOM =E9 congruente ao pol=EDgono BOM.=20 Dessa congru=EAncia, decorre que os =E2ngulos AMO e BMO s=E3o con= gruentes. Por=E9m eles tamb=E9m s=E3o suplementares e adjacentes. Por defin= i=E7=E3o, os =E2ngulos AMO e BMO s=E3o retos. Assim, a reta OM =E9 a mediat= riz da corda AB, pois OM =E9 perpendicular ao segmento AB e passa pelo seu = ponto m=E9dio. Tendo em vista que a mediatriz de um segmento existe e = =E9 =FAnica (na geometria plana), conclu=EDmos, enfim, que a proposi=E7=E3o= da quest=E3o cinco =E9 verdadeira. Date: Fri, 21 Dec 2007 20:31:59 -0300 From: fagner_mat23@yahoo.com.br Subject: RE: [obm-l] Geometria . To: obm-l@mat.puc-rio.br obrigado ,Muito boa suas solu=E7=F5es. Na 5 o Iezzi da a segui= nte dica : Usando o caso de congruencia LLL pode se provar a propriedade= como seria essa prova ? Tales Prates Correia escreveu: =20 4 - A afirma=E7=E3o prop=F5e um novo caso de congru=EAncia, a sab= er, o caso "lado-lado-=E2ngulo". Usando a figura fornecida, =E9 poss=EDvel = mostrar porque esse crit=E9rio n=E3o =E9 v=E1lido: segundo esse novo caso, os tr= i=E2ngulos ROP e QOP deveriam ser congruentes, por=E9m isto =E9 uma inverdade, uma vez que o teorema do angulo externo aplicado ao tri=E2ngulo QOR nos p= ermite afirmar que o =E2ngulo PQO =E9 maior do que PRO. 5 - Por defini=E7=E3o, uma corda de uma circunfer=EAncia =E9 um s= egmento de reta cujas extremidades pertencem a essa circunfer=EAncia. A med= iatriz de um segmento de reta =E9 o lugar geom=E9trico dos pontos eq=FCidis= tantes das extremidades desse segmento. Ora, uma vez que as extremidades da corda pertencem =E0 circunfer=EAncia, as dist=E2ncias desses pont= os ao centro desta s=E3o iguais e congruentes ao raio. Por conseguinte, a m= ediatriz "passar=E1" pelo centro da circunfer=EAncia. = = Q.E.D. 6 - Todas as afirma=E7=F5es s=E3o verdadeiras. Item a: Propriedade fundamental dos paralelogramos que decorre do= teorema angular de Tales. Item b: Por defini=E7=E3o, um losango =E9 um quadril=E1tero plano= convexo cujos quatro lados s=E3o congruentes entre si. Usando essa defini= =E7=E3o e a propriedade caracter=EDstica dos paralelogramos referida no item = anterior, pode-se demonstrar essa afirma=E7=E3o. Item c: Propriedade dos ret=E2ngulos que pode ser demonstrada usa= ndo a defini=E7=E3o dessa figura geom=E9trica e as propriedade dos paralelo= gramos, uma vez que todo ret=E2ngulo =E9 um paralelogramo (fato tamb=E9m = justific=E1vel). Item d: Propriedade decorrente da defini=E7=E3o de losango e das propriedades do paralelogramo, j=E1 que esta figura geom=E9t= rica tamb=E9m um=20 paralelogramo. Item e: A veracidade dessa afirma=E7=E3o decorre da defini=E7=E3o= de losango e do seguinte teorema: Todo losango =E9 um paralelogramo. Date: Thu, 20 Dec 2007 18:26:46 -0300 From: fagner_mat23@yahoo.com.br Subject: [obm-l] Geometria . To: obm-l@mat.puc-rio.br http://imagetoker.com/viewer.php?id=3D890318geometria.JPG http://imagetoker.com/viewer.php?id=3D541398geometria2.JPG Quem puder= =20 ajudar valeu =20 Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para ar= mazenamento!=20 Encontre o que voc=EA procura com mais efici=EAncia! Instale j=E1 a Bar= ra de Ferramentas com Windows Desktop Search! =C9 GR=C1TIS!=20 =20 Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento!=20 _________________________________________________________________ Confira v=EDdeos com not=EDcias do NY Times, gols direto do Lance, videocas= setadas e muito mais no MSN Video! http://video.msn.com/?mkt=3Dpt-br= --_77ba98cb-bc00-41de-bd65-c3c7a204871f_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable            A fim de mostr= ar a validade de tal afirma=E7=E3o, simbolizaremos pela letra C a circunfer= =EAncia, pela letra O o seu centro e pela letra R o seu raio.

 =          1=BA caso: a corda passa p= elo centro

          Se= jam A e B as extremidades da corda. J=E1 que os segmentos AO e BO s=E3o con= gruentes (pois possuem o mesmo comprimento R) e os pontos

 &nb= sp;        A, O e B s=E3o colineares, O = =E9 o ponto m=E9dio da corda (di=E2metro) AB. Consecutivamente, a reta perp= endicular ao segmento AB conduzida por seu

    &= nbsp;     ponto m=E9dio passa pelo centro O de C.
          2=B0 caso: a corda= n=E3o passa pelo centro

       &= nbsp;  Nesse caso, a reuni=E3o dos segmentos determinados pelos pontos= A, O e B corresponde a um tri=E2ngulo. Haja visto que AO =3D OB, AM =3D MB= e OM

          =E9 com= um aos dois tri=E2ngulos AOM e BOM, em que M =E9 o ponto m=E9dio da corda A= B, conclui-se pelo crit=E9rio de congru=EAncia de tri=E2ngulos LLL que
<= br>          o pol=EDgono AOM = =E9 congruente ao pol=EDgono BOM.

     &nb= sp;    Dessa congru=EAncia, decorre que os =E2ngulos AMO e B= MO s=E3o congruentes. Por=E9m eles tamb=E9m s=E3o suplementares e adjacente= s. Por defini=E7=E3o,

       &nbs= p;  os =E2ngulos AMO e BMO s=E3o retos. Assim, a reta OM =E9 a mediatr= iz da corda AB, pois OM =E9 perpendicular ao segmento AB e passa pelo seu p= onto

          m=E9dio.= Tendo em vista que a mediatriz de um segmento existe e =E9 =FAnica (na geo= metria plana), conclu=EDmos, enfim, que a proposi=E7=E3o da quest=E3o
          cinco =E9 verdadei= ra.
Date: Fri, 21 Dec 2007 20:31:59 -0300
From: fagne= r_mat23@yahoo.com.br
Subject: RE: [obm-l] Geometria .
To: obm-l@mat.p= uc-rio.br

obrigado ,Muito boa  suas  solu=E7=F5e= s.
 
Na  5  o    Iezzi&nbs= p; da  a seguinte dica :
Usando o caso de congruencia &nbs= p;LLL pode se  provar a propriedade
como  seria = essa  prova ?

Tales Prates Correia <tales1337@hotmail= .com> escreveu:

          4 - A = afirma=E7=E3o prop=F5e um novo caso de congru=EAncia, a saber, o caso "lado= -lado-=E2ngulo". Usando a figura fornecida, =E9 poss=EDvel mostrar porque
          esse crit=E9ri= o n=E3o =E9 v=E1lido: segundo esse novo caso, os tri=E2ngulos ROP e QOP dev= eriam ser congruentes, por=E9m isto =E9 uma inverdade, uma vez

      = ;    que o teorema do angulo externo aplicado ao tri=E2ngulo= QOR nos permite afirmar que o =E2ngulo PQO =E9 maior do que PRO.

&n= bsp;         5 - Por defini=E7=E3o,= uma corda de uma circunfer=EAncia =E9 um segmento de reta cujas extremidad= es pertencem a essa circunfer=EAncia. A mediatriz de

  &nb= sp;       um segmento de reta =E9 o lugar geo= m=E9trico dos pontos eq=FCidistantes das extremidades desse segmento. Ora, = uma vez que as extremidades da

      &= nbsp;   corda pertencem =E0 circunfer=EAncia, as dist=E2ncias des= ses pontos ao centro desta s=E3o iguais e congruentes ao raio. Por consegui= nte, a mediatriz

        &nb= sp; "passar=E1" pelo centro da circunfer=EAncia.         &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;  Q.E.D.

        &nb= sp; 6 - Todas as afirma=E7=F5es s=E3o verdadeiras.

         = Item a: Propriedade fundamental dos paralelogramos que decorre do teorema = angular de Tales.

        &n= bsp; Item b: Por defini=E7=E3o, um losango =E9 um quadril=E1tero plano conv= exo cujos quatro lados s=E3o congruentes entre si. Usando essa defini=E7=E3= o e a

          proprie= dade caracter=EDstica dos paralelogramos referida no item anterior, pode-se= demonstrar essa afirma=E7=E3o.

      =     Item c: Propriedade dos ret=E2ngulos que pode ser demons= trada usando a defini=E7=E3o dessa figura geom=E9trica e as propriedade dos= paralelogramos,

        &nb= sp; uma vez que todo ret=E2ngulo =E9 um paralelogramo (fato tamb=E9m justif= ic=E1vel).

          It= em d: Propriedade decorrente da defini=E7=E3o de losango e das propriedades do paralelogramo, j=E1 que esta figura geom=E9t= rica tamb=E9m um

        &n= bsp; paralelogramo.

        =   Item e: A veracidade dessa afirma=E7=E3o decorre da defini=E7=E3o de= losango e do seguinte teorema: Todo losango =E9 um paralelogramo.

<= br>
Date: Thu, 20 Dec 2007 18:26:46 -0300
From: fag= ner_mat23@yahoo.com.br
Subject: [obm-l] Geometria .
To: obm-l@mat.puc= -rio.br



http://imagetoker.com/viewer.php?id=3D890318geometria.JPG=

http://imagetoker.= com/viewer.php?id=3D541398geometria2.JPG
 
Quem puder  ajudar  valeu
 
 



Abra sua conta= no Yahoo! Mail, o =FAnico sem limite de espa= =E7o para armazenamento!

Encontre o que voc=EA pro= cura com mais efici=EAncia! Instale j=E1 a Barra de Ferramentas com Windows= Desktop Search! =C9 GR=C1TIS!



=20
Abra sua conta no Yahoo! M= ail, o =FAnico sem limite de espa=E7o para armazenamento!=20

Not=EDcias direto do New York Times, gols do Lance= , videocassetadas e muitos outros v=EDdeos no MSN Videos! Confira j=E1! = --_77ba98cb-bc00-41de-bd65-c3c7a204871f_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 10:30:21 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNCRi8l028954 for ; Sun, 23 Dec 2007 10:27:44 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNCRiw7028952 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 10:27:44 -0200 Received: from smtp.bol.com.br (smtpout2.bol.com.br [200.221.4.213]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNCRh8l028949 for ; Sun, 23 Dec 2007 10:27:43 -0200 Received: from localhost (localhost [127.0.0.1]) by smart4.bol.com.br (Postfix) with ESMTP id 3B88A48001594 for ; Sun, 23 Dec 2007 11:30:08 -0200 (BRST) Received: from pai (unknown [201.88.134.242]) by smart4.bol.com.br (Postfix) with ESMTP id 11141480015A3 for ; Sun, 23 Dec 2007 11:30:07 -0200 (BRST) Message-ID: <001201c84568$428e5a80$6601a8c0@pai> From: "Tio Cabri st" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?tangente_ao_gr=E1fico?= Date: Sun, 23 Dec 2007 11:32:26 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 450e36eac59de124e18309759fa9f130 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Bom dia. Desejo a todos boas festas e um feliz 2008. Sei que talvez não seja um bom dia para postar algo. Mas... Estou precisando de ajuda (só uma luz já é o suficiente) no seguinte exercício: Determinar todos os pontos (a,b) de R2, tais que por (a,b) passem duas retas tangentes ao gráfico de f(x)=x^2. Resposta: (a,b) tal que b Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNDYq8l032751 for ; Sun, 23 Dec 2007 11:34:52 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNDYpAj032749 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 11:34:51 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNDYn8l032744 for ; Sun, 23 Dec 2007 11:34:50 -0200 Received: by rv-out-0910.google.com with SMTP id c27so795218rvf.9 for ; Sun, 23 Dec 2007 06:36:27 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=ygSer03Dgpg0G73Oqw6XSriDlVqHc1bPh+HxW/QX3cs=; b=QJ6UKmHLO0mKcsmyguIgu1xzSOMq0NU7yys8qc9N6gqgF6DURjJlnj5D+YH4QZE4j/hWZEXTHwWyMN6z34KL/Wjdtd34M7w7MV/YiMSGxCO30g7IESVdRGwKxvaJ5OJ6eeCqYR49zEYWV+INV428ADszc1ar9veNW1SJkSV4jZg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=SR3WoUpVaj5KyAtUBNu/YaNH2VFhK/2WbIZI+jEvya4r7LcE9CYpYGMNyvRFjXlAj05LjuyEZ928HSQNpKLzpikwTcXAM+ylvCA1QP4GLxXLgSmc760vYvj1pIB/4fm9UGsEmKGOe35uitw+HeLtdq+qWG7H+BoaJ9p+JL8Pzwc= Received: by 10.141.83.15 with SMTP id k15mr1825983rvl.120.1198420587353; Sun, 23 Dec 2007 06:36:27 -0800 (PST) Received: by 10.141.87.17 with HTTP; Sun, 23 Dec 2007 06:36:27 -0800 (PST) Message-ID: <2b5739960712230636xc3edfe6nf74746add4ce52eb@mail.gmail.com> Date: Sun, 23 Dec 2007 12:36:27 -0200 From: "Rogerio Ponce" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_tangente_ao_gr=E1fico?= In-Reply-To: <001201c84568$428e5a80$6601a8c0@pai> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <001201c84568$428e5a80$6601a8c0@pai> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBNDYp8l032747 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rogerio Ponce" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola' Tio Cabri e colegas da lista, tambem desejo boas festas e feliz 2008 a todos. A dica e' que basta voce estar "do lado de fora" da parabola, isto e', a parabola divide o plano em duas regioes, e para tracar 2 tangentes 'a curva, basta que voce esteja na regiao "externa". Assim, para um determinado X, o Y precisa ser menor que X**2. Abracos, Rogerio Ponce Em 23/12/07, Tio Cabri st escreveu: > Bom dia. > Desejo a todos boas festas e um feliz 2008. > > Sei que talvez não seja um bom dia para postar algo. Mas... > Estou precisando de ajuda (só uma luz já é o suficiente) no seguinte > exercício: > > Determinar todos os pontos (a,b) de R2, tais que por (a,b) passem duas retas > tangentes ao gráfico de f(x)=x^2. > > Resposta: (a,b) tal que b > Abraços > Cabri > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 12:40:18 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNEc68l004320 for ; Sun, 23 Dec 2007 12:38:06 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNEc6UN004318 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 12:38:06 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.240]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNEc48l004314 for ; Sun, 23 Dec 2007 12:38:05 -0200 Received: by hs-out-2122.google.com with SMTP id m63so760797hsc.13 for ; Sun, 23 Dec 2007 07:39:43 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=Q3TuicGBKmseT5jKKfCx7FBtDzxP0sazLKFYCDq4ZWI=; b=TO9mNehNvDj8IbfANEaa9S4HDCWnGCkqWVy3pQyzM2TQ1T8zu+wLuzEXrP0QnwBYZiVECuE/6wSd4R3SsN8YFgIMspIxNs0A/4UmgeHQESVWpf8jsPVd3OM5bpeRCe/3uZKsF/bZN3jG/cAxwGRG/05sCgLNHT+GuuwO8yWh2Fo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=e+14gGGcQPjoYZhLq3vUgPGfmQhEs2hxJ98Yb0Gx49W3o3MReP5CK4YrnIEksMIHM3V97vsvJNJYahu6QlpYMeRuWaDLSUwFUE07GOCzgS/UEb8kHoDg0JtmdE6sqqX1K8v5bYL0cPEDPbR9fgIEXY4EaPLV7fYVRWFLsU/ayn8= Received: by 10.150.98.18 with SMTP id v18mr981185ybb.117.1198424383046; Sun, 23 Dec 2007 07:39:43 -0800 (PST) Received: by 10.150.96.3 with HTTP; Sun, 23 Dec 2007 07:39:43 -0800 (PST) Message-ID: <9f4be2240712230739g61ea0533gae337574ad64f5d9@mail.gmail.com> Date: Sun, 23 Dec 2007 13:39:43 -0200 From: "Lucas Prado Melo" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Demonstra=E7=F5es?= In-Reply-To: <000c01c84050$09433560$01fea8c0@svs> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <000c01c84050$09433560$01fea8c0@svs> X-Google-Sender-Auth: 162aacb7bdcaba90 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBNEc58l004316 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Lucas Prado Melo" X-Spam-Status: No, hits=3.7 required=5.0 tests=GAPPY_TEXT,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** On Dec 16, 2007 11:56 PM, Sérgio Martins da Silva wrote: > Doutores, > > Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > "demonstração". Por isto, gostaria de saber como se demonstra que uma > demonstração está correta. E mais, que é completa. Quais são os requisitos, > condições, etc ? > > Abraços, > > Sérgio > Oi, Se eu estiver errado, por favor me corrijam, Demonstrar que uma demonstração é válida é provar que a conclusão deriva das premissas. (isso é lógica matemática) Se, ao analisarmos uma prova a partir de suas premissas, chegamos (por implicações sempre verdadeiras (também chamadas tautológicas)) à mesma conclusão que a prova chegou, então a prova é válida, caso contrário não. Uma prova é dita completa quando não existem axiomas não declarados (se eu não me engano). Ex: Se Alberto viajar e Bruno ir à praia Então Daniel vai ao mercado Prova: Sabemos isso também: - Se Alberto vai viajar e Bruno ir à praia, então Creuza vai limpar a casa de Alberto - Se Daniel não vai ao mercado, então Creuza não vai limpar a casa de Alberto ou Alberto não vai viajar Por lógica matemática: A := Alberto ir viajar B := Bruno ir à praia C := Creuza ir limpar a casa de Alberto D := Daniel ir ao mercado Temos: A e B e ( A e B -> C ) e ( ¬D -> ¬C ou ¬A ) Usando algumas regras de lógica: ( ¬D -> ¬C ou ¬A ) = ( A e C -> D ) A e B e ( A e B -> C ) = C A e C e ( A e C -> D ) = D Ou seja, D é verdade... Resumindo (para não-leigos): uma prova é válida sse a conjunção das premissas implica a conclusão da prova. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 17:11:27 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJ9Q8l027534 for ; Sun, 23 Dec 2007 17:09:26 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNJ9QUF027529 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 17:09:26 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJ9N8l027517 for ; Sun, 23 Dec 2007 17:09:24 -0200 Received: by an-out-0708.google.com with SMTP id c31so256705ana.120 for ; Sun, 23 Dec 2007 12:11:02 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=192DJIMM1eTMWzRDg6JA6G4RNPWKbZT+H3PwdrPaRw8=; b=aE20jTXzHVlJA2vp2IdGlVBYLiDEYz3SWI5ye4GccGp4s85PGboQdM9ijBw2F+GjZJLX1tIe276tMHRX895sedmq4yGqv+OU7boSfUePuwtttecjwhw4wdpaQfj4bdgbdxZirFE+rAhBTiR4EMr0n8oKXCCNM9gxkxIQwF1I8M8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=v8F0SW4SxORHuFN1W5M7n6XkycLp1aCBN4o0z03CUrF/bMDg9TUoP/rZZPpW2L1c242fDDKkne3oNm/eCoQ44sw+menW0icYWGntcSSHQ/qlXBPu/rcNoypUKPsHgxV5XmYA4cujtqH1+ElW+W0rwyrXwEdeg+9VD20UcWC2f2E= Received: by 10.100.110.15 with SMTP id i15mr7858199anc.76.1198440662256; Sun, 23 Dec 2007 12:11:02 -0800 (PST) Received: from svs ( [201.51.8.103]) by mx.google.com with ESMTPS id 31sm5767242wri.24.2007.12.23.12.10.59 (version=SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 12:11:00 -0800 (PST) Message-ID: <003e01c845a0$1ea76570$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> Subject: [obm-l] =?Windows-1252?Q?Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Demonstra=E7=F5es?= Date: Sun, 23 Dec 2007 18:12:15 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: No, hits=4.7 required=5.0 tests=QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Rodrigo, Link interessante. Um abraço, Sérgio ----- Original Message ----- From: To: Sent: Monday, December 17, 2007 2:14 AM Subject: [obm-l] Re: [obm-l] Demonstrações > Acredito que uma "demonstração de demonstração" seria algo como "chover no > molhado". Uma demonstração está correta se, em última instância, está de > acordo com os axiomas mais básicos da matéria. Então, uma demonstração de > demontração recorreria, também em última análise, exatamente aos mesmos > axiomas, sendo assim redundante. > > Se você fala inglês, aqui está um fórum onde há diversos debates > interessantes sobre esses assuntos, além de resolução técnica de questões de > matemática, física química, engenharia em geral, etc... > > http://www.physicsforums.com/ > > abraços > > ----- Original Message ----- > From: "Sérgio Martins da Silva" > To: "Lista OBM" > Sent: Sunday, December 16, 2007 10:56 PM > Subject: [obm-l] Demonstrações > > > > Doutores, > > > > Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > > "demonstração". Por isto, gostaria de saber como se demonstra que uma > > demonstração está correta. E mais, que é completa. Quais são os > > requisitos, > > condições, etc ? > > > > Abraços, > > > > Sérgio > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 17:17:08 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJFM8l027755 for ; Sun, 23 Dec 2007 17:15:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNJFLdY027753 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 17:15:21 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.248]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJFJ8l027748 for ; Sun, 23 Dec 2007 17:15:20 -0200 Received: by an-out-0708.google.com with SMTP id c31so257102ana.120 for ; Sun, 23 Dec 2007 12:16:58 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=Wlw3FR+K24GoZo09Bbd9GmMUn42bcD7iTCj4dQ0pi1o=; b=TAbES7BbY4eJy5rpd1f7IYdn2/gvRiPwUUMfRtZKHYIvBntVQXPvW+53MdB1yEXXLvBWWukLxedDw6q7stKYA2Pb1yKj+dNrD1szoiKbAmdET7lpqaTptRzWt7ieQFoZIg2qg27dSV/wYHLpi+ILuS8jDoSjxDFMa4O/hgvblaQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=x0bSUicRtEwUbsoErvf0D7dETeM7VCQ37ppME/PyuXXxShCT1qrQFDWtFATrCXrY1meo+u9SSDtyijl1Dbd8GMJ7xnQueRjNkkPRwjsO2X6AAVqIiC9d+9AuIHCfRyQWh1FYqXv+uKt+N1sHf4zCLrFxWHspgw2DdRIHmE1m+2A= Received: by 10.100.252.16 with SMTP id z16mr386926anh.89.1198441018291; Sun, 23 Dec 2007 12:16:58 -0800 (PST) Received: from svs ( [201.51.8.103]) by mx.google.com with ESMTPS id 32sm5772751wri.9.2007.12.23.12.16.55 (version=SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 12:16:56 -0800 (PST) Message-ID: <005801c845a0$f2e3abf0$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> <4766061A.4020102@gmail.com> Subject: [obm-l] =?Windows-1252?Q?Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Demonstra=E7=F5es?= Date: Sun, 23 Dec 2007 18:18:12 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: No, hits=4.7 required=5.0 tests=QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Arcguede, Você poderia me explicar porque o problema NP é o "terceiro problema do milênio"? Estou completamente desinformado sobre o assunto. Sérgio ----- Original Message ----- From: To: Sent: Monday, December 17, 2007 3:16 AM Subject: Re: [obm-l] Re: [obm-l] Demonstrações > Acho que isso nos remete ao "terceiro problema do milênio" - o problema NP. > > rodrigocientista@yahoo.com.br escreveu: > > Acredito que uma "demonstração de demonstração" seria algo como > > "chover no molhado". Uma demonstração está correta se, em última > > instância, está de acordo com os axiomas mais básicos da matéria. > > Então, uma demonstração de demontração recorreria, também em última > > análise, exatamente aos mesmos axiomas, sendo assim redundante. > > > > Se você fala inglês, aqui está um fórum onde há diversos debates > > interessantes sobre esses assuntos, além de resolução técnica de > > questões de matemática, física química, engenharia em geral, etc... > > > > http://www.physicsforums.com/ > > > > abraços > > > > ----- Original Message ----- From: "Sérgio Martins da Silva" > > > > To: "Lista OBM" > > Sent: Sunday, December 16, 2007 10:56 PM > > Subject: [obm-l] Demonstrações > > > > > >> Doutores, > >> > >> Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > >> "demonstração". Por isto, gostaria de saber como se demonstra que uma > >> demonstração está correta. E mais, que é completa. Quais são os > >> requisitos, > >> condições, etc ? > >> > >> Abraços, > >> > >> Sérgio > >> > >> ========================================================================= > >> > >> Instruções para entrar na lista, sair da lista e usar a lista em > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >> ========================================================================= > > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 17:20:39 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJJ18l027901 for ; Sun, 23 Dec 2007 17:19:01 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNJJ0DF027898 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 17:19:00 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.248]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJIu8l027892 for ; Sun, 23 Dec 2007 17:18:57 -0200 Received: by an-out-0708.google.com with SMTP id c31so257331ana.120 for ; Sun, 23 Dec 2007 12:20:35 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=pkCmzl9T27ouBToYNYbRNyZawsUGNCCV+dQFNqpRbOM=; b=xUQGwkFdo2SPDqCfif7pTuNahYGdAy/cRrq02kLEpzppNLJPP2gWIdp8UOXSU7EZpyTi9acTTxgGoSdjWeEhOHuZfhF5rRbTc41Es2n8Cj0/wQwrUQL/+yIhntOEEUzWhvPhT/8IwZQloTUSs3lBpe8RGvnD3msl9uT5BBtvRjQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=Bu36r3Q4QP/rZR+IGtidJ5KKi19aqKk+wenyAXoAOojC+TcbvBZ94A2Eq7E5Hfb8OVHC1l9cNNmUPYhCrQfYWdZrfIp+V+ueA0XC8HohjKdmmoNs+QTt/wLNwAHycvCDn2xtxPXk5wQJx4Wst0DS/Vf3qF73neQRzhOLw8IHwkg= Received: by 10.100.239.11 with SMTP id m11mr7872473anh.87.1198441235793; Sun, 23 Dec 2007 12:20:35 -0800 (PST) Received: from svs ( [201.51.8.103]) by mx.google.com with ESMTPS id 74sm1458830wra.37.2007.12.23.12.20.33 (version=SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 12:20:34 -0800 (PST) Message-ID: <005e01c845a1$74d5f7d0$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> <4766061A.4020102@gmail.com> <00ca01c84120$28301da0$02270269@rodrigo7a25356> Subject: [obm-l] =?Windows-1252?Q?Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Demons?= =?Windows-1252?Q?tra=E7=F5es?= Date: Sun, 23 Dec 2007 18:21:50 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: No, hits=4.7 required=5.0 tests=QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caros Rodrigo e arcguede, Poderiam me esclarecer o que demonstração de uma demonstração tem a ver com problemas NP? Qual bibliografia recomendam sobre isso? Abraços, Sérgio ----- Original Message ----- From: To: Sent: Tuesday, December 18, 2007 12:46 AM Subject: [obm-l] Re: [obm-l] Re: [obm-l] Demonstrações > Acredito que o problema NP seja provar que existe ou não uma forma > matemática, objetiva, de transformar problemas NP (com tempo de > processamento não polinomial) em problemas P (tempo de processamento > polinomial). Correto? > > qual seria a remissão a que você se referiu? > > ----- Original Message ----- > From: > To: > Sent: Monday, December 17, 2007 2:16 AM > Subject: Re: [obm-l] Re: [obm-l] Demonstrações > > > > Acho que isso nos remete ao "terceiro problema do milênio" - o problema > > NP. > > > > rodrigocientista@yahoo.com.br escreveu: > >> Acredito que uma "demonstração de demonstração" seria algo como > >> "chover no molhado". Uma demonstração está correta se, em última > >> instância, está de acordo com os axiomas mais básicos da matéria. > >> Então, uma demonstração de demontração recorreria, também em última > >> análise, exatamente aos mesmos axiomas, sendo assim redundante. > >> > >> Se você fala inglês, aqui está um fórum onde há diversos debates > >> interessantes sobre esses assuntos, além de resolução técnica de > >> questões de matemática, física química, engenharia em geral, etc... > >> > >> http://www.physicsforums.com/ > >> > >> abraços > >> > >> ----- Original Message ----- From: "Sérgio Martins da Silva" > >> > >> To: "Lista OBM" > >> Sent: Sunday, December 16, 2007 10:56 PM > >> Subject: [obm-l] Demonstrações > >> > >> > >>> Doutores, > >>> > >>> Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > >>> "demonstração". Por isto, gostaria de saber como se demonstra que uma > >>> demonstração está correta. E mais, que é completa. Quais são os > >>> requisitos, > >>> condições, etc ? > >>> > >>> Abraços, > >>> > >>> Sérgio > >>> > >>> ========================================================================= > >>> > >>> Instruções para entrar na lista, sair da lista e usar a lista em > >>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >>> ========================================================================= > >> > >> > >> ========================================================================= > >> Instruções para entrar na lista, sair da lista e usar a lista em > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >> ========================================================================= > >> > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 17:43:20 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJgM8l031831 for ; Sun, 23 Dec 2007 17:42:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNJgM9C031826 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 17:42:22 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.244]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNJgJ8l031785 for ; Sun, 23 Dec 2007 17:42:20 -0200 Received: by an-out-0708.google.com with SMTP id c31so258702ana.120 for ; Sun, 23 Dec 2007 12:43:58 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=Au2I0WVc9Jby868uvBb6wY+Rg5GY2/0VhILs8CeBw1s=; b=q8TUMpILtlIOqbKRUnx4l2J6RyB9ageB5LGnxroD8Du0KbGKWTC4kcQ6k96wR2aVUhF+vj8vfHFzqlOKa9xnSeCdrbkwWTrzaCzXp456HBMwneVedmDpc9DMgtZ1wkj4T48O5C0CaJUdg9W55Vqljbu77zaEcEjuAJ006gm+uXQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:references:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=gtgmTKAAx1LPVGg2YKH4InTAvKJ5hCm2iic5lbVrU+Dh3uEwu5ePNBCSxHDk0i1L394GQ3p7AeUl3qt0n6533kEoWRIWBSTHYT1bf/vMBvV6Eg6s/8vM3uxq0yBBC2UAZ8HA1O/Tc+UPpIVcrLot4o4Gw1hlNKKRt2QG31AqMC8= Received: by 10.100.127.18 with SMTP id z18mr6053267anc.39.1198442638321; Sun, 23 Dec 2007 12:43:58 -0800 (PST) Received: from svs ( [201.51.8.103]) by mx.google.com with ESMTPS id q34sm5770217wrq.11.2007.12.23.12.43.55 (version=SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 12:43:56 -0800 (PST) Message-ID: <006401c845a4$b889c990$01fea8c0@svs> From: =?iso-8859-1?Q?S=E9rgio_Martins_da_Silva?= To: References: <000c01c84050$09433560$01fea8c0@svs> <9f4be2240712230739g61ea0533gae337574ad64f5d9@mail.gmail.com> Subject: [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_Demonstra=E7=F5es?= Date: Sun, 23 Dec 2007 18:45:12 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: No, hits=4.7 required=5.0 tests=QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Lucas, Gostei do exemplo. Ele poderia ser generalizado e formalizado como um teorema? Pode me indicar links ou bibbliografia sobre o tema? Um abraço, Sérgio ----- Original Message ----- From: "Lucas Prado Melo" To: Sent: Sunday, December 23, 2007 1:39 PM Subject: Re: [obm-l] Demonstrações > On Dec 16, 2007 11:56 PM, Sérgio Martins da Silva wrote: > > Doutores, > > > > Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > > "demonstração". Por isto, gostaria de saber como se demonstra que uma > > demonstração está correta. E mais, que é completa. Quais são os requisitos, > > condições, etc ? > > > > Abraços, > > > > Sérgio > > > Oi, > Se eu estiver errado, por favor me corrijam, > Demonstrar que uma demonstração é válida é provar que a conclusão > deriva das premissas. (isso é lógica matemática) > Se, ao analisarmos uma prova a partir de suas premissas, chegamos (por > implicações sempre verdadeiras (também chamadas tautológicas)) à mesma > conclusão que a prova chegou, então a prova é válida, caso contrário > não. > Uma prova é dita completa quando não existem axiomas não declarados > (se eu não me engano). > Ex: > Se Alberto viajar e Bruno ir à praia > Então Daniel vai ao mercado > Prova: > Sabemos isso também: > - Se Alberto vai viajar e Bruno ir à praia, então Creuza vai limpar a > casa de Alberto > - Se Daniel não vai ao mercado, então Creuza não vai limpar a casa de > Alberto ou Alberto não vai viajar > Por lógica matemática: > A := Alberto ir viajar > B := Bruno ir à praia > C := Creuza ir limpar a casa de Alberto > D := Daniel ir ao mercado > Temos: > A e B e ( A e B -> C ) e ( ¬D -> ¬C ou ¬A ) > Usando algumas regras de lógica: > ( ¬D -> ¬C ou ¬A ) = ( A e C -> D ) > A e B e ( A e B -> C ) = C > A e C e ( A e C -> D ) = D > Ou seja, D é verdade... > > Resumindo (para não-leigos): uma prova é válida sse a conjunção das > premissas implica a conclusão da prova. > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 19:00:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNKxR8l008622 for ; Sun, 23 Dec 2007 18:59:27 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNKxLbp008619 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 18:59:21 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.240]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNKx38l008601 for ; Sun, 23 Dec 2007 18:59:04 -0200 Received: by an-out-0708.google.com with SMTP id c31so263500ana.120 for ; Sun, 23 Dec 2007 14:00:41 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; bh=KQlPMlQKGTHbX7ylC8FJ3KcWeNzjlvibDwgsrKZ8cG4=; b=Krj/G2+4FXhHdTaEFTjWuuIKk71M6k6vLnC/YingEYyzyoBg+1JrfLe5IUPLLozH8HEQdrfJd19r+z1NbnXbxzJE9eGNq4RNU9aKGFNiFheXL0GI8F9UPBpuyTKZVwZZN0kn5sKfWoLRSJ0G4K07r1nJSe9t4cAcMyNee8Cumpc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; b=OONXLHKHqQaMvVYFCRCmhe4c0Ph94JgE+9pT8bQMJNZieHlfMkOSKbnGaO/MPR2sdKLPi0004ZvRbQOCJTqJ++twpgFquZ1nCVIvxGiLsy09FjkfwukNpTvMbUN9rOjgWYht7FWbJrqP313XNnxKAKuEgSFC+IEsd2iLlGx+idw= Received: by 10.100.239.11 with SMTP id m11mr8031472anh.87.1198447239440; Sun, 23 Dec 2007 14:00:39 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.228.254]) by mx.google.com with ESMTPS id 1sm5434799agb.16.2007.12.23.14.00.36 (version=TLSv1/SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 14:00:38 -0800 (PST) Message-ID: <476EDA82.6010003@gmail.com> Date: Sun, 23 Dec 2007 20:00:34 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [obm-l] =?windows-1252?Q?Re=3A_=5Bobm-l=5D_Re=3A_=5Bobm-l=5D_Re=3A?= =?windows-1252?Q?_=5Bobm-l=5D_Re=3A_=5Bobm-l=5D_Demonstra=E7=F5e?= =?windows-1252?Q?s?= References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> <4766061A.4020102@gmail.com> <00ca01c84120$28301da0$02270269@rodrigo7a25356> <005e01c845a1$74d5f7d0$01fea8c0@svs> In-Reply-To: <005e01c845a1$74d5f7d0$01fea8c0@svs> Content-Type: multipart/alternative; boundary="------------050501000606080009090805" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=4.8 required=5.0 tests=IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,US_DOLLARS_3,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** This is a multi-part message in MIME format. --------------050501000606080009090805 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable Realmente eu deixei pouco claro o modo como escrevi sobre o problema. Eu quis dizer que a correla=E7=E3o com o problema P versus NP =E9 a=20 "demonstra=E7=E3o de uma demonstra=E7=E3o" =E9 que =E9 preciso provar se existe uma "demonstra=E7=E3o" para demonstra=E7=E3o= antes de=20 tentar achar uma. Isso est=E1 no ambito de pesquisa do problema NP. Quanto aos problemas do mil=EAnio S=E9rgio, s=E3o 7 problemas matem=E1tic= os=20 apresentados pelo Instituto de matem=E1tica Clay, e eles est=E3o=20 oferecerendo $ 1.000.000,00 por problema para quem os resolver. O link oficial dos problemas: http://www.claymath.org/millennium/ Para uma vers=E3o em portugues http://www.dm.ufscar.br/hp/hp853/hp853001/hp853001.html Um noticia legal =E9 que foi apresenteada este ano a solu=E7=E3o de um do= s=20 problemas do mil=EAnio - a conjectura de Poincar=E9 - ele foi resolvido p= elo matem=E1tico russo Grigory Perelman. O cara faturou um milh=E3o de verdinhas alem de ganhar a medalha Fields -= =20 o nobel da matem=E1tica. Aqui tem a noticia: http://www.e-escola.pt/site/destaque.asp?dest=3D87 Ainda t=EAm os problemas de Hilbert, caso voc=EA n=E3o conhe=E7a: http://pt.wikipedia.org/wiki/Problemas_de_Hilbert Espero ter te inspirado ainda mais a pratica da matem=E1tica. Pra mim=20 estes problemas s=E3o extremamente estimulantes, alem claro do meu gosto = natural pela matematica. Abra=E7os. S=E9rgio Martins da Silva escreveu: > Caros Rodrigo e arcguede, > > Poderiam me esclarecer o que demonstra=E7=E3o de uma demonstra=E7=E3o t= em a ver com > problemas NP? Qual bibliografia recomendam sobre isso? > > Abra=E7os, > > S=E9rgio > > ----- Original Message -----=20 > From: > To: > Sent: Tuesday, December 18, 2007 12:46 AM > Subject: [obm-l] Re: [obm-l] Re: [obm-l] Demonstra=E7=F5es > > > =20 >> Acredito que o problema NP seja provar que existe ou n=E3o uma forma >> matem=E1tica, objetiva, de transformar problemas NP (com tempo de >> processamento n=E3o polinomial) em problemas P (tempo de processamento= >> polinomial). Correto? >> >> qual seria a remiss=E3o a que voc=EA se referiu? >> >> ----- Original Message -----=20 >> From: >> To: >> Sent: Monday, December 17, 2007 2:16 AM >> Subject: Re: [obm-l] Re: [obm-l] Demonstra=E7=F5es >> >> >> =20 >>> Acho que isso nos remete ao "terceiro problema do mil=EAnio" - o pro= blema >>> NP. >>> >>> rodrigocientista@yahoo.com.br escreveu: >>> =20 >>>> Acredito que uma "demonstra=E7=E3o de demonstra=E7=E3o" seria algo c= omo >>>> "chover no molhado". Uma demonstra=E7=E3o est=E1 correta se, em =FAl= tima >>>> inst=E2ncia, est=E1 de acordo com os axiomas mais b=E1sicos da mat=E9= ria. >>>> Ent=E3o, uma demonstra=E7=E3o de demontra=E7=E3o recorreria, tamb=E9= m em =FAltima >>>> an=E1lise, exatamente aos mesmos axiomas, sendo assim redundante. >>>> >>>> Se voc=EA fala ingl=EAs, aqui est=E1 um f=F3rum onde h=E1 diversos d= ebates >>>> interessantes sobre esses assuntos, al=E9m de resolu=E7=E3o t=E9cnic= a de >>>> quest=F5es de matem=E1tica, f=EDsica qu=EDmica, engenharia em geral,= etc... >>>> >>>> http://www.physicsforums.com/ >>>> >>>> abra=E7os >>>> >>>> ----- Original Message ----- From: "S=E9rgio Martins da Silva" >>>> >>>> To: "Lista OBM" >>>> Sent: Sunday, December 16, 2007 10:56 PM >>>> Subject: [obm-l] Demonstra=E7=F5es >>>> >>>> >>>> =20 >>>>> Doutores, >>>>> >>>>> Penso que a palavra mais comum nesta lista e, qui=E7=E1, da matem=E1= tica =E9 >>>>> "demonstra=E7=E3o". Por isto, gostaria de saber como se demonstra q= ue uma >>>>> demonstra=E7=E3o est=E1 correta. E mais, que =E9 completa. Quais s=E3= o os >>>>> requisitos, >>>>> condi=E7=F5es, etc ? >>>>> >>>>> Abra=E7os, >>>>> >>>>> S=E9rgio >>>>> >>>>> >>>>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >>>>> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista e= m >>>>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >>>>> >>>>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >>>> >>>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >>>> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em= >>>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >>>> >>>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >>> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em >>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >>> >>> =20 > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > =20 >> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D >> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D >> =20 > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > =20 --------------050501000606080009090805 Content-Type: text/html; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Realmente eu deixei pouco claro o modo como escrevi sobre o problema.
= Eu quis dizer que a correla=E7=E3o com o problema P versus NP =E9 a "demonstra=E7=E3o de uma demonstra=E7=E3o" =E9 que
=E9 preciso provar se existe uma "demonstra=E7=E3o" para demonstra=E7=E3o= antes de tentar achar uma.
Isso est=E1 no ambito de pesquisa do problema NP.

Quanto aos problemas do mil=EAnio S=E9rgio, s=E3o 7 problemas matem=E1tic= os apresentados pelo Instituto de matem=E1tica Clay, e eles est=E3o oferecerendo $ 1.000.000,00 por problema para quem os resolver.

O link oficial dos problemas:

http://www.claymath.org/millennium/

Para uma vers=E3o em portugues

http://www.dm.ufscar.br/hp/hp853/hp853001/hp85= 3001.html

Um noticia legal =E9 que foi apresenteada este ano a solu=E7=E3o de um do= s problemas do mil=EAnio - a conjectura de Poincar=E9 - ele foi resolvido pelo
matem=E1tico russo Grigory Perelman.
O cara faturou um milh=E3o de verdinhas alem de ganhar a medalha Fields -= o nobel da matem=E1tica.
Aqui tem a noticia:
http://www.e-escola.pt/site/destaque.asp?dest=3D87<= /a>

Ainda t=EAm os problemas de Hilbert, caso voc=EA n=E3o conhe=E7a:

http://pt.wikipedia.org/wiki/Problemas_de_Hilbert

Espero ter te inspirado ainda mais a pratica da matem=E1tica. Pra mim estes problemas s=E3o extremamente estimulantes, alem claro do meu gosto natural pela matematica.
Abra=E7os.

S=E9rgio Martins da Silva escreveu: 
Caros Rodrigo e arcguede,

Poderiam me esclarecer o que demonstra=E7=E3o de uma demonstra=E7=E3o tem=
 a ver com
problemas NP? Qual bibliografia recomendam sobre isso?

Abra=E7os,

S=E9rgio

----- Original Message -----=20
From: <rodrigocientista@yahoo.com.br>
To: <obm-l@mat.puc-rio.br>
Sent: Tuesday, December 18, 2007 12:46 AM
Subject: [obm-l] Re: [obm-l] Re: [obm-l] Demonstra=E7=F5es


  
Acredito que o problema NP seja provar que existe ou n=
=E3o uma forma
matem=E1tica, objetiva, de transformar problemas NP (com tempo de
processamento n=E3o polinomial) em problemas P (tempo de processamento
polinomial). Correto?

qual seria a remiss=E3o a que voc=EA se referiu?

----- Original Message -----=20
From: <arcguede@gmail.com>
To: <obm-l@mat.puc-rio.br>
Sent: Monday, December 17, 2007 2:16 AM
Subject: Re: [obm-l] Re: [obm-l] Demonstra=E7=F5es


    
Acho que isso nos remete ao "terceiro problema do mi=
l=EAnio" -  o problema
NP.

rodrigocientista@yahoo.com.br escreveu:
      
Acredito que uma "demonstra=E7=E3o de demonstra=E7=
=E3o" seria algo como
"chover no molhado". Uma demonstra=E7=E3o est=E1 correta se, em =FAltima
inst=E2ncia, est=E1 de acordo com os axiomas mais b=E1sicos da mat=E9ria.=

Ent=E3o, uma demonstra=E7=E3o de demontra=E7=E3o recorreria, tamb=E9m em =
=FAltima
an=E1lise, exatamente aos mesmos axiomas, sendo assim redundante.

Se voc=EA fala ingl=EAs, aqui est=E1 um f=F3rum onde h=E1 diversos debate=
s
interessantes sobre esses assuntos, al=E9m de resolu=E7=E3o t=E9cnica de
quest=F5es de matem=E1tica, f=EDsica qu=EDmica, engenharia em geral, etc.=
=2E.

http://www.physicsforums.com/

abra=E7os

----- Original Message ----- From: "S=E9rgio Martins da Silva"
&=
lt;sms.sergio@gmail.com>
To: "Lista OBM" <obm-l@mat.puc-rio.br>
Sent: Sunday, December 16, 2007 10:56 PM
Subject: [obm-l] Demonstra=E7=F5es


        
Doutores,

Penso que a palavra mais comum nesta lista e, qui=E7=E1, da matem=E1tica =
=E9
"demonstra=E7=E3o". Por isto, gostaria de saber como se demonstra que uma=

demonstra=E7=E3o est=E1 correta. E mais, que =E9 completa. Quais s=E3o os=

requisitos,
condi=E7=F5es, etc ?

Abra=E7os,

S=E9rgio


          
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D
  
Instru=E7=F5es para entrar na lista, sair da lis=
ta e usar a lista em
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--------------050501000606080009090805-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 20:04:27 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNM2I8l013006 for ; Sun, 23 Dec 2007 20:02:18 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNM2IVe013004 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 20:02:18 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.243]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNM2G8l013000 for ; Sun, 23 Dec 2007 20:02:17 -0200 Received: by an-out-0708.google.com with SMTP id c31so267063ana.120 for ; Sun, 23 Dec 2007 15:03:55 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; bh=RWUAjrAvU7YzusysMChxaNgoU/68a2wwQTdiu/wkHkI=; b=Pz9vPzqTZ5VF3H2NMCwmJR3wIwZjIlp9ZSgC5jCkpmBMa7aWwtqZ/NbZTcJE6RpLXJhXrefNElkyzgV4OrXDNL5aY0TjIOFYntzf9XTVskqqfrgMSbDPtL2O8BgudypPacwIMbo6MgR4rpCiV78245QVwJQ1Bwbr9en6Ws08Kvo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; b=a4QiQo0oov2fhopd7jhhEs3OQkP6tJJsnjqAaS7gv2HIfVI0GWlkJBTeyXbLTVV4MS13jjgOqJtovJLA4jB0USm9aIm1scTdmZeZZMByEmn+2N026pMOEU4GrybmP2DR6obP7zr7aCDaIO2in1YPW8AU57D+mXJ7id3+k8qAHA0= Received: by 10.100.239.11 with SMTP id m11mr8150774anh.15.1198451035276; Sun, 23 Dec 2007 15:03:55 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.228.254]) by mx.google.com with ESMTPS id 32sm5496189aga.13.2007.12.23.15.03.53 (version=TLSv1/SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 15:03:54 -0800 (PST) Message-ID: <476EE950.6000304@gmail.com> Date: Sun, 23 Dec 2007 21:03:44 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Simbolos para emails Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from base64 to 8bit by saci.mat.puc-rio.br id lBNM2H8l013002 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: Yes, hits=5.3 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SUPERLONG_LINE,USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 243.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 243.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Tabelinha de símbolos em ASCII para quem quiser incrementar suas mensagens.Os caracteres a e b sao apenas para comparação. a ≠ ba Ù§ ba Ù¨ ba ∇ ba Õˆ ba â—¦ ba ± ba • ba ⊙ ba â—ˆ ba 丄 ba ⊥ ba 丅 ba ã…œ ba √ ba ⊥ ba ⊿ ba Õ‡ ba ≮ ba ⌒ ba ≯ ba ≤ ba ≥ ba ∠ba × ba Ö… ba ∞ ba â— ba ‰ ba ² ba ༠ba ∫ ba Õ¸ ba Ö ba ÑŒ ba Õ° ba Õ¦ ba Õ½ ba Ö… ba ×’ ba ½ ba ¼ ba ¾ ba â…“ ba â…” ba â…› ba â…œ ba â… ba â…ž ba £ ba â„¢ ba Ö… ba ∴ ba ∵ ba ∷ b ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 20:46:25 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNMjM8l021057 for ; Sun, 23 Dec 2007 20:45:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNMjL20021051 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 20:45:21 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNMjF8l020977 for ; Sun, 23 Dec 2007 20:45:18 -0200 Received: by rv-out-0910.google.com with SMTP id c27so935356rvf.9 for ; Sun, 23 Dec 2007 15:46:54 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=3Owr+VkVLb0TQRsXyfjKF/hJNMnD5pqzzacMYK3RaZ8=; b=LxcvOgNQImsY86nDy43wxtpHuo1m2FhX7/v8IjrnCAWQ8J1Pnk9cHztU1EjeUO2tglunt07pF40Dp/MyTVpkDMB8VfnNhcqZ4ok605Ss1SyYuCmNgCF4Ya7e7EXNZVzAQiBNhLGKhzmmi7maYcQaEmJWDfxRv28B5IxbIUg3olQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=CRMvrLdss500e4aTxzyPueL5wUeg/JYypmhgz1KKsCyTtoXsxR8RWbPY2rrn29X541eNJfYx5BIbT1FiruLLfViRsB9KwGmhcRrpFVAQYVAXRV3RqmkEf47lcsYOLF1+A1Kk4dgHx2mLuaYDtCCEZuAFZgoRAVyvkyrASRNhjrg= Received: by 10.141.99.4 with SMTP id b4mr2010971rvm.254.1198453614161; Sun, 23 Dec 2007 15:46:54 -0800 (PST) Received: by 10.141.99.13 with HTTP; Sun, 23 Dec 2007 15:46:54 -0800 (PST) Message-ID: <99886d920712231546y239af375jf573e2977faf012c@mail.gmail.com> Date: Mon, 24 Dec 2007 00:46:54 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Simbolos para emails In-Reply-To: <476EE950.6000304@gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_5300_3998823.1198453614153" References: <476EE950.6000304@gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_5300_3998823.1198453614153 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Esses caracteres s=E3o bonitos, desde que quem os leia tenha seu navegador/leitor de emails a codifica=E7=E3o de caracteres configurada como Unicode (aka UTF-8). Em outras codifica=E7=F5es (como ISO-8859-1, a codific= a=E7=E3o predominante em computadores de brasileiros), a maioria desses s=EDmbolos n= =E3o pode ser exibida, e eles aparecem normalmente como um quadradinho branco d= e borda preta. Fora que para digitar esses simbolos, ou vc tem que ter um editor de emails que eles sejam muito faceis de serem colocados, ou vc tem que conhecer de cabe=E7a um codigo para inserir cada um desses s=EDmbolos ou tem que ficar procurando com o mouse em uma longa lista de simbolos, que tamb=E9m ter=E1 = todas as letras gregas e muitas e muitas outras coisas, ou, agora que vc nos enviou a tabela, teremos que abrir seu email, selecionar o que quisermos, CTRL+C e CTRL+V. Nenhuma dessas op=E7=F5es me parece muito pr=E1tica. Assim como n=E3o acho = pratico o estabelecimento de normas para a escrita de emails para a lista, conforme foi sugerido h=E1 algumas semanas. Nem tampouco o uso de nota=E7=E3o LaTeX,= que, embora muito clara para quem saiba do que estou falando, n=E3o =E9 l=E1 mui= to pr=E1tica para escrever em diversos casos, e =E9 desnecess=E1ria para uma l= ista que n=E3o discute a publica=E7=E3o e editora=E7=E3o profissional de artigos= em revistas. Acho melhor continuarmos como sempre foi: usando o bom senso aliado =E0 vontade de ser compreendido na hora de enviar um email, que certamente far= =E1 com que o autor seja compreendido por pelo menos um membro da lista. Abra=E7os, Bruno 2007/12/24, albert richerd carnier guedes : > > Tabelinha de s=EDmbolos em ASCII para quem quiser incrementar suas > mensagens.Os caracteres a e b sao apenas para compara=E7=E3o. > [...] > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_5300_3998823.1198453614153 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Esses caracteres s=E3o bonitos, desde que quem os leia tenha seu navegador/= leitor de emails a codifica=E7=E3o de caracteres configurada como Unicode (= aka UTF-8). Em outras codifica=E7=F5es (como ISO-8859-1, a codifica=E7=E3o = predominante em computadores de brasileiros), a maioria desses s=EDmbolos n= =E3o pode ser exibida, e  eles aparecem normalmente como um quadradinh= o branco de borda preta.

Fora que para digitar esses simbolos, ou vc tem que ter um editor d= e emails que eles sejam muito faceis de serem colocados, ou vc tem que conh= ecer de cabe=E7a um codigo para inserir cada um desses s=EDmbolos ou tem qu= e ficar procurando com o mouse em uma longa lista de simbolos, que tamb=E9m= ter=E1 todas as letras gregas e muitas e muitas outras coisas, ou, agora q= ue vc nos enviou a tabela, teremos que abrir seu email, selecionar o que qu= isermos, CTRL+C e CTRL+V.

Nenhuma dessas op=E7=F5es me parece muito pr=E1tica. Assim como n= =E3o acho pratico o estabelecimento de normas para a escrita de emails para= a lista, conforme foi sugerido h=E1 algumas semanas. Nem tampouco o uso de= nota=E7=E3o LaTeX, que, embora muito clara para quem saiba do que estou fa= lando, n=E3o =E9 l=E1 muito pr=E1tica para escrever em diversos casos, e = =E9 desnecess=E1ria para uma lista que n=E3o discute a publica=E7=E3o e edi= tora=E7=E3o profissional de artigos em revistas.

Acho melhor continuarmos como sempre foi: usando o bom senso aliado= =E0 vontade de ser compreendido na hora de enviar um email, que certamente= far=E1 com que o autor seja compreendido por pelo menos um membro da lista= .

Abra=E7os,
Bruno



--
Bruno FRAN=C7A DOS REIS

msn: = brunoreis666@hotmail.com
skype: brunoreis666
tel: +33 (0)6 28 43 = 42 16

e^(pi*i)+1=3D0 ------=_Part_5300_3998823.1198453614153-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 20:47:15 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNMkL8l021469 for ; Sun, 23 Dec 2007 20:46:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNMkKIB021466 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 20:46:20 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.249]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNMkH8l021413 for ; Sun, 23 Dec 2007 20:46:18 -0200 Received: by an-out-0708.google.com with SMTP id c31so269588ana.120 for ; Sun, 23 Dec 2007 15:47:56 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:references:subject:date:mime-version:content-type:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=HSFDVg17Nenh82LZ4Q0T12fFH05DwmK7d9VUiCp49wI=; b=Cn5+CWxTRLS1DTivQslN5eLugDRBpUg37uyLduaF7H2Q9YUjUsNyED5NlSaKz0Qr7mTwL5yLzh8NPriRR166R2ondV1NCkalbWe54iSrXht4xiCiGwQUPwtLfdWvKBYEi1twEAIV3TS0Lyf+4Gqv0Vc/uu/WWhIW5qml506eZ3E= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:references:subject:date:mime-version:content-type:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=jRp8R8yviDmnNwGzdi2OvAb5gdgeDxsR1Ba9Vsl1arCG9pSKn+6IKb57NWvL4D+373L5xlUBwOq1VIzhbv9ja0mFEpa3YNKv7ZTmChmU3LMJL291GdekW0WQ/fpd4DFqzLCXQE3khtibw69UaAesPShALOjqPRvNy1IVFux8jIE= Received: by 10.101.70.5 with SMTP id x5mr8199061ank.27.1198453672667; Sun, 23 Dec 2007 15:47:52 -0800 (PST) Received: from svs ( [201.51.8.103]) by mx.google.com with ESMTPS id g3sm4664951wra.19.2007.12.23.15.47.49 (version=SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 15:47:50 -0800 (PST) Message-ID: <001101c845be$692515c0$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> <4766061A.4020102@gmail.com> <00ca01c84120$28301da0$02270269@rodrigo7a25356> <005e01c845a1$74d5f7d0$01fea8c0@svs> <476EDA82.6010003@gmail.com> Subject: [SPAM] [obm-l] =?Windows-1252?Q?Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Re:_=5Bo?= =?Windows-1252?Q?bm-l=5D_Re:_=5Bobm-l=5D_Demonstra=E7=F5es?= Date: Sun, 23 Dec 2007 21:49:05 -0200 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: Yes, hits=6.1 required=5.0 tests=MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,US_DOLLARS_3, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_000E_01C845AD.A394DD00" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.10 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: US_DOLLARS_3 (0.4 points) BODY: Nigerian scam key phrase ($NN,NNN,NNN.NN) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 249.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 249.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_000E_01C845AD.A394DD00 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Albert, Obrigado pelos links. Navegando e aprendendo. S=E9rgio ----- Original Message -----=20 From: albert richerd carnier guedes=20 To: obm-l@mat.puc-rio.br=20 Sent: Sunday, December 23, 2007 8:00 PM Subject: [obm-l] Re: [obm-l] Re: [obm-l] Re: [obm-l] Re: [obm-l] = Demonstra=E7=F5es Realmente eu deixei pouco claro o modo como escrevi sobre o problema. Eu quis dizer que a correla=E7=E3o com o problema P versus NP =E9 a = "demonstra=E7=E3o de uma demonstra=E7=E3o" =E9 que =E9 preciso provar se existe uma "demonstra=E7=E3o" para = demonstra=E7=E3o antes de tentar achar uma. Isso est=E1 no ambito de pesquisa do problema NP. Quanto aos problemas do mil=EAnio S=E9rgio, s=E3o 7 problemas = matem=E1ticos apresentados pelo Instituto de matem=E1tica Clay, e eles = est=E3o oferecerendo $ 1.000.000,00 por problema para quem os resolver. O link oficial dos problemas: http://www.claymath.org/millennium/ Para uma vers=E3o em portugues http://www.dm.ufscar.br/hp/hp853/hp853001/hp853001.html Um noticia legal =E9 que foi apresenteada este ano a solu=E7=E3o de um = dos problemas do mil=EAnio - a conjectura de Poincar=E9 - ele foi = resolvido pelo=20 matem=E1tico russo Grigory Perelman. O cara faturou um milh=E3o de verdinhas alem de ganhar a medalha = Fields - o nobel da matem=E1tica. Aqui tem a noticia: http://www.e-escola.pt/site/destaque.asp?dest=3D87 Ainda t=EAm os problemas de Hilbert, caso voc=EA n=E3o conhe=E7a: http://pt.wikipedia.org/wiki/Problemas_de_Hilbert Espero ter te inspirado ainda mais a pratica da matem=E1tica. Pra mim = estes problemas s=E3o extremamente estimulantes, alem claro do meu gosto = natural pela matematica. Abra=E7os. ------=_NextPart_000_000E_01C845AD.A394DD00 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable
Albert,
 
    Obrigado pelos = links. Navegando=20 e aprendendo.
 
S=E9rgio
----- Original Message -----
From:=20 albert richerd=20 carnier guedes
I) Tecnicamente, isto depende do n=FAmero de bolinhas que voc=EA tem. = Se voc=EA tiver 3 bolinhas de cada cor, por exemplo, em 10 bolinhas sortead= as sem reposi=E7=E3o voc=EA tem 100% de probabilidade de ter as 4 cores!
 
Vou interpretar de outro jeito (que =E9 equivalente a tomar o n=FAmero= de bolinhas indo para infinito, ou supor que as bolinhas s=E3o sorteadas *= *com** reposi=E7=E3o): vou fazer 10 sorteios independentes; cada sorteio co= nsiste em escolher uma de 4 cores, todas com a mesma probabilidade 1/4= . A pergunta =E9: qual a chance de faltar alguma cor no decorrer dos 1= 0 sorteios?
 
Vou usar M (aMarelo), Z (aZul), V (verde) e B (branco) para = denotar o n=FAmero de vezes que cada cor apareceu nos 10 sorteio. Note que = M+Z+V+B=3D10. Queremos Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0).
 
i) Pr(M=3D0)=3DPr(Z=3D0)=3DPr(V=3D0)=3DPr(B=3D0)=3D(3/4)^10
(3/4 de chance em cada sorteio daquela cor espec=EDfica n=E3o aparecer= )
 
ii) Pr(M=3DZ=3D0)=3DPr(M=3DV=3D0)=3D...=3DPr(B=3DV=3D0)=3D(2/4)^10
(2/4 de chance em cada sorteio de ambas aquelas cores n=E3o aparecerem= )
 
iii) Pr(M=3DZ=3DV=3D0)=3DPr(M=3DZ=3DB=3D0)=3D...=3D(1/4)^10
(basicamente, cada um destes significa "tudo de uma cor s=F3"= ;)
 
Pelo princ=EDpio da inclus=E3o-exclus=E3o, queremos
Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0) =3D
=3D Pr(M=3D0)+Pr(Z=3D0)+...+Pr(B=3D0)
-(Pr(M=3D0 e Z=3D0)+Pr(M=3D0 e V=3D0)+...Pr(B=3DV=3D0))
+Pr(M=3DZ=3DV=3D0)+Pr(M=3DZ=3DB=3D0)+...
-Pr(M=3DZ=3DV=3DB=3D0) =3D
=3D 4.(3/4)^10-6.(2/4)^10+4.(1/4)^10 - 0 =3D 230056/(2^20) =3D 21.94%<= /div>
 
II) De novo, s=F3 d=E1 para achar um n=FAmero se a gente supuser que a= s bolinhas s=E3o sorteadas COM reposi=E7=E3o (que =E9 equivalente ao n=FAme= ro de bolinhas tender a infinito). O m=E9todo =E9 igual ao de ali em cima: = usarei a mesma nota=E7=E3o Z (# de aZuis), V (# de Vermelhas) e M (# de aMa= relas). Note que Z+V+M=3D18.
 
i) Pr(Z=3D18)=3DPr(V=3D18)=3DPr(M=3D18)=3D(1/3)^18
Ent=E3o Pr(todas da mesma cor) =3D 3.(1/3)^18 - 1/9(3^17) =3D 7.74(10^= -9)
 
ii) Pr(Z=3D0)=3DPr(V=3D0)=3DPr(M=3D0)=3D(2/3)^18
Ent=E3o Pr(Z=3D0 ou V=3D0 ou M=3D0) =3D
=3D Pr(Z=3D0)+Pr(V=3D0)+Pr(M=3D0)
-Pr(Z=3DV=3D0)-Pr(Z=3DM=3D0)-Pr(V=3DM=3D0)
+Pr(Z=3DV=3DM=3D0) =3D
=3D 3.(2/3)^18-3.(1/3)^18+0 =3D 0.203%
 
iii) Queremos Pr(Z<>0 e V<>0 e M<>0) que =E9 exatame= nte o complementar do item anterior. Ent=E3o a resposta =E9
1-(3.(2/3)^18-3.(1/3)^18) =3D 99.797%
 
 
On 12/4/07, = crmoraes@claretianas.com.br<= /a> <crmoraes@clareti= anas.com.br > wrote:
Podem me ajudar com esses proble= mas?

I-)Tenho o mesmo n=FAmero de bolinhas de gude verdes, amarelas,= azuis e
brancas.
1. Qual a probabilidade de, em 10 bolinhas, n=E3o ter as 4 = cores?


II-) Tenho o mesmo n=FAmero de bolinhas de gude azuis, ve= rmelhas e amarelas.
1. Qual a probabilidade de, em 18 bolinhas, todas se= rem da mesma cor?
2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores
= (quaisquer)?
3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos = 1 de cada cor?


--
Mensagem verificada contra virus.
Proved= or Claretianas.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em=
http://www.= mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D

------=_Part_310_5344121.1196790133468-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 14:46:43 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4GjP8l015330 for ; Tue, 4 Dec 2007 14:45:26 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4GjNQ3015327 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 14:45:23 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.241]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4Gin8l015296 for ; Tue, 4 Dec 2007 14:44:52 -0200 Received: by an-out-0708.google.com with SMTP id c31so847038ana for ; Tue, 04 Dec 2007 09:46:11 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=xxqqOva94REs/Z87JMSSXLosRpbLi4+mvcgsmIFbEWk=; b=RA5HPRN8+VICKj8OH8O3ozPGllvksAM8pts61atCwR4lAphoOcEmAB6niqbiWhKclwMZAoGJ36mHbikMrQkZlhi+yTW1L20ry4Lx5TF3uw38/FfEoh2FtmwlC9QTWaoPa3jQ5j8Wd4hpRcairMLHmKwjzYhG09kgjb2WYpcIEO0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=paasd8vbCzsKJxRDhJJihM47I12ZhgUAZhZh2f1i0ONORpW48UeoVbEq620Q/ni1haGlynILxei2ROfXS92S+tiMYBvNsz8QUFVhMhQ/F7DyHJXqQtnaEUx6oJ+IHiy8m0FK0QciTVpmLpN2ctAEgSG7+WMzfEHH814MyPWHZbM= Received: by 10.101.68.19 with SMTP id v19mr1966486ank.1196790371296; Tue, 04 Dec 2007 09:46:11 -0800 (PST) Received: by 10.90.49.13 with HTTP; Tue, 4 Dec 2007 09:46:11 -0800 (PST) Message-ID: <2d483c770712040946p7875455fl5be2b75237a36c5b@mail.gmail.com> Date: Tue, 4 Dec 2007 14:46:11 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] probabilidades In-Reply-To: <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_316_24686357.1196790371286" References: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=3.4 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_316_24686357.1196790371286 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline On 12/4/07, Ralph Teixeira wrote: > > I) Tecnicamente, isto depende do n=FAmero de bolinhas que voc=EA tem. Se = voc=EA > tiver 3 bolinhas de cada cor, por exemplo, em 10 bolinhas sorteadas sem > reposi=E7=E3o voc=EA tem 100% de probabilidade de ter as 4 cores! > > Vou interpretar de outro jeito (que =E9 equivalente a tomar o n=FAmero de > bolinhas indo para infinito, ou supor que as bolinhas s=E3o sorteadas **c= om** > reposi=E7=E3o): vou fazer 10 sorteios independentes; cada sorteio consist= e > em escolher uma de 4 cores, todas com a mesma probabilidade 1/4. A pergun= ta > =E9: qual a chance de faltar alguma cor no decorrer dos 10 sorteios? > > Vou usar M (aMarelo), Z (aZul), V (verde) e B (branco) para denotar o > n=FAmero de vezes que cada cor apareceu nos 10 sorteio. Note que M+Z+V+B= =3D10. > Queremos Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0). > > i) Pr(M=3D0)=3DPr(Z=3D0)=3DPr(V=3D0)=3DPr(B=3D0)=3D(3/4)^10 > (3/4 de chance em cada sorteio daquela cor espec=EDfica n=E3o aparecer) > > ii) Pr(M=3DZ=3D0)=3DPr(M=3DV=3D0)=3D...=3DPr(B=3DV=3D0)=3D(2/4)^10 > (2/4 de chance em cada sorteio de ambas aquelas cores n=E3o aparecerem) > > iii) Pr(M=3DZ=3DV=3D0)=3DPr(M=3DZ=3DB=3D0)=3D...=3D(1/4)^10 > (basicamente, cada um destes significa "tudo de uma cor s=F3") > > Pelo princ=EDpio da inclus=E3o-exclus=E3o, queremos > Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0) =3D > =3D Pr(M=3D0)+Pr(Z=3D0)+...+Pr(B=3D0) > -(Pr(M=3D0 e Z=3D0)+Pr(M=3D0 e V=3D0)+...Pr(B=3DV=3D0)) > +Pr(M=3DZ=3DV=3D0)+Pr(M=3DZ=3DB=3D0)+... > -Pr(M=3DZ=3DV=3DB=3D0) =3D > =3D 4.(3/4)^10-6.(2/4)^10+4.(1/4)^10 - 0 =3D 230056/(2^20) =3D 21.94% > > II) De novo, s=F3 d=E1 para achar um n=FAmero se a gente supuser que as b= olinhas > s=E3o sorteadas COM reposi=E7=E3o (que =E9 equivalente ao n=FAmero de bol= inhas tender > a infinito). O m=E9todo =E9 igual ao de ali em cima: usarei a mesma nota= =E7=E3o Z (# > de aZuis), V (# de Vermelhas) e M (# de aMarelas). Note que Z+V+M=3D18. > > i) Pr(Z=3D18)=3DPr(V=3D18)=3DPr(M=3D18)=3D(1/3)^18 > Ent=E3o Pr(todas da mesma cor) =3D 3.(1/3)^18 - 1/9(3^17) =3D 7.74(10^-9) > > ii) Pr(Z=3D0)=3DPr(V=3D0)=3DPr(M=3D0)=3D(2/3)^18 > Ent=E3o Pr(Z=3D0 ou V=3D0 ou M=3D0) =3D > =3D Pr(Z=3D0)+Pr(V=3D0)+Pr(M=3D0) > -Pr(Z=3DV=3D0)-Pr(Z=3DM=3D0)-Pr(V=3DM=3D0) > +Pr(Z=3DV=3DM=3D0) =3D > =3D 3.(2/3)^18-3.(1/3)^18 > (Observa=E7=E3o: o que eu fiz foi a probabilidade de aparecem 2 cores OU ME= NOS). Se voc=EA quiser a probabilidade de aparecerem EXATAMENTE cores, tem que subtrair de novo a probabilidade de aparecer 1 cor s=F3: Pr(EXATAMENTE 2 cores) =3D 3.(2/3)^18-3.(1/3)^18 - (3.(1/3)^18 - 1/9(3^17))= . Na pr=E1tica, a diferen=E7a =E9 pouca.) > iii) Queremos Pr(Z<>0 e V<>0 e M<>0) que =E9 exatamente o complementar do > item anterior. Ent=E3o a resposta =E9 > 1-(3.(2/3)^18-3.(1/3)^18) =3D 99.797% > > > On 12/4/07, crmoraes@claretianas.com.br > wrote: > > > > Podem me ajudar com esses problemas? > > > > I-)Tenho o mesmo n=FAmero de bolinhas de gude verdes, amarelas, azuis e > > brancas. > > 1. Qual a probabilidade de, em 10 bolinhas, n=E3o ter as 4 cores? > > > > > > II-) Tenho o mesmo n=FAmero de bolinhas de gude azuis, vermelhas e > > amarelas. > > 1. Qual a probabilidade de, em 18 bolinhas, todas serem da mesma cor? > > 2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores > > (quaisquer)? > > 3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos 1 de cada > > cor? > > > > > > -- > > Mensagem verificada contra virus. > > Provedor Claretianas. > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > ------=_Part_316_24686357.1196790371286 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline

On 12/4/07, = Ralph Teixeira <ralphct@gmail.c= om> wrote:
I) Tecnicamente, isto depende do n=FAmero de bolinhas que voc=EA tem. = Se voc=EA tiver 3 bolinhas de cada cor, por exemplo, em 10 bolinhas sortead= as sem reposi=E7=E3o voc=EA tem 100% de probabilidade de ter as 4 cores!
 
Vou interpretar de outro jeito (que =E9 equivalente a tomar o n=FAmero= de bolinhas indo para infinito, ou supor que as bolinhas s=E3o sorteadas *= *com** reposi=E7=E3o): vou fazer 10 sorteios independentes; cada sorteio co= nsiste em escolher uma de 4 cores, todas com a mesma probabilidade 1/4= . A pergunta =E9: qual a chance de faltar alguma cor no decorrer dos 1= 0 sorteios?=20
 
Vou usar M (aMarelo), Z (aZul), V (verde) e B (branco) para = denotar o n=FAmero de vezes que cada cor apareceu nos 10 sorteio. Note que = M+Z+V+B=3D10. Queremos Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0).
 
i) Pr(M=3D0)=3DPr(Z=3D0)=3DPr(V=3D0)=3DPr(B=3D0)=3D(3/4)^10
(3/4 de chance em cada sorteio daquela cor espec=EDfica n=E3o aparecer= )
 
ii) Pr(M=3DZ=3D0)=3DPr(M=3DV=3D0)=3D...=3DPr(B=3DV=3D0)=3D(2/4)^10
(2/4 de chance em cada sorteio de ambas aquelas cores n=E3o aparecerem= )
 
iii) Pr(M=3DZ=3DV=3D0)=3DPr(M=3DZ=3DB=3D0)=3D...=3D(1/4)^10
(basicamente, cada um destes significa "tudo de uma cor s=F3"= ;)
 
Pelo princ=EDpio da inclus=E3o-exclus=E3o, queremos
Pr(M=3D0 ou Z=3D0 ou V=3D0 ou B=3D0) =3D
=3D Pr(M=3D0)+Pr(Z=3D0)+...+Pr(B=3D0)
-(Pr(M=3D0 e Z=3D0)+Pr(M=3D0 e V=3D0)+...Pr(B=3DV=3D0))
+Pr(M=3DZ=3DV=3D0)+Pr(M=3DZ=3DB=3D0)+...
-Pr(M=3DZ=3DV=3DB=3D0) =3D
=3D 4.(3/4)^10-6.(2/4)^10+4.(1/4)^10 - 0 =3D 230056/(2^20) =3D 21.94%<= /div>
 
II) De novo, s=F3 d=E1 para achar um n=FAmero se a gente supuser que a= s bolinhas s=E3o sorteadas COM reposi=E7=E3o (que =E9 equivalente ao n=FAme= ro de bolinhas tender a infinito). O m=E9todo =E9 igual ao de ali em cima: = usarei a mesma nota=E7=E3o Z (# de aZuis), V (# de Vermelhas) e M (# de aMa= relas). Note que Z+V+M=3D18.=20
 
i) Pr(Z=3D18)=3DPr(V=3D18)=3DPr(M=3D18)=3D(1/3)^18
Ent=E3o Pr(todas da mesma cor) =3D 3.(1/3)^18 - 1/9(3^17) =3D 7.74(10^= -9)
 
ii) Pr(Z=3D0)=3DPr(V=3D0)=3DPr(M=3D0)=3D(2/3)^18
Ent=E3o Pr(Z=3D0 ou V=3D0 ou M=3D0) =3D
=3D Pr(Z=3D0)+Pr(V=3D0)+Pr(M=3D0)
-Pr(Z=3DV=3D0)-Pr(Z=3DM=3D0)-Pr(V=3DM=3D0)
+Pr(Z=3DV=3DM=3D0) =3D
=3D 3.(2/3)^18-3.(1/3)^18
 
(Observa=E7=E3o: o que eu fiz foi a probabilidade de aparecem 2 cores = OU MENOS). Se voc=EA quiser a probabilidade de aparecerem EXATAMENTE c= ores, tem que subtrair de novo a probabilidade de aparecer 1 cor s=F3:=
Pr(EXATAMENTE 2 cores) =3D 3.(2/3)^18-3.(1/3)^18 - (3.(1/3)^18 - 1/9(3= ^17)). Na pr=E1tica, a diferen=E7a =E9 pouca.)


 
iii) Queremos Pr(Z<>0 e V<>0 e M<>0) que =E9 exatame= nte o complementar do item anterior. Ent=E3o a resposta =E9
1-(3.(2/3)^18-3.(1/3)^18) =3D 99.797%
 
 
On 12/4/07, = crmoraes@claretianas.com.br<= /a> <crmoraes@claretianas.co= m.br > wrote:=20
Podem me ajudar com esses proble= mas?

I-)Tenho o mesmo n=FAmero de bolinhas de gude verdes, amarelas,= azuis e=20
brancas.
1. Qual a probabilidade de, em 10 bolinhas, n=E3o ter as 4 = cores?


II-) Tenho o mesmo n=FAmero de bolinhas de gude azuis, ve= rmelhas e amarelas.
1. Qual a probabilidade de, em 18 bolinhas, todas se= rem da mesma cor?=20
2. Qual a probabilidade de, em 18 bolinhas, serem apenas de 2 cores
= (quaisquer)?
3. Qual a probabilidade de, em 18 bolinhas, ter pelo menos = 1 de cada cor?


--
Mensagem verificada contra virus.
Proved= or Claretianas.=20

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em=
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
<= br>

------=_Part_316_24686357.1196790371286-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 4 15:33:29 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4HW98l020203 for ; Tue, 4 Dec 2007 15:32:09 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB4HW9ui020201 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 15:32:09 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB4HW48l020192 for ; Tue, 4 Dec 2007 15:32:05 -0200 Received: by an-out-0708.google.com with SMTP id c31so852111ana for ; Tue, 04 Dec 2007 10:33:26 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=H1mU3uoNhZ+09g1sH+DzZpTzO+adLCt3YArbzk3VA5A=; b=OKc2colPr5IJHjNG4OQyqFqQPikbuZrJDIZ6r06UYSNmiLG7k3cXwhahtXc/qH2IF7WmR1YoJKGaZ9ZQs2Ct1iCyeQIr3ULSqsA0Nn4MQSvrWbH71DOioZeRglkfZpOaQXC0wEfjJXyqoVwPNOkxOW0feEpQpLR3iLywuXWILoI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=hBAXR/sDnef9uHGuE5Cgaq9pTp5lIXnn37uoeEP65pry/DU07GrLeAc7bvU9zO06CO/nTux6vJOMELSabD97wB+RE8FpRoId07ZLLSQvAi6wjVbMGx/4fyexKPYUUnq4o5TAKDW3E48zUAKySvb0HiUEApEeK4KQVKNsV+sI4UQ= Received: by 10.100.196.17 with SMTP id t17mr2087063anf.1196793206714; Tue, 04 Dec 2007 10:33:26 -0800 (PST) Received: by 10.90.49.13 with HTTP; Tue, 4 Dec 2007 10:33:26 -0800 (PST) Message-ID: <2d483c770712041033s3a7cafa7sf4a3a37ea6c06f11@mail.gmail.com> Date: Tue, 4 Dec 2007 15:33:26 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] probabilidade In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_57_29732824.1196793206701" References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,LINES_OF_YELLING, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_57_29732824.1196793206701 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Desculpa, Pedro, mas os eventos que voc=EA escolheu contar ****n=E3o**** s= =E3o igualmente prov=E1veis! =C9 t=E3o prov=E1vel ter 0,0,0,10 bolinhas de cada = cor quanto 3,3,3,1? N=E3o, o segundo evento =E9 bem mais prov=E1vel! Isso dito, sua contagem combinat=F3ria est=E1 muito bacana -- a gente tem q= ue **inventar** agora um problema cuja solu=E7=E3o seja a sua, de t=E3o bonita= que ela =E9.... Ser=E1 que tem alguma maneira natural de sortear solu=E7=F5es d= a equa=E7=E3o x+y+z+t=3D10 de maneira que todas sejam igualmente prov=E1veis? ---- ---- Por outro lado, este erro =E9 o mais comum (e sutil!) que h=E1 em probabili= dade (basta ver os =FAltimos 100 problemas de probabilidade aqui mesmo na lista = -- 85.34% deles tem esse erro ;p ;p ;p). A culpa =E9 de n=F3s professores e no= ssos livros-texto, que marretam na cabe=E7a a f=F3rmula: PROBABILIDADE =3D # DE CASOS FAVOR=C1VEIS / # DE CASOS POSS=CDVEIS assim, com letras garrafais, e a=ED colocam em letras pequeninas no cantinh= o do rodap=E9 do ap=EAndice que isto s=F3 vale se os eventos forem igualmente prov=E1veis. A=ED a gente acostuma a contar # de casos para l=E1 e para c= =E1 (h=E1bito refor=E7ado por centenas de problemas de contagem combinat=F3ria) e erra um monte de problemas de probabilidade apesar de fazer um monte de contas complicadas... Eu estou numa cruzada contra esta apresenta=E7=E3o da f=F3rm= ula acima por este motivo. :) :) :) Ent=E3o fica assim: todo mundo, junto comigo: Probabilidade =3D casos poss=EDveis/casos favor=E1veis (em fonte pequeninin= ina) APENAS QUANDO OS CASOS CONTADOS FOREM ABSOLUTAMENTE IRREFUTAVELMENTE SEM D=DAVIDA TOTALMENTE IGUALMENTE PROV=C1VEIS!!!! (EM FONTE ****COLOSS=C1=C1=C1=C1=C1=C1L****!!!!) (quando der aula disso, repita a =FAltima frase com o entusiasmo com que o cara do Rock Gol diz CL=C9=C9=C9=C9=C9=C9=C9=C9=C9=C9RSON!!! -- ou sei l= =E1 que nome ele diz :) :) :) :) ) ---- ---- Abra=E7o, Ralph On 12/4/07, Pedro Cardoso wrote: > > > Cmoraes, eu recomendo que voc=EA escreve no google "solu=E7=F5es inteiras > n=E3o-negativas". > > I) Depende do n=FAmero de bolinhas. Se houver mais de 9 bolinhas de cada > cor, tudo bem. Caso contr=E1rio, fica mais complicado, eu acho. Supondo q= ue > sejam mais de 9 de cada cor... > > Sejam x1 o n=FAmero de bolinhas verdes, x2 o n=FAmero de amarelas, x3 o > de azuis, x4 o de brancas. > P(A) =E9 a probabilidade de ocorrer o evento A. > Al=E9m disso, o sinal '>=3D" significa 'maior ou igual'. > > x1+x2+x3+x4 =3D 10 > > O n=FAmero de solu=E7=F5es inteiras n=E3o-negativas dessa equa=E7=E3o cor= responde ao > n=FAmero de casos poss=EDveis para os grupos de 10 bolinhas (desde que a = ordem > das bolinhas n=E3o importe). Casos poss=EDveis =3D 13!/(3!10!) =3D 260. > > P(n=E3o haver quatro cores) =3D 1 - P(haver quatro cores) > > Para que hajam quatro cores, devemos ter x1,x2,x3,x4>0. Considere y um > inteiro maior ou igual a 0. > Assim, satisfazendo as condi=E7=F5es do problema, x1 =3D y1+1; x2 =3D y2+= 1; x3 =3D > y3+1; x4 =3D y4+1 > > Como x1+x2+x3+x4 =3D 10, (y1+1)+(y2+1)+(y3+1)+(y4+1) =3D 10 .:. y1+y2+y3+= y4 =3D > 6 (y>=3D0) > > Os casos favor=E1veis s=E3o as solu=E7=F5es dessa =FAltima equa=E7=E3o. > N=FAmero de casos favor=E1veis =3D 9!/(3!6!) =3D 84. > > P(haver quatro cores) =3D 84/260 =3D 21/65 > P(n=E3o haver quatro cores) =3D 1 - 21/65 =3D 44/65. > > O II =E9 parecido, ent=E3o, entendendo o I, acho que voc=EA consegue reso= lv=EA-lo. > > *Eu considerei x>=3D10 porque, caso contr=E1rio, na equa=E7=E3o x1+x2+x3+= x4 =3D10, > eu teria que trabalhar com v=E1rios casos. > A solu=E7=E3o x1 =3D10, x2,x3,x4 =3D 0 n=E3o valeria, por exemplo. > > At=E9. Espero ter ajudado. > > > ------------------------------ > Conhe=E7a o Windows Live Spaces, o site de relacionamentos do Messenger! = Crie > j=E1 o seu! > ------=_Part_57_29732824.1196793206701 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Desculpa, Pedro, mas os eventos que voc=EA escolheu contar ****n=E3o**= ** s=E3o igualmente prov=E1veis! =C9 t=E3o prov=E1vel ter 0,0,0,10 bol= inhas de cada cor quanto 3,3,3,1? N=E3o, o segundo evento =E9 bem mais prov= =E1vel!
 
Isso dito, sua contagem combinat=F3ria est=E1 muito bacana -- a gente = tem que **inventar** agora um problema cuja solu=E7=E3o seja a sua, de t=E3= o bonita que ela =E9.... Ser=E1 que tem alguma maneira natural de sortear s= olu=E7=F5es da equa=E7=E3o x+y+z+t=3D10 de maneira que todas sejam igualmen= te prov=E1veis?
 
---- <begin reclama=E7=E3o ranzinza e rabugenta, n=E3o ligue para m= im n=E3o, ignore se desejar> ----
Por outro lado, este erro =E9 o mais comum (e sutil!) que h=E1 em prob= abilidade (basta ver os =FAltimos 100 problemas de probabilidade aqui mesmo= na lista -- 85.34% deles tem esse erro ;p ;p ;p). A culpa =E9 de= n=F3s professores e nossos livros-texto, que marretam na cabe=E7a&nbs= p;a f=F3rmula:
 
PROBABILIDADE =3D # DE CASOS FAVOR=C1VEIS / # DE CASOS POSS= =CDVEIS
 
assim, com letras garrafais, e a=ED colocam em letras pequeninas no ca= ntinho do rodap=E9 do ap=EAndice que isto s=F3 vale se os eventos forem igu= almente prov=E1veis. A=ED a gente acostuma a contar # de casos para l=E1 e = para c=E1 (h=E1bito refor=E7ado por centenas de problemas de contagem = combinat=F3ria) e erra um monte de problemas de probabilidade apesar de faz= er um monte de contas complicadas... Eu estou numa cruzada contra esta apre= senta=E7=E3o da f=F3rmula acima por este motivo. :) :) :)
 
Ent=E3o fica assim: todo mundo, junto comigo:
 
Probabilidade =3D casos poss=EDveis/casos favor=E1veis (em fonte peque= nininina)
APENAS QUANDO OS CASOS CONTADOS FOREM ABSOLUTAMENTE IRREFUTAVELMENTE S= EM D=DAVIDA TOTALMENTE IGUALMENTE PROV=C1VEIS!!!! (EM FONTE ****COLOSS=C1= =C1=C1=C1=C1=C1L****!!!!)
(quando der aula disso, repita a =FAltima frase com o entusiasmo&= nbsp;com que o cara do Rock Gol diz CL=C9=C9=C9=C9=C9=C9=C9=C9=C9=C9RS= ON!!! -- ou sei l=E1 que nome ele diz :) :) :) :) )
---- <end reclama=E7=E3o ranzinza e rabugenta, pode voltar a ler>= ; ----
 
Abra=E7o,
       Ralph
 
On 12/4/07, = Pedro Cardoso <pedrolazer= a@hotmail.com> wrote:

Cmoraes, eu recomendo que voc=EA escreve no google "solu= =E7=F5es inteiras n=E3o-negativas".
 
I) Depende do n=FAmer= o de bolinhas. Se houver mais de 9 bolinhas de cada cor, tudo bem= . Caso contr=E1rio, fica mais complicado, eu acho. Supondo que sejam mais d= e 9 de cada cor...
 
Sejam x1 o n=FAmero de bolinhas verdes, x2  o = n=FAmero de amarelas, x3 o de azuis, x4 o de = brancas.
P(A) =E9 a probabilidade de ocorrer o evento A.
Al=E9m dis= so, o sinal '>=3D" significa 'maior ou igual'.
 
x1+x2+x3+x4 =3D 10 
 
O n=FAmero de solu=E7= =F5es inteiras n=E3o-negativas dessa equa=E7=E3o corresponde ao n=FAmero de= casos poss=EDveis para os grupos de 10 bolinhas (desde que a ordem das bol= inhas n=E3o importe). Casos poss=EDveis =3D 13!/(3!10!) =3D 260.
 
P(n=E3o haver quatro cores) =3D 1 - P(haver quatro cores)
=  
Para que hajam quatro cores, devemos ter x1,x2,x3,x4>0. Consid= ere y um inteiro maior ou igual a 0.
Assim, satisfazendo as condi=E7=F5e= s do problema, x1 =3D y1+1; x2 =3D y2+1; x3 =3D y3+1; x4 =3D y4+1
 
Como x1+x2+x3+x4 =3D 10, (y1+1)+(y2+1)+(y3+1)+(y4+1) =3D 10 .= :. y1+y2+y3+y4 =3D 6 (y>=3D0)
 
Os casos favor=E1veis s=E3o a= s solu=E7=F5es dessa =FAltima equa=E7=E3o.
N=FAmero de casos favor=E1vei= s =3D 9!/(3!6!) =3D 84.
 
P(haver quatro cores) =3D 84/260 =3D 2= 1/65
P(n=E3o haver quatro cores) =3D 1 - 21/65 =3D 44/65.
 
O II = =E9 parecido, ent=E3o, entendendo o I, acho que voc=EA consegue resolv=EA-l= o.
 
*Eu considerei x>=3D10 porque, caso contr=E1rio, na equa= =E7=E3o x1+x2+x3+x4 =3D10, eu teria que trabalhar com v=E1rios casos.
A solu=E7=E3o x1 =3D10, x2,x3,x4 =3D 0 n=E3o valeria, por exemplo.
=  
At=E9. Espero ter ajudado.


Conhe=E7a o Windows Live Spaces, o site de relacionamentos do Messenger! Crie j=E1 o seu!

------=_Part_57_29732824.1196793206701-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 07:39:37 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB59b28l026840 for ; Wed, 5 Dec 2007 07:37:02 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB59b1GN026835 for obm-l-MllGbsmmN; Wed, 5 Dec 2007 07:37:01 -0200 Received: from aacpdlotus.net.ms.gov.br (aacpdlotus.net.ms.gov.br [200.181.116.8]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB59aw8l026781 for ; Wed, 5 Dec 2007 07:36:59 -0200 To: obm-l@mat.puc-rio.br MIME-Version: 1.0 From: JoaoCarlos_Junior@net.ms.gov.br Importance: X-Priority: Subject: [SPAM] Re: [obm-l] probabilidade (OFF) Sensitivity: Date: Wed, 5 Dec 2007 07:38:27 -0400 Message-ID: X-Mailer: Lotus Domino Web Server Release 6.5.5 November 30, 2005 X-MIMETrack: Serialize by Router on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 05/12/2007 07:38:34 MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: JoaoCarlos_Junior@net.ms.gov.br X-Spam-Status: Yes, hits=6.5 required=5.0 tests=AWL,CTYPE_JUST_HTML,EMAIL_ATTRIBUTION,HTML_FONT_COLOR_BLUE, MAILTO_LINK,NO_REAL_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 X-Spam-Prev-Content-Transfer-Encoding: quoted-printable SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.50 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: EMAIL_ATTRIBUTION (-1.6 points) BODY: Contains what looks like an email attribution SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 8.116.181.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 8.116.181.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: CTYPE_JUST_HTML (0.4 points) HTML-only mail, with no text version SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results ---------------------

=C9 isso a=ED. Ralph, obrigado!

Matem=E1tica =E9 vida, sem emo=E7=E3o, ela= n=E3o existe, =E9 morta, e ficamos tamb=E9m amortalhados. =

P=F5e tua luz para fora, Ralph, auxilinado= -nos no despertar da nossa.

Fraternalmente, Jo=E3o.&nb= sp;


Desculpa, Pedro, mas os eventos que = voc=EA escolheu contar ****n=E3o**** s=E3o igualmente prov=E1veis! =C9= t=E3o prov=E1vel ter 0,0,0,10 bolinhas de cada cor quanto 3,3,3,1? N=E3o, = o segundo evento =E9 bem mais prov=E1vel!
 
Isso dito, sua co= ntagem combinat=F3ria est=E1 muito bacana -- a gente tem que **inventar** a= gora um problema cuja solu=E7=E3o seja a sua, de t=E3o bonita que ela =E9..= .. Ser=E1 que tem alguma maneira natural de sortear solu=E7=F5es da equa=E7= =E3o x+y+z+t=3D10 de maneira que todas sejam igualmente prov=E1veis?
 
---- <begin reclama=E7=E3o ranzinza e rabugenta, n=E3o ligue = para mim n=E3o, ignore se desejar> ----
Por outro lado, este erro =E9 o mais comum (e sutil!) que h=E1 em= probabilidade (basta ver os =FAltimos 100 problemas de probabilidade aqui = mesmo na lista -- 85.34% deles tem esse erro ;p ;p ;p). A culpa = =E9 de n=F3s professores e nossos livros-texto, que marretam na cabe= =E7a a f=F3rmula:
 
PROBABILIDADE =3D # DE CASOS F= AVOR=C1VEIS / # DE CASOS POSS=CDVEIS
 
assim, com letras= garrafais, e a=ED colocam em letras pequeninas no cantinho do rodap=E9 do = ap=EAndice que isto s=F3 vale se os eventos forem igualmente prov=E1veis. A= =ED a gente acostuma a contar # de casos para l=E1 e para c=E1 (h=E1bito re= for=E7ado por centenas de problemas de contagem combinat=F3ria) e erra= um monte de problemas de probabilidade apesar de fazer um monte de contas = complicadas... Eu estou numa cruzada contra esta apresenta=E7=E3o da f=F3rm= ula acima por este motivo. :) :) :)
 
Ent=E3o fica assim: to= do mundo, junto comigo:
 
Probabilidade =3D casos poss=EDveis= /casos favor=E1veis (em fonte pequenininina)
APENAS QUANDO OS CASOS CONTADOS FOREM ABSOLUTAMENTE IRREFUTAVEL= MENTE SEM D=DAVIDA TOTALMENTE IGUALMENTE PROV=C1VEIS!!!! (EM FONTE ****COLO= SS=C1=C1=C1=C1=C1=C1L****!!!!)
(q= uando der aula disso, repita a =FAltima frase com o entusiasmo co= m que o cara do Rock Gol diz CL=C9=C9=C9=C9=C9=C9=C9=C9=C9=C9RSON!!! -= - ou sei l=E1 que nome ele diz :) :) :) :) )
---- <end reclama=E7=E3o ranzinza e rabugenta, pode voltar a= ler> ----
 
Abra=E7o,
       Ralph
 
On 12/4/0= 7, Pedro Cardoso <pedrolazera@hotmail.com> wrote:

C= moraes, eu recomendo que voc=EA escreve no google "solu=E7=F5es inteir= as n=E3o-negativas".
 
I) Depende do n=FAmero de bolinhas. Se=  houver mais de 9 bolinhas de cada cor, tudo bem. Caso contr=E1ri= o, fica mais complicado, eu acho. Supondo que sejam mais de 9 de cada cor..= .
 
Sejam x1 o n=FAmero de bolinhas verdes, x2 &= nbsp;o n=FAmero de amarelas, x3 o de azuis, x4 o d= e brancas.
P(A) =E9 a proba= bilidade de ocorrer o evento A.
= Al=E9m disso, o sinal '>=3D" significa 'maior ou igual'.
 
 =
O n=FAmero de solu=E7=F5es intei= ras n=E3o-negativas dessa equa=E7=E3o corresponde ao n=FAmero de casos poss= =EDveis para os grupos de 10 bolinhas (desde que a ordem das bolinhas n=E3o= importe). Casos poss=EDveis =3D 13!/(3!10!) =3D 260.
 
P(n= =E3o haver quatro cores) =3D 1 - P(haver quatro cores)
 
Para= que hajam quatro cores, devemos ter x1,x2,x3,x4>0. Considere y um intei= ro maior ou igual a 0.
Assim, sat= isfazendo as condi=E7=F5es do problema, x1 =3D y1+1; x2 =3D y2+1; x3 = =3D y3+1; x4 =3D y4+1
 
Como x1+x2+x3+x4 =3D 10, (y1+1)+(y2+= 1)+(y3+1)+(y4+1) =3D 10 .:. y1+y2+y3+y4 =3D 6 (y>=3D0)
 
O= s casos favor=E1veis s=E3o as solu=E7=F5es dessa =FAltima equa=E7=E3o.
N=FAmero de casos favor=E1veis =3D 9!= /(3!6!) =3D 84.
 
= P(haver quatro cores) =3D 84/260 =3D 21/65 =
P(n=E3o haver quatro cores) =3D = 1 - 21/65 =3D 44/65.
 
O II =E9 parecido, ent=E3o, entendendo= o I, acho que voc=EA consegue resolv=EA-lo.
 
*Eu considerei= x>=3D10 porque, caso contr=E1rio, na equa=E7=E3o x1+x2+x3+x4 =3D10, eu = teria que trabalhar com v=E1rios casos.
A solu=E7=E3o x1 =3D10, x2,x3,x4 =3D 0 n=E3o valeria, por exemplo. =
 
At=E9. Espero ter ajudado.



Conhe=E7a o Windows Live Spaces,= o site de relacionamentos do Messenger! Crie= j=E1 o seu!

= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 08:23:15 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB51J6G7032455 for ; Tue, 4 Dec 2007 23:24:42 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB50NKxR028700 for obm-l-MllGbsmmN; Tue, 4 Dec 2007 22:23:20 -0200 Received: from bay0-omc2-s29.bay0.hotmail.com (bay0-omc2-s29.bay0.hotmail.com [65.54.246.165]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB50N98l028608 for ; Tue, 4 Dec 2007 22:23:10 -0200 Received: from BAY112-W36 ([64.4.26.136]) by bay0-omc2-s29.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Tue, 4 Dec 2007 17:22:30 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_37cc7fee-4293-4834-a07e-de1901a1b719_" X-Originating-IP: [201.37.214.138] From: Pedro Cardoso To: Subject: RE: [obm-l] probabilidades Date: Wed, 5 Dec 2007 04:22:30 +0300 Importance: Normal In-Reply-To: <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> References: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> MIME-Version: 1.0 X-OriginalArrivalTime: 05 Dec 2007 01:22:30.0279 (UTC) FILETIME=[4DE82170:01C836DD] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_37cc7fee-4293-4834-a07e-de1901a1b719_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Opa, Ralph. =20 Eu j=E1 tinha lido outros e-mails seus com essa advert=EAncia, mas s=F3 ago= ra percebi que nesse caso* seu alerta tamb=E9m era v=E1lido. Sou um dos alu= nos novos que aprenderam assim - que probabilidade =E9 "caso favor=E1vel/ca= so poss=EDvel". Vou at=E9 testar meu professor! =20 *me refiro ao e-mail do ralph sobre o problema de probabilidade enviado pel= o crmoraes, sobre sorteio de bolinha de gude. =20 Enfim, muito obrigado (pelo elogio e pela aula). _________________________________________________________________ Veja mapas e encontre as melhores rotas para fugir do tr=E2nsito com o Live= Search Maps! http://www.livemaps.com.br/index.aspx?tr=3Dtrue= --_37cc7fee-4293-4834-a07e-de1901a1b719_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Opa, Ralph.
 
Eu j=E1 tinha lido outros e-mails seus com essa advert=EAncia, mas s=F3 ago= ra percebi que nesse caso* seu alerta tamb=E9m era v=E1lido. Sou um dos alu= nos novos que aprenderam assim - que probabilidade =E9 "caso favor=E1v= el/caso poss=EDvel". Vou at=E9 testar meu professor!
 
*me refiro ao e-mail do ralph sobre o problema de probabilidade enviado pel= o crmoraes, sobre sorteio de bolinha de gude.
 
Enfim, muito obrigado (pelo elogio e pela aula).

Veja mapas e encontre as melhores rotas para fugir do tr=E2nsito com o Li= ve Search Maps! Experimente j=E1! = --_37cc7fee-4293-4834-a07e-de1901a1b719_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 09:09:16 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5B868l021003 for ; Wed, 5 Dec 2007 09:08:06 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB5B86dD020998 for obm-l-MllGbsmmN; Wed, 5 Dec 2007 09:08:06 -0200 Received: from hermes1.fapesp.br (hermes1.fapesp.br [143.108.10.60]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5B848l020967 for ; Wed, 5 Dec 2007 09:08:04 -0200 Received: by hermes1.fapesp.br (GEOPreProc, from userid 1000) id A0184D3CD29; Wed, 5 Dec 2007 10:07:34 -0200 (BRST) Received: from TRIESTE.FAPESP.BR (iliadas.fapesp.br [10.11.0.2]) by hermes1.fapesp.br (GEOPreProc) with ESMTP id 7FB91D3CD23 for ; Wed, 5 Dec 2007 10:07:32 -0200 (BRST) Received: from ILIADAS/SpoolDir by TRIESTE.FAPESP.BR (Mercury 1.48); 5 Dec 07 10:10:02 -0300 Received: from SpoolDir by ILIADAS (Mercury 1.48); 5 Dec 07 10:09:40 -0300 Received: from trieste.fapesp.br (10.12.0.33) by TRIESTE.FAPESP.BR (Mercury 1.48) with ESMTP; 5 Dec 07 10:09:36 -0300 Message-ID: <47569500.A9EAC40A@trieste.fapesp.br> Date: Wed, 05 Dec 2007 10:09:36 -0200 From: ralonso Organization: fapesp X-Mailer: Mozilla 4.8 [en] (Windows NT 5.0; U) X-Accept-Language: en MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [obm-l] Vagas para Graduados na USP References: <1305.200.232.239.58.1196782036.squirrel@mail.claretianas.com.br> <2d483c770712040942w1eedbae8odf6fe08c1b80c487@mail.gmail.com> Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: ralonso X-Spam-Status: No, hits=-1.3 required=5.0 tests=AWL,NOSPAM_INC,REFERENCES,SPAM_PHRASE_00_01,X_ACCEPT_LANG, X_MAILING_LIST version=2.44 X-Spam-Level: Inscrição e Seleção de Graduados - 2008 De acordo com o Estatuto da USP, poderá ser concedida matrícula, nos cursos da USP, a portadores de diploma de curso superior devidamente registrado. A matrícula poderá ser deferida para o primeiro período letivo do curso, se resultarem vagas após a matrícula de alunos classificados em concurso vestibular e após o atendimento das transferências regimentais. A critério da Comissão de Graduação, poderá ser deferida para outros períodos letivos do curso, se resultarem vagas após a matrícula dos alunos regulares e o atendimento das transferências regimentais, estando os alunos sujeitos às adaptações curriculares necessárias. (Informações Acadêmicas - 2007). Número de vagas : Bacharelado em Matemática: 16 Bacharelado em Estatística: não há vagas Bacharelado em Matemática Aplicada: 06 Bacharelado em Matemática Aplicada e Computacional: 01 Bacharelado em Ciência da Computação: 04 Licenciatura em Matemática - diurno: 07 Licenciatura em Matemática - noturno: 32 Inscrição: 08 e 09 de janeiro de 2008, na Secretaria da Comissão de Graduação - sala 13 do Bloco B do IME. Documentos necessários: cópia de diploma, devidamente registrado, e do histórico escolar, ementa das disciplinas cursadas. Candidatos graduados em curso do IME ou de outra unidade da USP poderão apresentar apenas atestado de conclusão de curso. Critérios de Seleção: 1. Bacharelado em Matemática: serão selecionados para entrevista os candidatos que obtiverem nota maior ou igual a 5,0 (cinco) na prova de Cálculo Diferencial e Integral. Candidatos graduados pela USP não estão dispensados da prova. A classificação final dos candidatos será feita levando-se em conta a nota atribuída na prova, a entrevista e o currículo do candidato. Programa da prova de Cálculo Diferencial e Integral: Funções polinomiais, racionais, exponenciais, logarítmicas e trigonométricas; função composta e função inversa. Limites: propriedades algébricas, cálculo de limites, Teorema do Confronto. Continuidade. Derivadas: definição, interpretações geométricas, regras de derivação, regra da cadeia, derivada da função inversa e derivação implícita. Aplicações. Máximos e mínimos, Teorema do Valor Médio. Gráficos. Aplicações. Fórmula de Taylor e aproximações de funções. Regras de L'Hospital. Aplicações. Integral de Riemann. Técnicas de integração. Aplicações: cálculos de volumes de revolução, comprimento de curvas, trabalho, densidade e massa. Referências Bibliográficas: 1)* *J. Stewart, “Cálculo”, vol. I, 4a. ed., Pioneira. 2) H. L. Guidorizzi, “Um Curso de Cálculo”, vol. I e II, ed. LTC, 2002. 2. Bacharelado em Estatística: serão selecionados os candidatos que obtiverem nota maior ou igual a 5,0 (cinco) em prova de Introdução à Probabilidade e Estatística. Candidatos graduados pela USP não estão dispensados da prova. A classificação dos candidatos será feita pela nota atribuída na prova e análise do currículo. No caso de empate a classificação será feita com base em uma entrevista. Programa da prova de Introdução à Probabilidade e Estatística: 1. Estatística Descritiva, 2. Probabilidades, 3. Variáveis Aleatórias Discretas. Principais modelos: Uniforme, Bernoulli, Binomial, Geométrica, Poisson e Hipergeométrica, 4. Variáveis Aleatórias Discretas Bidimensionais, 5. Variáveis Aleatórias Contínuas, 6. Estimação Pontual e por intervalo, 7. Testes de Hipóteses para média e proporção, 8. Testes de Qui-quadrado, 9. Testes de Comparação de Médias, 10. Regressão e Correlação. 3. Bacharelados em Matemática Aplicada e Matemática Aplicada e Computacional: serão selecionados os candidatos que obtiverem nota maior ou igual a 5,0 (cinco) na prova de Cálculo de Funções de uma Variável. Candidatos graduados pela USP não estão dispensados da prova. A classificação dos candidatos será feita pela nota atribuída na prova. No caso de empate a classificação será feita com base na análise do currículo ou entrevista. Programa da prova de Cálculo de Funções de uma Variável: Funções polinomiais, racionais, exponenciais, logarítmicas e trigonométricas; função composta e função inversa. Limites: noção intuitiva e definição, propriedades algébricas, Teorema do Confronto. Continuidade. Derivadas: definição, interpretações geométricas, regras de derivação, regra da cadeia, derivada da função inversa e derivação implícita. Aplicações. Máximos e mínimos, Teorema do Valor Médio. Gráficos. Aplicações. Fórmula de Taylor e aproximações de funções. Regras de L'Hospital. Aplicações. Integral de Riemann. Integral definida e indefinida. Técnicas de integração. Teorema fundamental de cálculo. Aplicações: cálculo de áreas e volumes, trabalho, densidade e massa. 4. Bacharelado em Ciência da Computação: serão selecionados os candidatos que obtiverem nota maior ou igual a 7,0 (sete) na prova de Introdução à Computação. Candidatos graduados pela USP não estão dispensados da prova. A classificação dos candidatos será feita pela nota atribuída na prova. No caso de empate a classificação será feita com base na análise do currículo e eventual entrevista. Programa da prova de Introdução à Computação: Algoritmos: caracterização, notação e estruturas básicas. Conceitos de linguagem algorítmicas: expressões, comandos seqüenciais, seletivos e repetitivos. Entrada e saída, variáveis estruturadas e funções. Desenvolvimento de programas. Extensa prática de programação e depuração de programas. Conhecimentos básicos da linguagem de programação C. Referências Bibliograficas: Material didático para disciplinas de Introdução à Computação", Projeto MAC Multimídia, «http://www.ime.usp.br/~macmulti/». E. Roberts, "The Art and Science of C", Addison-Wesley, 1995. B.W. Kernighan, D.M. Ritchie, "A Linguagem de Programação C, padrão ANSI", Campus, 1990. 5. Licenciatura em Matemática: serão selecionados os candidatos que obtiverem nota maior ou igual a 5,0 (cinco) na prova de Cálculo Diferencial e Integral. Candidatos graduados pela USP não estão dispensados da prova. A classificação dos candidatos será feita pela nota atribuída na prova. No caso de empate a classificação será feita com base na análise do currículo ou entrevista. Programa da prova de Cálculo Diferencial e Integral: Funções polinomiais, racionais, exponenciais, logarítmicas e trigonométricas; função composta e função inversa. Limites: noção intuitiva, propriedades algébricas, Teorema do Confronto. Continuidade. Derivadas: definição, interpretações geométricas, regras de derivação, regra da cadeia, derivada da função inversa e derivação implícita. Aplicações. Máximos e mínimos, Teorema do Valor Médio. Gráficos. Aplicações. Fórmula de Taylor e aproximações de funções. Regras de L'Hospital. Aplicações. Integral de Riemann. Técnicas de integração. Aplicações: cálculos de volumes de revolução, comprimento de curvas, trabalho, densidade e massa. Referências Bibliográficas: Hughes Hallett, D et alii, “Cálculo”, vol. I, ed. Edgard Blücher Ltda, São Paulo, 1999. C. G. Simmons, “Cálculo com Geometria Analítica”, vol. I, MacGraw-Hill, São Paulo, 1987. J. Stewart, “Cálculo”, vol. I, ed. Pioneira – Thomson Learning, São Paulo, 2001. Data e local das provas Bacharelados em Matemática : 13 de fevereiro de 2008 às 14 horas na sala 05 do bloco B do IME Bacharelados em Matemática Aplicada e Bacharelado em Matemática Aplicada e Computacional: 14 de fevereiro de 2008 às 14 horas na sala 05 do bloco B do IME. Bacharelado em Ciência da Computação: 12 de fevereiro de 2008 às 14 horas na sala 05 do bloco B do IME Licenciatura em Matemática : 11 de fevereiro de 2008 às 14 horas na sala 05 do bloco B do IME OBS. As provas terão duração de 2 horas e os candidatos devem comparecer com documento de identidade. Divulgação dos Resultados: 18 de fevereiro de 2008 no mural do Serviço de Aluno de Graduação (em frente à sala 14 do Bloco B). Matrícula dos aprovados: de 18 a 22 de fevereiro 2008 Início das aulas: 25 de fevereiro de 2008. Os candidatos não selecionados poderão retirar os documentos encaminhados até 18 de março de 2008 na Secretaria da Comissão de Graduação. O IME não se responsabiliza pelos documentos não retirados até esta data. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 10:03:40 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5C268l026774 for ; Wed, 5 Dec 2007 10:02:06 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB5C25To026772 for obm-l-MllGbsmmN; Wed, 5 Dec 2007 10:02:05 -0200 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5C238l026766 for ; Wed, 5 Dec 2007 10:02:04 -0200 Received: by py-out-1112.google.com with SMTP id a29so12546453pyi for ; Wed, 05 Dec 2007 05:03:26 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=xHtURJCvqNYED/R+BjzLWVJ9IS2lhA+8oMA+9JhLg9w=; b=qB2zHcIWNqPPkTX+Xy+jOB6ig7pdEJBbxidHWsRUxw4ihhp/Zv6XOlmpu1Y1a8xZe/pvHsZzFypVL48bw4PpYsnOPd0HBlXIUK6zFaD1zXT2Ay/7jYzOzZ1fXbhpyrBxp/Y7wuoGyvOe8k9MjSncroTMQGGQ54oOLWaJGa6XogM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=kL7cZS2T1nTF/2Qc7elOfzr1XjfNVizYs9pQ/IbaTwTMIXlK8zmHknnXXQ0HShSnXRrL7dKF28T1KvJZGy5Aj2g/cIwAeva0eJ5LpNy2Mxf+EMamqLAnagWhvtaBfUmH4JnomE811V79/jovLLZfw7F4OIXJHEVo76yQearoIsM= Received: by 10.142.103.6 with SMTP id a6mr848592wfc.1196859805960; Wed, 05 Dec 2007 05:03:25 -0800 (PST) Received: by 10.142.144.16 with HTTP; Wed, 5 Dec 2007 05:03:25 -0800 (PST) Message-ID: Date: Wed, 5 Dec 2007 11:03:25 -0200 From: "Fernando Oliveira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Exercicio olimpico In-Reply-To: <001301c83611$6723ea10$02270269@rodrigo7a25356> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_695_19864347.1196859805978" References: <782792.89014.qm@web50601.mail.re2.yahoo.com> <001301c83611$6723ea10$02270269@rodrigo7a25356> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando Oliveira" X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_695_19864347.1196859805978 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Se algu=E9m souber ingl=EAs, pode tentar decifrar o que escreveram aqui: http://www.mathlinks.ro/viewtopic.php?t=3D173020 --=20 Fernando Oliveira ------=_Part_695_19864347.1196859805978 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Se algu=E9m souber ingl=EAs, pode tentar decifrar o que escreveram aqui: http://www.mathl= inks.ro/viewtopic.php?t=3D173020

--
Fernando Oliveira ------=_Part_695_19864347.1196859805978-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 15:47:33 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5HiI8l017544 for ; Wed, 5 Dec 2007 15:44:18 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB5HiHHV017542 for obm-l-MllGbsmmN; Wed, 5 Dec 2007 15:44:17 -0200 Received: from bay0-omc2-s7.bay0.hotmail.com (bay0-omc2-s7.bay0.hotmail.com [65.54.246.143]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5HiF8l017537 for ; Wed, 5 Dec 2007 15:44:16 -0200 Received: from BAY135-W31 ([65.55.140.66]) by bay0-omc2-s7.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Wed, 5 Dec 2007 10:45:38 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_2b32a2c6-2445-414c-9a00-232b825e987d_" X-Originating-IP: [161.148.50.188] From: Anselmo Alves de Sousa To: Subject: RE: [obm-l] Exercicio olimpico Date: Wed, 5 Dec 2007 21:45:38 +0300 Importance: Normal In-Reply-To: References: <782792.89014.qm@web50601.mail.re2.yahoo.com> <001301c83611$6723ea10$02270269@rodrigo7a25356> MIME-Version: 1.0 X-OriginalArrivalTime: 05 Dec 2007 18:45:38.0586 (UTC) FILETIME=[0771DFA0:01C8376F] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Anselmo Alves de Sousa X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,WEB_BUGS, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_2b32a2c6-2445-414c-9a00-232b825e987d_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 has at least 2007 distinct prime factors. (in English: prove that exists a= positive integer such that has at least 2007 distinct prime factors.) Pr= ove que a express=E3o tem pelo menos 2007 fatores primos distintos. =20 =20 Date: Wed, 5 Dec 2007 11:03:25 -0200From: fetofs@gmail.comTo: obm-l@mat.puc= -rio.brSubject: Re: [obm-l] Exercicio olimpicoSe algu=E9m souber ingl=EAs, = pode tentar decifrar o que escreveram aqui: http://www.mathlinks.ro/viewtop= ic.php?t=3D173020-- Fernando Oliveira=20 _________________________________________________________________ Receba as =FAltimas not=EDcias do Brasil e do mundo direto no seu Messenger= com Alertas MSN! =C9 GR=C1TIS! http://alertas.br.msn.com/= --_2b32a2c6-2445-414c-9a00-232b825e987d_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable  
3D"\exists = has at least 2007 distinct prime factors.

(in English: prove that e= xists a positive integer such that 3D"\frac{a^{29} has at least 2007 distinct prime factors.) = ;

Prove que a express=E3o tem pelo menos 2007 fatores primos distint= os.
 





 
Date: Wed, 5 Dec 2007 11:03:25 -0200
From: fetofs@gmail.com
To: obm-l= @mat.puc-rio.br
Subject: Re: [obm-l] Exercicio olimpico

Se algu= =E9m souber ingl=EAs, pode tentar decifrar o que escreveram aqui: http:= //www.mathlinks.ro/viewtopic.php?t=3D173020

--
Fernando Oliv= eira

Receba as =FAltimas not=EDcias do Brasil e do= mundo direto no seu Messenger! =C9 GR=C1TIS! Assine j=E1! = --_2b32a2c6-2445-414c-9a00-232b825e987d_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 5 18:02:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB5JxD8l003292 for ; Wed, 5 Dec 2007 17:59:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB5JxDUD003288 for obm-l-MllGbsmmN; Wed, 5 Dec 2007 17:59:13 -0200 Received: from smtp103.mail.mud.yahoo.com (smtp103.mail.mud.yahoo.com [209.191.85.213]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB5Jx98l003242 for ; Wed, 5 Dec 2007 17:59:09 -0200 Received: (qmail 81727 invoked from network); 5 Dec 2007 21:00:31 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=fIRdSBDF5GglzFPpjlEOtt5aR/Bb+MLFSEMlnCn3sSqEB49elStErBaBSpS5GXPzEDSsx/mrDCPwaUEgwwXlxi904DFbbe0ROkC6IH8SZZrvoajeDy5wDg2G4t30o7RrvrR+F4d4jMvbcnZGBR6grM4JF5P6az3e28L1/H+EO8I= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp103.mail.mud.yahoo.com with SMTP; 5 Dec 2007 21:00:30 -0000 X-YMail-OSG: mjoU7KMVM1ktIUAVteIIaTbwl226ZzMvfwEZkMwMR_LSzdTcvUhbKiQr.NmBt1zOynEiLbjKeFdFANPkqqRP6MfkkY6W.QpV8dpjK.m37VgC7Vc1XQk- Message-ID: <009501c83781$deac6cd0$02270269@rodrigo7a25356> From: To: References: <782792.89014.qm@web50601.mail.re2.yahoo.com> <001301c83611$6723ea10$02270269@rodrigo7a25356> Subject: [SPAM] Re: [obm-l] Exercicio olimpico Date: Wed, 5 Dec 2007 18:00:20 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MAILTO_LINK,NO_REAL_NAME, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0092_01C83768.B30C66C0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.80 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 213.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 213.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0092_01C83768.B30C66C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable rust escreveu: se p divide (a^29 - 1)/(a - 1), com p>29, ent=E3o p =3D=3D 1 mod 29 e = para todo primo p =3D=3D 1 mod 29 existe pelo menos um a_p incongruente = a 1 mod p tal que p divide [(a + lp)^29 - 1]/(a + lp - 1). Assim, pelo = teorema do resto chin=EAs, podemos escolher um a tal que a =3D=3D a_p = mod p_i, i =3D 1,2,3,...,n >=3D 2007 ----- Original Message -----=20 From: Fernando Oliveira=20 To: obm-l@mat.puc-rio.br=20 Sent: Wednesday, December 05, 2007 10:03 AM Subject: Re: [obm-l] Exercicio olimpico Se algu=E9m souber ingl=EAs, pode tentar decifrar o que escreveram = aqui: http://www.mathlinks.ro/viewtopic.php?t=3D173020 --=20 Fernando Oliveira ------=_NextPart_000_0092_01C83768.B30C66C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
rust escreveu:
 
se p divide (a^29 - 1)/(a - 1), com = p>29, ent=E3o=20 p =3D=3D 1 mod 29 e para todo primo p =3D=3D 1 mod 29 existe pelo menos = um a_p=20 incongruente a 1 mod p tal que p divide [(a + lp)^29 - 1]/(a + lp - = 1).=20 Assim, pelo teorema do resto chin=EAs, podemos escolher um a tal que a = =3D=3D a_p mod=20 p_i, i =3D 1,2,3,...,n >=3D 2007
----- Original Message -----
From:=20 Fernando = Oliveira=20
Sent: Wednesday, December 05, = 2007 10:03=20 AM
Subject: Re: [obm-l] Exercicio=20 olimpico

Se algu=E9m souber ingl=EAs, pode tentar decifrar o que = escreveram=20 aqui: http://www.math= links.ro/viewtopic.php?t=3D173020

--=20
Fernando Oliveira ------=_NextPart_000_0092_01C83768.B30C66C0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 6 15:09:11 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB6H5c8l002235 for ; Thu, 6 Dec 2007 15:05:38 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB6H5cpU002233 for obm-l-MllGbsmmN; Thu, 6 Dec 2007 15:05:38 -0200 Received: from web63303.mail.re1.yahoo.com (web63303.mail.re1.yahoo.com [69.147.97.28]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB6H5a8l002227 for ; Thu, 6 Dec 2007 15:05:36 -0200 Received: (qmail 20890 invoked by uid 60001); 6 Dec 2007 18:06:59 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=vvnNbnP2PngFhqe45uv3PQ8ES0/Fam5nPngUKWn9g90AlfX4MCbPrwUGxus2Vv2gLAJjbJYygokgyxUY7L8/cS7zkWqmkFfhhW3SqhzIqxKs0lL9+aPTBz1nRJPpsz2tlNgbLQJCNSayv+2X8lW+q2cZ5mKo3VNYCAZWAklZYNk=; X-YMail-OSG: bdnQ6RwVM1m616Re.Fs8HOJ6AsIGTkEFJJ1U2Isif0hUY2MBekbS3Fozj_JroZaY7ipRDrKiUOkMmGewZvkIscohNLo8Lnk3y9J_ Received: from [146.164.38.4] by web63303.mail.re1.yahoo.com via HTTP; Thu, 06 Dec 2007 15:06:59 ART Date: Thu, 6 Dec 2007 15:06:59 -0300 (ART) From: =?iso-8859-1?q?Jo=E3o=20Pedro=20de=20Gusm=E3o=20Silva?= Subject: [SPAM] [obm-l] =?iso-8859-1?q?Um=20problema=20de=20c=F4nicas?= To: OBM MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <267706.20647.qm@web63303.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?Jo=E3o=20Pedro=20de=20Gusm=E3o=20Silva?= X-Spam-Status: Yes, hits=7.6 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1543680865-1196964419=:20647" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 28.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 28.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1543680865-1196964419=:20647 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Amigos me ajudem nos seguintes exercícios: 1) Por um ponto J exterior a uma elipse tracemos as retas tangentes à elipse, JM e JN, onde M e N são os pontos de tangência. Seja P o ponto médio de MN, mostre que a reta JP passa pelo centro dessa cônica. 2) Análogo ao anterior para hipérbole. 3) O aconteceria se a cônica fosse uma parábola? Obrigado. --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1543680865-1196964419=:20647 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Amigos me ajudem nos seguintes exercícios:

1) Por um ponto J exterior a uma elipse tracemos as retas tangentes à elipse, JM e JN, onde M e N são os pontos de tangência.  Seja P o ponto médio de MN, mostre que a reta JP passa pelo centro dessa cônica.

2) Análogo ao anterior para hipérbole.

3) O aconteceria se a cônica fosse uma parábola?

Obrigado.

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1543680865-1196964419=:20647-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 6 16:02:50 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB6I0b8l018852 for ; Thu, 6 Dec 2007 16:00:37 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB6I0bIP018849 for obm-l-MllGbsmmN; Thu, 6 Dec 2007 16:00:37 -0200 Received: from relay3.uol.com.br (relay3.uol.com.br [200.221.4.110]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB6I0Y8l018802 for ; Thu, 6 Dec 2007 16:00:34 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper3.uol.com.br (Postfix) with ESMTP id 0D042B0027DA for ; Thu, 6 Dec 2007 17:01:59 -0200 (BRST) Received: from uol.com.br (whisky4.mail.sys.intranet [172.26.5.88]) by sniper3.uol.com.br (Postfix) with ESMTP id D2BC6B0027CC for ; Thu, 6 Dec 2007 17:01:58 -0200 (BRST) Date: Thu, 6 Dec 2007 17:01:58 -0200 Message-Id: Subject: [obm-l] boa de combinatoria MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1196967718.2A.575978.42.3940.52.42.007.1320062884" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.70.135.138 X-SIG5: 4ff42e3321d07f686de1075871cc78cc Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.1 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1196967718.2A.575978.42.3940.52.42.007.1320062884 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Caros colegas... Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero de fun=E7= =F5es f: In --> Im tais que: a) f seja crescente b) f seja n=E3o-decrescente desde j=E1 grato.... --_=__=_XaM3_.1196967718.2A.575978.42.3940.52.42.007.1320062884 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Caros colegas...
 
 
Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero de = fun=E7=F5es f: In --> Im tais que:
 
 
a) f seja crescente
 
b) f seja n=E3o-decrescente
 
desde j=E1 grato....
--_=__=_XaM3_.1196967718.2A.575978.42.3940.52.42.007.1320062884-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 6 17:19:49 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB6JIK8l001106 for ; Thu, 6 Dec 2007 17:18:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB6JIKsl001104 for obm-l-MllGbsmmN; Thu, 6 Dec 2007 17:18:20 -0200 Received: from web50606.mail.re2.yahoo.com (web50606.mail.re2.yahoo.com [206.190.38.93]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB6JII8l001090 for ; Thu, 6 Dec 2007 17:18:19 -0200 Received: (qmail 65012 invoked by uid 60001); 6 Dec 2007 20:19:41 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=fnSvIwd5NVK9bFoGSMN7Xq8PgsIAI3eItBA4bOzZUFYdCL8OXETBZECEHfC0i2v4TR+kxDwTojyXhbmkoQRHv8OslmmI9jPJL2tX1P/EFGg8ugWB9PNXPJcLiniy0BclFvllu+sfxaaGXBove7Za5i9qImp+oE+i1ar0oBastks=; X-YMail-OSG: XzHTjZEVM1mde9sCI6XgZ5AMnt0P5r6ReicuifWQ6Ot0Z_9BygnUL3ARXErNRLcY_VBUO0kuRXSKTZOFBb0AWre7CKJ1Qg6A69EtH5T9AaSuScTKGp2Zljwo5mkR_NO96ZKcUDZAHNGnu4c- Received: from [161.148.199.2] by web50606.mail.re2.yahoo.com via HTTP; Thu, 06 Dec 2007 12:19:41 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Thu, 6 Dec 2007 12:19:41 -0800 (PST) From: Rodrigo Cientista Subject: [SPAM] [obm-l] =?utf-8?B?c2VndW5kYSBmYXNlIC0gbsOtdmVsIHVuaXZlcnNpdMOhcmlvIDIwMDc=?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Message-ID: <921472.64705.qm@web50606.mail.re2.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lB6JIJ8l001101 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Rodrigo Cientista X-Spam-Status: Yes, hits=7.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 93.38.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 93.38.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- PROBLEMA 2: Dado um inteiro positivo n, mostre que existe um inteiro positivo N com a seguinte propriedade: se A é um subconjunto de {1,2,...,N} com pelo menos N/2 elementos, então existe um inteiro positivo m<= N - n tal que |A interseção com {m+1, m+2,..., m+k}|>=k/2 para todo k = 1, 2, …, n. ************************************************************************************************************************** (gostaria de comentários sobre esta demonstração, falhas, se conhecem alguma demonstração pra esse problema, pois ainda não tem o gabarito) suponha existir x > N - n tal que |A interseção com {x+1, x+2,..., x+k}|>=k/2 como x + n > N, pelo menos um elemento de {x+1, x+2,..., x+k} será maior que qualquer elemento de A; escolhendo-se um n = 1, a afirmação acima é falsa assim, se |A interseção com {m+1, m+2,..., m+k}|>=k/2 ==> existe m <= N - n chamemos S = {m+1, m+2,..., m+k} m + n <= N ==> m + k <= N para todo k = 1, 2, …, n ==> ==> S é subconjunto de {1,2,...,N}, ou é o próprio conjunto {1,2,...,N} na hipótese em que N = n quando N = n é trivial que |A interseção com {m+1, m+2,..., m+k}|>=k/2 (= k/2 na verdade) suponha N > n ==> N/2 > n/2 ==> |{1,2,...,N}| > |S| ==> |A| > |S|/2 = n/2 como S está contido em {1,2,...,N} ==> é sempre possível tomar-se um subconjunto A de {1,2,...,N} tal que S/2 esteja contido em A Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 08:02:58 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7A158l032664 for ; Fri, 7 Dec 2007 08:01:05 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7A14ZS032656 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 08:01:04 -0200 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.168]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7A118l032599 for ; Fri, 7 Dec 2007 08:01:01 -0200 Received: by ug-out-1314.google.com with SMTP id q7so987568uge for ; Fri, 07 Dec 2007 03:02:25 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=7amiLi/y1sRTXiOj/f+g8e924lLQ3l2wpX8RQfmhJeI=; b=A5PfqxcZO65NdPOiw5jtuD6xT2mXDbIV/RRyHO3cD2u/QAagkjYB8ZNW3XTxO0C67hpZqz8WbndEn7OqzBuflCgw7xLuXc945ZVoiDjaopfJJ1ci0NjzqzI9GUyyCVqbZeQZIWqHQBbgO4JCLF5mHpIRofffUBlFbuaQyZaMiW8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=sJgNdM6jAxocr+ly42uswJMn0sjt4TUrERl117ypuX0J+dxo9OKBnnRLBhzm2vJ1jXaTbKLHytG0omRMSkeJVP0zgIx46YVaIFRRYiYt6EDXjFuPt0gRmwUOnVc8FwSAgQyG6KOs3wATD5J3Eox+WD/szDdnf8ommchW6DsIkxg= Received: by 10.67.116.2 with SMTP id t2mr554802ugm.1197025345090; Fri, 07 Dec 2007 03:02:25 -0800 (PST) Received: by 10.66.218.12 with HTTP; Fri, 7 Dec 2007 03:02:24 -0800 (PST) Message-ID: Date: Fri, 7 Dec 2007 09:02:24 -0200 From: jose To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?ahlfors_-_an=E1lise_complexa?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: jose X-Spam-Status: Yes, hits=5.8 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_2621_19280387.1197025345081" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 168.92.249.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 168.92.249.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_2621_19280387.1197025345081 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Caros amigo, Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise complexa= do livro do Ahlfors. N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja estu= dou o cap. 5 e 6 desse livro, ent=E3o pe=E7o que me ajude. Uma das quest=F5es =E9: "prove that in any region A the family of analytic functions with positive real part is normal. Under what added condition is it locally bounded? Hint= : consider the funtin exp(*-f*)." desde j=E1 agrade=E7o J. Gondin ------=_Part_2621_19280387.1197025345081 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Caros amigo,
 
Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise com= plexa do livro do Ahlfors.
N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja= estudou o cap. 5 e 6 desse  livro, ent=E3o  pe=E7o que me a= jude.
 
Uma das quest=F5es =E9:
 
"prove that in any region A  the family of analytic function= s with positive real part is normal. Under what added condition is it local= ly bounded? Hint: consider the funtin exp(-f)."
 
desde j=E1 agrade=E7o
 
J. Gondin
------=_Part_2621_19280387.1197025345081-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 08:53:34 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7AqR8l010315 for ; Fri, 7 Dec 2007 08:52:27 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7AqQZN010313 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 08:52:26 -0200 Received: from web33704.mail.mud.yahoo.com (web33704.mail.mud.yahoo.com [68.142.201.201]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB7AqO8l010309 for ; Fri, 7 Dec 2007 08:52:25 -0200 Received: (qmail 61536 invoked by uid 60001); 7 Dec 2007 11:53:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=GZgQhqXPdb2zGq9YjTlPNBuGBPy1nYI3Hc3FxMd0ox5lSRdsZ9MfK8eb6/QVLi58K8JctiF2yFIUnrGyIbEWFBpd1uCE7BS/RVGc3MTJ/KEEr32lyazBAd+kN4W9IT7GnGm0t7xr8iCcqmzOPlUl+VwyZOvrtIjZxf2M65TYOsI=; X-YMail-OSG: ZIL0Z88VM1lJ8Y4pWgX3T_Um9WdDlt2QJIeIpGzWEkuDomWGDfyS2N_JS_0AFo.RhOWJ.Ue6wPnRe4RIfbrC7jCNeTWF_YHXCN55NwhkUcmQOL0E1mSX_52XHIOsZw-- Received: from [201.68.191.47] by web33704.mail.mud.yahoo.com via HTTP; Fri, 07 Dec 2007 03:53:48 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Fri, 7 Dec 2007 03:53:48 -0800 (PST) From: Eduardo Estrada Subject: [SPAM] Res: [obm-l] boa de combinatoria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <652649.61224.qm@web33704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=8.6 required=5.0 tests=FORGED_YAHOO_RCVD,MIME_EXCESSIVE_QP,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1656022518-1197028428=:61224" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 201.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 201.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1656022518-1197028428=:61224 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Ol=C3=A1, Vit=C3=B3rio,=0A=0AMe parece que a resolu=C3=A7=C3=A3o =C3=A9 a s= eguinte:=0A=0Aa) Fun=C3=A7=C3=B5es crescentes;=0A=0ABasta que, do contradom= =C3=ADnio com m elementos, selecionem-se n. A cada sele=C3=A7=C3=A3o, assoc= ia-se uma =C3=BAnica fun=C3=A7=C3=A3o crescente, e vice-versa. Asim, a resp= osta =C3=A9 Cm,n. Observe que, quando m=0APara: obm-l =0AEnviadas: Quinta-feira, = 6 de Dezembro de 2007 17:01:58=0AAssunto: [obm-l] boa de combinatoria=0A=0A= Caros colegas...=0A=0A =0A=0A =0A=0ASeja In =3D {1,2,...,n}, analogamente I= m, determinar o n=C3=BAmero de fun=C3=A7=C3=B5es f: In --> Im tais que:=0A= =0A =0A=0A =0A=0Aa) f seja crescente=0A=0A =0A=0Ab) f seja n=C3=A3o-decresc= ente=0A=0A =0A=0Adesde j=C3=A1 grato....=0A=0A=0A=0A=0A=0A=0A=0A Abra = sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armaz= enamento!=0Ahttp://br.mail.yahoo.com/ --0-1656022518-1197028428=:61224 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Ol=C3=A1, Vit=C3=B3rio,

Me parece que a resolu= =C3=A7=C3=A3o =C3=A9 a seguinte:

a) Fun=C3=A7=C3=B5es crescentes;
Basta que, do contradom=C3=ADnio com m elementos, selecionem-se n. A c= ada sele=C3=A7=C3=A3o, associa-se uma =C3=BAnica fun=C3=A7=C3=A3o crescente= , e vice-versa. Asim, a resposta =C3=A9 Cm,n. Observe que, quando m<n, o= valor obtido =C3=A9 zero, o que =C3=A9 perfeitamente coerente.

b) F= un=C3=A7=C3=B5es n=C3=A3o decrescentes;

Analogamente, o total de fun= =C3=A7=C3=B5es decrescentes =C3= =A9 Cm,n (de fato, observe que, a cada fun=C3=A7=C3=A3o crescente, associa-= se uma =C3=BAnica fun=C3=A7=C3=A3o decrescente, e vice-versa). Como o total= de fun=C3=A7=C3=B5es (de qualquer tipo) =C3=A9 m^n, temos que o valor proc= urado =C3=A9 m^n - Cm,n.

Espero ter ajudado, um abra=C3=A7o!
Eduardo L. Estrada

----- Mensagem origin= al ----
De: vitoriogauss <vitoriogauss@uol.com.br>
Para: obm-l = <obm-l@mat.puc-rio.br>
Enviadas: Quinta-feira, 6 de Dezembro de 20= 07 17:01:58
Assunto: [obm-l] boa de combinatoria

Caros coleg= as...
=0A
 
=0A
 
=0A
Seja In =3D {1,2= ,...,n}, analogamente Im, determinar o n=C3=BAmero de fun=C3=A7=C3=B5es f: = In --> Im tais que:
=0A
 
=0A
 
=0Aa) f seja crescente
=0A
 
=0A
b) f seja n=C3=A3o-de= crescente
=0A
 
=0A
desde j=C3=A1 grato....
=0A=


=0A=0A=0A
Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamen= to! =0A --0-1656022518-1197028428=:61224-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 09:20:48 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7BJ48l011443 for ; Fri, 7 Dec 2007 09:19:04 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7BJ3ft011441 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 09:19:03 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7BJ18l011438 for ; Fri, 7 Dec 2007 09:19:02 -0200 Received: by wa-out-1112.google.com with SMTP id m28so1541661wag for ; Fri, 07 Dec 2007 04:20:25 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Bi1SohxOd0BrarjYerJCaCX9xHpVRRGoxuX4tDIHG9U=; b=csKL51bxebrW9M3jsg/oNQxv0AJ9/mVJwEjtwcQmfVAhVhGbH+cMoalkCUMhJBt6BgIMiPlM8y/Xk23VDgg+K04xlYvHRLWLqWGLT6fdJcgeJysWJNqp9YcvJ6w7q24o7Mlz+Z5O4ki2gZZplo8sY7Awe++/VM0j0ZeTNq+OQoM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=TU+LskkEb63yxwMDthhQSYZkfpmkHULFobUlsmbHRpkx0G+27wYLgHeTCF8rKlCT9LCY5W3lc+YxrxWRAGF5f15eq6trYmvaNvECYZLgqH2ft0ICjX5D233HqeGNH4mFQkMYrqd9ztRUwLoK/gNbioK5A1Za5tj6GxrE2M8WxPE= Received: by 10.115.49.16 with SMTP id b16mr3462588wak.1197030025679; Fri, 07 Dec 2007 04:20:25 -0800 (PST) Received: by 10.114.168.15 with HTTP; Fri, 7 Dec 2007 04:20:25 -0800 (PST) Message-ID: <2eaf8c650712070420q68e318c4n1c4c820769c0c61a@mail.gmail.com> Date: Fri, 7 Dec 2007 06:20:25 -0600 From: colombo To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_ahlfors_-_an=E1lise_complexa?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_18563_16343047.1197030025625" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: colombo X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_18563_16343047.1197030025625 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline J. Gordon, o que significa dizer que a: parte real =E9 normal? Tem algum= a outra defini=E7=E3o al=E9m do prosaico "normal"? Pois se for somente isto,= n=E3o sei exatamente o que precisa ser verificado. Fico aguardando. Jones On Dec 7, 2007 5:02 AM, jose wrote: > Caros amigo, > > Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise comple= xa > do livro do Ahlfors. > N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja > estudou o cap. 5 e 6 desse livro, ent=E3o pe=E7o que me ajude. > > Uma das quest=F5es =E9: > > "prove that in any region A the family of analytic functions with > positive real part is normal. Under what added condition is it locally > bounded? Hint: consider the funtin exp(*-f*)." > > desde j=E1 agrade=E7o > > J. Gondin > ------=_Part_18563_16343047.1197030025625 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline   J. Gordon, o que significa dizer que a:  parte real =E9 normal?= Tem alguma outra defini=E7=E3o al=E9m do prosaico "normal"? = ; Pois se for somente isto, n=E3o sei exatamente o que precisa ser verifica= do.
Fico aguardando.
Jones
On Dec 7, 2007 5:02 AM, jose <gondintw@gmail.com> wrote:
Caros amigo,
 
Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise com= plexa do livro do Ahlfors.
N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja= estudou o cap. 5 e 6 desse  livro, ent=E3o  pe=E7o que me a= jude.
 
Uma das quest=F5es =E9:
 
"prove that in any region A  the family of analytic function= s with positive real part is normal. Under what added condition is it local= ly bounded? Hint: consider the funtin exp(-f)."
 
desde j=E1 agrade=E7o
 
J. Gondin

------=_Part_18563_16343047.1197030025625-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 10:36:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7CZG8l021313 for ; Fri, 7 Dec 2007 10:35:16 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7CZFam021310 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 10:35:15 -0200 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7CZB8l021247 for ; Fri, 7 Dec 2007 10:35:13 -0200 Received: by wr-out-0506.google.com with SMTP id c8so683666wra for ; Fri, 07 Dec 2007 05:36:36 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=YQKKB6yFhx8N1zZznahcuoj5bKxCk2GofJhK3o1c8OM=; b=C1vtLjH12gxg9VC9Nn/lLsBfyvPJgcspYbrckcAQgBjFNJfxHi9HCSl1lrSdV8uDakcUkEHFb8gE/IHI1nYeSm0lp2mryvLh5XjlSJac6+9hoSFnQjpUlN+JKtnolwO/jZ+qu0MLo/2zLElAURS3sVYKWkOKMDUnonsNqRtlEa0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=gHsIQL77iArciYcV5AwlGAUtFicx1ev+z2S6o1ZcRgAGvflHEIiGKuOeBcn2pmq3tjwm3k9rTfio8CSb6YRj8Kd9Ym2DNkl9cyLGko187p3luPMj1K2JQLdnrmU9yIMZrshyhYac1vJlvd3xgrfVbimb/9vRVlS7aNCT7ik6GWg= Received: by 10.150.156.9 with SMTP id d9mr1568802ybe.1197034595691; Fri, 07 Dec 2007 05:36:35 -0800 (PST) Received: by 10.150.50.8 with HTTP; Fri, 7 Dec 2007 05:36:35 -0800 (PST) Message-ID: <39794f250712070536l77d0e5beobd65eb68853d2f7e@mail.gmail.com> Date: Fri, 7 Dec 2007 11:36:35 -0200 From: "Kleber Bastos" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?an=E1lise_complexa?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Kleber Bastos" X-Spam-Status: Yes, hits=6.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_2665_30983635.1197034595698" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 235.184.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 235.184.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_2665_30983635.1197034595698 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Seja f: U --> C ( complexos ) uma fun=E7=E3o holomorfa, onde U =E9 um dom=EDnio.Suponha que exista um ponto (a) pertencente a U tal que |f(a)|<=3D|f(z)| para todo ponto z pertencente a U. Mostre que , ou bem f(a)=3D0, ou bem f =E9 uma fun=E7=E3o constante. --=20 Kleber B. Bastos ------=_Part_2665_30983635.1197034595698 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Seja f: U --> C ( complexos ) uma fun=E7=E3o holomorfa, onde U =E9 = um dom=EDnio.Suponha que exista um ponto (a) pertencente a U tal que
|f(a)|<=3D|f(z)| para todo ponto z pertencente a U. Mostre que , ou= bem f(a)=3D0, ou bem f =E9 uma fun=E7=E3o constante.

= --
Kleber B. Bastos
------=_Part_2665_30983635.1197034595698-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 11:43:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7Dff8l008495 for ; Fri, 7 Dec 2007 11:41:41 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7DfeQe008487 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 11:41:40 -0200 Received: from nz-out-0506.google.com (nz-out-0506.google.com [64.233.162.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7DfY8l008402 for ; Fri, 7 Dec 2007 11:41:36 -0200 Received: by nz-out-0506.google.com with SMTP id z6so234204nzd for ; Fri, 07 Dec 2007 06:42:59 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=DMXe+0UDa3f8w98+c9Nb+9R/P0Ka4Fq3YR/G96tpB5Y=; b=S5qE0kkLiDM2UPv5hCOAKEKGLYktWfFlMjdehovElNAW8Vv5ctmwiMpXdZPnaNzoHoVuIPxv0ekc2elNORTyG9ipQR119FdMG4PWG0fIbsM/FTI8MH1wN4zBeNxHnPSTO6QoNu1SlV+P15UmwiHWq0b+H8Ssi9FSMK81WnLPgjg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=xg/Q77Yfa9kd6WfBDOBPaiz4g0btF2TOI89QuAftMryG3kfddpMX5qTUT6atdrTHzP++YZrysve/os1Pz1hY69RkwfIesbtj4Klh+5of4YckNIaOfoqh1SU4DaIcDFYnR2uNjZXiSqBFHWZ+xuuMLiGufKrIvkBw9dlLVkNf2r4= Received: by 10.142.142.16 with SMTP id p16mr2154722wfd.1197038578369; Fri, 07 Dec 2007 06:42:58 -0800 (PST) Received: by 10.142.144.16 with HTTP; Fri, 7 Dec 2007 06:42:58 -0800 (PST) Message-ID: Date: Fri, 7 Dec 2007 12:42:58 -0200 From: "Fernando Oliveira" To: obm-l@mat.puc-rio.br Subject: [obm-l] Resultado da OBM MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_11021_20119293.1197038578383" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando Oliveira" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_11021_20119293.1197038578383 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Leitores da lista, Me parece que li em algum lugar uma data para a divulga=E7=E3o dos resultad= os da OBM de 2008. Estou ficando doido ou h=E1 mesmo uma estimativa para a divulga=E7=E3o? --=20 Fernando Oliveira ------=_Part_11021_20119293.1197038578383 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Leitores da lista,

Me parece que li em algum lugar uma data para a d= ivulga=E7=E3o dos resultados da OBM de 2008. Estou ficando doido ou h=E1 me= smo uma estimativa para a divulga=E7=E3o?

--
Ferna= ndo Oliveira ------=_Part_11021_20119293.1197038578383-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 14:18:11 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7GGX8l021908 for ; Fri, 7 Dec 2007 14:16:33 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7GGXuf021906 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 14:16:33 -0200 Received: from relay3.uol.com.br (relay3.uol.com.br [200.221.4.110]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7GGV8l021902 for ; Fri, 7 Dec 2007 14:16:31 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper3.uol.com.br (Postfix) with ESMTP id B1630B001A7B for ; Fri, 7 Dec 2007 15:17:56 -0200 (BRST) Received: from uol.com.br (whisky3.mail.sys.intranet [172.26.5.87]) by sniper3.uol.com.br (Postfix) with ESMTP id 7E089B001996 for ; Fri, 7 Dec 2007 15:17:56 -0200 (BRST) Date: Fri, 7 Dec 2007 14:17:56 -0300 Message-Id: Subject: Re:Res: [obm-l] boa de combinatoria MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197047876.2A.403595.42.27190.52.42.007.2028710894" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.70.135.138 X-SIG5: 197cf941851187bcdf9b2e7827c3863e Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,SUPERLONG_LINE,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197047876.2A.403595.42.27190.52.42.007.2028710894 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable T=E3o simples asimm !!!!! Eu pensei nisso... mas n=E3o acreditei... Obrigado Ol=E1, Vit=F3rio, > > Me parece que a resolu=E7=E3o =E9 a seguinte: > > a) Fun=E7=F5es crescentes; > > Basta que, do contradom=EDnio com m elementos, selecionem-se n. A cada = sele=E7=E3o, associa-se uma =FAnica fun=E7=E3o crescente, e vice-versa. A= sim, a resposta =E9 Cm,n. Observe que, quando m > > b) Fun=E7=F5es n=E3o decrescentes; > > Analogamente, o total de fun=E7=F5es decrescentes =E9 Cm,n (de fato, ob= serve que, a cada fun=E7=E3o crescente, associa-se uma =FAnica fun=E7=E3o= decrescente, e vice-versa). Como o total de fun=E7=F5es (de qualquer tip= o) =E9 m^n, temos que o valor procurado =E9 m^n - Cm,n. > > Espero ter ajudado, um abra=E7o! > Eduardo L. Estrada > > ----- Mensagem original ---- > De: vitoriogauss > Para: obm-l > Enviadas: Quinta-feira, 6 de Dezembro de 2007 17:01:58 > Assunto: [obm-l] boa de combinatoria > > Caros colegas... > > > > > > Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero de fun=E7= =F5es f: In --> Im tais que: > > > > > > a) f seja crescente > > > > b) f seja n=E3o-decrescente > > > > desde j=E1 grato.... > > > > > > > > Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para ar= mazenamento! > http://br.mail.yahoo.com/ Vit=F3rio Gauss --_=__=_XaM3_.1197047876.2A.403595.42.27190.52.42.007.2028710894 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
T=E3o simples asimm !!!!!
 
Eu pensei nisso... mas n=E3o acreditei...
 
Obrigado
 
 
 
 
 Ol=E1, Vit=F3rio,
>
> Me parece que a resolu=E7=E3o =E9 a seguinte:
>
> a) Fun=E7=F5es crescentes;
>
> Basta que, do contradom=EDnio com m elementos, selecionem-se n.= A cada sele=E7=E3o, associa-se uma =FAnica fun=E7=E3o crescente, e vice-= versa. Asim, a resposta =E9 Cm,n. Observe que, quando m
>
> b) Fun=E7=F5es n=E3o decrescentes;
>
> Analogamente, o total de fun=E7=F5es decrescentes =E9 Cm,n (de = fato, observe que, a cada fun=E7=E3o crescente, associa-se uma =FAnica fu= n=E7=E3o decrescente, e vice-versa). Como o total de fun=E7=F5es (de qual= quer tipo) =E9 m^n, temos que o valor procurado =E9 m^n - Cm,n.
>
> Espero ter ajudado, um abra=E7o!
> Eduardo L. Estrada
>
> ----- Mensagem original ----
> De: vitoriogauss
> Para: obm-l
> Enviadas: Quinta-feira, 6 de Dezembro de 2007 17:01:58
> Assunto: [obm-l] boa de combinatoria
>
> Caros colegas...
>
>
>
>
>
> Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero= de fun=E7=F5es f: In --> Im tais que:
>
>
>
>
>
> a) f seja crescente
>
>
>
> b) f seja n=E3o-decrescente
>
>
>
> desde j=E1 grato....
>
>
>
>
>
>
>
> Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o= para armazenamento!
> http://br.mail.yahoo.com/
Vit=F3rio Gauss
--_=__=_XaM3_.1197047876.2A.403595.42.27190.52.42.007.2028710894-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 16:02:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7Hxk8l010625 for ; Fri, 7 Dec 2007 15:59:46 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7HxkmV010620 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 15:59:46 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.242]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7Hxg8l010560 for ; Fri, 7 Dec 2007 15:59:42 -0200 Received: by an-out-0708.google.com with SMTP id c31so174465ana for ; Fri, 07 Dec 2007 11:01:06 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=kG0l0Sb17InMZDne8uP0FuYv67ROFTTFSR1FGEex99M=; b=CRgl7LB+7zHRXFaxA6lPWiJJBcCK8A7ANSWYAphBQ7dhknUySUxMJ0rXQyoJc9u4JiGHQ9YHB9UjqVlLUveobOvBlPZqqD0Io8WiqTPgv6oKwz1F9TJSH3TPY1cw9u/1RjbL9Go4DVl6+CGGcugU1WZAiYEz18cVc8qp7+HQX3U= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=xFzAb//jyYD1tH5h7UM6f2YRlujq6KZDo8e5ThIGzOnV2/+2vioPlH9EoJDo+ZFKgRDzVy4QOyIjV3dchKmbiWgfJhZGmyhqfSfv/eU66A99gzWZtGuWwKSzQyrIvW1/4QjA37kZXQ/rLoSqq5ouLrNs4V3hOx2LxxbyfUJux9Q= Received: by 10.100.252.16 with SMTP id z16mr9852356anh.1197054066882; Fri, 07 Dec 2007 11:01:06 -0800 (PST) Received: by 10.90.49.13 with HTTP; Fri, 7 Dec 2007 11:01:06 -0800 (PST) Message-ID: <2d483c770712071101j71c719bbvd6817641cc0f4b2f@mail.gmail.com> Date: Fri, 7 Dec 2007 17:01:06 -0200 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] boa de combinatoria In-Reply-To: <652649.61224.qm@web33704.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_11586_32236275.1197054066866" References: <652649.61224.qm@web33704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=3.0 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_11586_32236275.1197054066866 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hmmm... infelizmente, uma fun=E7=E3o "n=E3o-decrescente" n=E3o =E9 o mesmo = que "uma fun=E7=E3o que n=E3o =E9 decrescente" -- =E9, eu concordo que =E9 uma p=E9s= sima p=E9ssima p=E9ssima denomina=E7=E3o, mas foi assim que os matem=E1ticos convencionara= m... Uma fun=E7=E3o decrescente =E9 uma que satisfaz f(x)>f(y) sempre que x wrote: > Ol=E1, Vit=F3rio, > > Me parece que a resolu=E7=E3o =E9 a seguinte: > > a) Fun=E7=F5es crescentes; > > Basta que, do contradom=EDnio com m elementos, selecionem-se n. A cada > sele=E7=E3o, associa-se uma =FAnica fun=E7=E3o crescente, e vice-versa. A= sim, a > resposta =E9 Cm,n. Observe que, quando m perfeitamente coerente. > > b) Fun=E7=F5es n=E3o decrescentes; > > Analogamente, o total de fun=E7=F5es decrescentes =E9 Cm,n (de fato, obse= rve > que, a cada fun=E7=E3o crescente, associa-se uma =FAnica fun=E7=E3o decre= scente, e > vice-versa). Como o total de fun=E7=F5es (de qualquer tipo) =E9 m^n, temo= s que o > valor procurado =E9 m^n - Cm,n. > > Espero ter ajudado, um abra=E7o! > Eduardo L. Estrada > > ----- Mensagem original ---- > De: vitoriogauss > Para: obm-l > Enviadas: Quinta-feira, 6 de Dezembro de 2007 17:01:58 > Assunto: [obm-l] boa de combinatoria > > Caros colegas... > > > Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero de fun=E7= =F5es f: > In --> Im tais que: > > > a) f seja crescente > > b) f seja n=E3o-decrescente > > desde j=E1 grato.... > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_11586_32236275.1197054066866 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Hmmm... infelizmente, uma fun=E7=E3o "n=E3o-decrescente" n= =E3o =E9 o mesmo que "uma fun=E7=E3o que n=E3o =E9 decrescente&qu= ot; -- =E9, eu concordo que =E9 uma p=E9ssima p=E9ssima p=E9ssima denomina= =E7=E3o, mas foi assim que os matem=E1ticos convencionaram...=20
 
Uma fun=E7=E3o decrescente =E9 uma que satisfaz f(x)>f(y) sempre qu= e x<y.
Uma fun=E7=E3o n=E3o-decrescente =E9 uma que satisfaz f(x)<=3Df(y) = sempre que x<y.
 
Por exemplo, se f(1)=3D3, f(2)=3D1 e f(3)=3D2 ent=E3o a fun=E7=E3o n= =E3o =E9 decrescente (pois cresce de f(2) para f(3)) nem "n=E3o-d= ecrescente" (pois decresce de f(1)=3D3 para f(2)=3D1). Denomina= =E7=E3o horr=EDvel, n=E9?
 
Solu=E7=E3o de (b): imagine bolinhas numeradas de 1 a m. Vamos colocar= , entre as bolinhas, barras indicando onde est=E1 cada um dos valores f(1),= f(2), ..., f(n). Por exemplo, se for n=3D3 e m=3D9 e escolhermos a fun=E7= =E3o f(1)=3D2, f(2)=3D5 e f(3)=3D5, temos o seguinte diagrama:
 
oo|ooo||oooo
 
A primeira barra diz que f(1)=3D2 (bolinhas =E0 esquerda dela); a segu= nda indica f(2)=3D5; a terceira indica f(3)=3D5 tamb=E9m.
 
Afirmamos que definir uma fun=E7=E3o n=E3o-decrescente =E9 equivalente= a escrever uma sucess=E3o de bolinhas e barras como acima -- dada uma fun= =E7=E3o existe uma =FAnica maneira de escrev=EA-la com bolas e barras, e da= da uma seq=FC=EAncia de n+m bolas e barras com m bolas e n barras existe um= a =FAnica fun=E7=E3o. Bom, para ser exato n=E3o vale come=E7ar com uma= barra (pois n=E3o vale f(1)=3D0), mas fora isso vale tudo. Vale at=E9= terminar com uma barra (seria f(n)=3Dm) ou v=E1rias (f(n)=3Df(n-1)=3D...= =3Dm). Uma fun=E7=E3o constante, por exemplo, teria todas as barras juntas = entre duas bolinhas.
 
Ent=E3o a pergunta =E9: quantas seq=FC=EAncias de (m-1) bolas e n barr= as existem (descartei a primeira bola que n=E3o pode ser mexida)? Ora,= s=E3o m+n-1 posi=E7=F5es, das quais tenho de escolher n posi=E7=F5es = para colocar n barras (os outros lugares ter=E3o de conter as bolas), ent= =E3o a resposta =E9 C(m+n-1,n).
 
Abra=E7o,
       Ralph
 
P.S.: n=E3o =E9 coinci=EAncia que este racioc=EDnio se parece com= a contagem do n=FAmero de solu=E7=F5es inteiras n=E3o-negativas de x1= +x2+...+xn+x(n+1)=3Dm -- basta identificar x1=3Df(1), x(i)=3Df(i)-f(i-1) pa= ra i=3D2,3,...,n e finalmente x(n+1)=3Dm-f(n). Cada solu=E7=E3o (x1,x2,...,= x(n+1)) corresponde a uma =FAnica f, e vice-versa.
 
On Dec 7, 2007 9:53 AM, Eduardo Estrada <eestradaitu@yahoo.com.br> wr= ote:
Ol=E1, Vit=F3rio,

Me parece que a resolu=E7=E3o =E9 a seguint= e:

a) Fun=E7=F5es crescentes;

Basta que, do contradom=EDnio c= om m elementos, selecionem-se n. A cada sele=E7=E3o, associa-se uma =FAnica= fun=E7=E3o crescente, e vice-versa. Asim, a resposta =E9 Cm,n. Observe que= , quando m<n, o valor obtido =E9 zero, o que =E9 perfeitamente coerente.

b) Fun=E7=F5es n=E3o decrescentes;

Analogamente, o total de = fun=E7=F5es decrescentes =E9 Cm,n= (de fato, observe que, a cada fun=E7=E3o crescente, associa-se uma =FAnica= fun=E7=E3o decrescente, e vice-versa). Como o total de fun=E7=F5es (de qua= lquer tipo) =E9 m^n, temos que o valor procurado =E9 m^n - Cm,n.

Espero ter ajudado, um abra=E7o!
Eduardo L. Estrada

----- Mensagem original ----
De: vitoriogauss <vitoriogauss@uol.com.br&g= t;
Para: obm-l <obm-l@mat.puc-rio.br>
Enviadas: Quinta-feira, 6 de Dezembro de= 2007 17:01:58
Assunto: [obm-l] boa de combinatoria

Caros colegas...
 
 
Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=FAmero de fun= =E7=F5es f: In --> Im tais que:
 
 
a) f seja crescente
 
b) f seja n=E3o-decrescente
 
desde j=E1 grato....


Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!

------=_Part_11586_32236275.1197054066866-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 7 21:00:51 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7Mx98l002640 for ; Fri, 7 Dec 2007 20:59:09 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB7Mx9KG002637 for obm-l-MllGbsmmN; Fri, 7 Dec 2007 20:59:09 -0200 Received: from bay0-omc1-s6.bay0.hotmail.com (bay0-omc1-s6.bay0.hotmail.com [65.54.246.78]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB7Mx68l002580 for ; Fri, 7 Dec 2007 20:59:06 -0200 Received: from hotmail.com ([65.54.161.40]) by bay0-omc1-s6.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Fri, 7 Dec 2007 16:00:30 -0800 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Fri, 7 Dec 2007 16:00:30 -0800 Message-ID: Received: from 65.54.161.200 by by106fd.bay106.hotmail.msn.com with HTTP; Sat, 08 Dec 2007 00:00:27 GMT X-Originating-IP: [144.226.230.36] X-Originating-Email: [leandrorecova@msn.com] X-Sender: leandrorecova@msn.com In-Reply-To: <39794f250712070536l77d0e5beobd65eb68853d2f7e@mail.gmail.com> From: "LEANDRO L RECOVA" To: obm-l@mat.puc-rio.br Subject: RE: [obm-l] análise complexa Date: Fri, 07 Dec 2007 16:00:27 -0800 Mime-Version: 1.0 Content-Type: text/plain; format=flowed X-OriginalArrivalTime: 08 Dec 2007 00:00:30.0517 (UTC) FILETIME=[58BD4650:01C8392D] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "LEANDRO L RECOVA" X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,MSG_ID_ADDED_BY_MTA_2, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Voce tentou usar o principio do Maximo? Leandro. >From: "Kleber Bastos" >Reply-To: obm-l@mat.puc-rio.br >To: obm-l@mat.puc-rio.br >Subject: [obm-l] análise complexa >Date: Fri, 7 Dec 2007 11:36:35 -0200 > >Seja f: U --> C ( complexos ) uma função holomorfa, onde U é um >domínio.Suponha que exista um ponto (a) pertencente a U tal que >|f(a)|<=|f(z)| para todo ponto z pertencente a U. Mostre que , ou bem >f(a)=0, ou bem f é uma função constante. > >-- >Kleber B. Bastos ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 8 15:28:53 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB8HQr8l021874 for ; Sat, 8 Dec 2007 15:26:53 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB8HQq0i021872 for obm-l-MllGbsmmN; Sat, 8 Dec 2007 15:26:52 -0200 Received: from web33715.mail.mud.yahoo.com (web33715.mail.mud.yahoo.com [68.142.201.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB8HQn8l021869 for ; Sat, 8 Dec 2007 15:26:50 -0200 Received: (qmail 36665 invoked by uid 60001); 8 Dec 2007 18:28:14 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=SFo797HBAYcrI9zR/wtDP2KTISeFQSNa9ehCdHPqfDLh61QB146HJ/Z4UA5ewPJ0Udre08kiQJDux6AHoxYVhzPP9c5O19sY8/8GWotc3fA7LVwS4tJP23TOFNl25502Kmg01/TMuPvSPEvk7fzpFBUM84m1KAsCoFRoEpPzlH8=; X-YMail-OSG: Vhkg_zMVM1m72xpUeNl3.VYa.LQhCbaanXJMCOxgq1m4_kIc8BcHgxmRIlSs_0S93VXo.2a2zfjKBDORQuTsHwpjXp3xcXT79ejZJqGFcZQpmEqmXUE- Received: from [201.68.127.127] by web33715.mail.mud.yahoo.com via HTTP; Sat, 08 Dec 2007 10:28:14 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Sat, 8 Dec 2007 10:28:14 -0800 (PST) From: Eduardo Estrada Subject: [SPAM] Res: [obm-l] boa de combinatoria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <851766.31124.qm@web33715.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=7.9 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,FORGED_YAHOO_RCVD,MAILTO_LINK, MIME_EXCESSIVE_QP,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2049830293-1197138494=:31124" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: EMAIL_ATTRIBUTION (-1.6 points) BODY: Contains what looks like an email attribution SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 212.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 212.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2049830293-1197138494=:31124 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Ok, Ralph,=0A=0ARespondi dizendo que atentei para minha distra=C3=A7=C3=A3o= logo que enviei a resposta anterior. Mas n=C3=A3o conhecia essa solu=C3=A7= =C3=A3o que voc=C3=AA apresentou. De fato, muito interessante.=0A=0AUm abra= =C3=A7o,=0AEduardo=0A=0A----- Mensagem original ----=0ADe: Ralph Teixeira <= ralphct@gmail.com>=0APara: obm-l@mat.puc-rio.br=0AEnviadas: Sexta-feira, 7 = de Dezembro de 2007 17:01:06=0AAssunto: Re: [obm-l] boa de combinatoria=0A= =0AHmmm... infelizmente, uma fun=C3=A7=C3=A3o "n=C3=A3o-decrescente" n=C3= =A3o =C3=A9 o mesmo que "uma fun=C3=A7=C3=A3o que n=C3=A3o =C3=A9 decrescen= te" -- =C3=A9, eu concordo que =C3=A9 uma p=C3=A9ssima p=C3=A9ssima p=C3=A9= ssima denomina=C3=A7=C3=A3o, mas foi assim que os matem=C3=A1ticos convenci= onaram... =0A=0A=0A =0A=0AUma fun=C3=A7=C3=A3o decrescente =C3=A9 uma que s= atisfaz f(x)>f(y) sempre que x wrote:=0A=0A=0A=0A=0AOl=C3=A1, Vit= =C3=B3rio,=0A=0AMe parece que a resolu=C3=A7=C3=A3o =C3=A9 a seguinte:=0A= =0Aa) Fun=C3=A7=C3=B5es crescentes;=0A=0ABasta que, do contradom=C3=ADnio c= om m elementos, selecionem-se n. A cada sele=C3=A7=C3=A3o, associa-se uma = =C3=BAnica fun=C3=A7=C3=A3o crescente, e vice-versa. Asim, a resposta =C3= =A9 Cm,n. Observe que, quando m=0A=0APara: obm-l =0AEnviadas: Quinta-= feira, 6 de Dezembro de 2007 17:01:58=0AAssunto: [obm-l] boa de combinatori= a=0A=0A=0ACaros colegas...=0A=0A =0A=0A =0A=0ASeja In =3D {1,2,...,n}, anal= ogamente Im, determinar o n=C3=BAmero de fun=C3=A7=C3=B5es f: In --> Im tai= s que:=0A=0A =0A=0A =0A=0Aa) f seja crescente=0A=0A =0A=0Ab) f seja n=C3=A3= o-decrescente=0A=0A =0A=0Adesde j=C3=A1 grato....=0A=0A=0A=0A=0A=0A=0A=0A= =0A=0A=0A=0A=0AAbra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de es= pa=C3=A7o para armazenamento! =0A=0A=0A=0A=0A=0A=0A=0A=0A=0A=0A Abra s= ua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armaze= namento!=0Ahttp://br.mail.yahoo.com/ --0-2049830293-1197138494=:31124 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Ok, Ralph,

Respondi dizendo que atentei para mi= nha distra=C3=A7=C3=A3o logo que enviei a resposta anterior. Mas n=C3=A3o c= onhecia essa solu=C3=A7=C3=A3o que voc=C3=AA apresentou. De fato, muito int= eressante.

Um abra=C3=A7o,
Eduardo

----- Mensagem = original ----
De: Ralph Teixeira <ralphct@gmail.com>
Para: obm-= l@mat.puc-rio.br
Enviadas: Sexta-feira, 7 de Dezembro de 2007 17:01:06Assunto: Re: [obm-l] boa de combinatoria

Hmmm... infelizmente= , uma fun=C3=A7=C3=A3o "n=C3=A3o-decrescente" n=C3=A3o =C3=A9 o mesmo = que "uma fun=C3=A7=C3=A3o que n=C3=A3o =C3=A9 decrescente" -- =C3=A9, eu co= ncordo que =C3=A9 uma p=C3=A9ssima p=C3=A9ssima p=C3=A9ssima denomina=C3=A7= =C3=A3o, mas foi assim que os matem=C3=A1ticos convencionaram... =0A
=0A
 =0A
Uma fun=C3=A7=C3=A3o decrescente =C3=A9 uma que satisfaz f(x)>= ;f(y) sempre que x<y.
=0A
Uma fun=C3=A7=C3=A3o n=C3=A3o-decresc= ente =C3=A9 uma que satisfaz f(x)<=3Df(y) sempre que x<y.
=0A 
=0A
Por exemplo, se f(1)=3D3, f(2)=3D1 e f(3)=3D2 ent=C3= =A3o a fun=C3=A7=C3=A3o n=C3=A3o =C3=A9 decrescente (pois cresce de f(2) pa= ra f(3)) nem "n=C3=A3o-decrescente" (pois decresce de f(1)=3D3 pa= ra f(2)=3D1). Denomina=C3=A7=C3=A3o horr=C3=ADvel, n=C3=A9?
=0A
&n= bsp;
=0A
Solu=C3=A7=C3=A3o de (b): imagine bolinhas numeradas de 1= a m. Vamos colocar, entre as bolinhas, barras indicando onde est=C3=A1 cad= a um dos valores f(1), f(2), ..., f(n). Por exemplo, se for n=3D3 e m=3D9 e= escolhermos a fun=C3=A7=C3=A3o f(1)=3D2, f(2)=3D5 e f(3)=3D5, temos o segu= inte diagrama:=0A
=0A
 
=0A
oo|ooo||oooo
=0A 
=0A
A primeira barra diz que f(1)=3D2 (bolinhas =C3=A0 es= querda dela); a segunda indica f(2)=3D5; a terceira indica f(3)=3D5 tamb=C3= =A9m.
=0A
 
=0A
Afirmamos que definir uma fun=C3=A7= =C3=A3o n=C3=A3o-decrescente =C3=A9 equivalente a escrever uma sucess=C3=A3= o de bolinhas e barras como acima -- dada uma fun=C3=A7=C3=A3o existe uma = =C3=BAnica maneira de escrev=C3=AA-la com bolas e barras, e dada uma seq=C3= =BC=C3=AAncia de n+m bolas e barras com m bolas e n barras existe uma =C3= =BAnica fun=C3=A7=C3=A3o. Bom, para ser exato n=C3=A3o vale come=C3=A7= ar com uma barra (pois n=C3=A3o vale f(1)=3D0), mas fora isso vale tudo.&nb= sp;Vale at=C3=A9 terminar com uma barra (seria f(n)=3Dm) ou v=C3=A1rias (f(= n)=3Df(n-1)=3D...=3Dm). Uma fun=C3=A7=C3=A3o constante, por exemplo, teria = todas as barras juntas entre duas bolinhas.=0A
=0A
 
=0A=
Ent=C3=A3o a pergunta =C3=A9: quantas seq=C3=BC=C3=AAncias de (m-1) bo= las e n barras existem (descartei a primeira bola que n=C3=A3o pode se= r mexida)? Ora, s=C3=A3o m+n-1 posi=C3=A7=C3=B5es, das quais tenho de escol= her n posi=C3=A7=C3=B5es para colocar n barras (os outros lugares ter= =C3=A3o de conter as bolas), ent=C3=A3o a resposta =C3=A9 C(m+n-1,n).=0A=0A
 
=0A
Abra=C3=A7o,
=0A
   =     Ralph
=0A
 
=0A
P.S.: n=C3=A3o = =C3=A9 coinci=C3=AAncia que este racioc=C3=ADnio se parece com a conta= gem do n=C3=BAmero de solu=C3=A7=C3=B5es inteiras n=C3=A3o-negativas de&nbs= p;x1+x2+...+xn+x(n+1)=3Dm -- basta identificar x1=3Df(1), x(i)=3Df(i)-f(i-1= ) para i=3D2,3,...,n e finalmente x(n+1)=3Dm-f(n). Cada solu=C3=A7=C3=A3o (= x1,x2,...,x(n+1)) corresponde a uma =C3=BAnica f, e vice-versa.=0A
=0A=
 
=0A
On Dec 7, 2007 9:53 AM, Edua= rdo Estrada <eestradaitu= @yahoo.com.br> wrote:
=0A
=0A
=0A
=0A
Ol=C3=A1, Vit=C3=B3rio,
Me parece que a resolu=C3=A7=C3=A3o =C3=A9 a seguinte:

a) Fun= =C3=A7=C3=B5es crescentes;

Basta que, do contradom=C3=ADnio com m el= ementos, selecionem-se n. A cada sele=C3=A7=C3=A3o, associa-se uma =C3=BAni= ca fun=C3=A7=C3=A3o crescente, e vice-versa. Asim, a resposta =C3=A9 Cm,n. = Observe que, quando m<n, o valor obtido =C3=A9 zero, o que =C3=A9 perfei= tamente coerente.=0A

b) Fun=C3=A7=C3=B5es n=C3=A3o decrescentes;
=
Analogamente, o total de fun=C3=A7=C3=B5es decrescentes =C3=A9 Cm,n (de fato, observe que, a cada fun= =C3=A7=C3=A3o crescente, associa-se uma =C3=BAnica fun=C3=A7=C3=A3o decresc= ente, e vice-versa). Como o total de fun=C3=A7=C3=B5es (de qualquer tipo) = =C3=A9 m^n, temos que o valor procurado =C3=A9 m^n - Cm,n.=0A

Espero= ter ajudado, um abra=C3=A7o!
Eduardo L. Estrada

=0A
-----= Mensagem original ----
De: vitoriogauss <vitoriogauss@uol.com.br>=0A
Para: obm-l <obm-l@mat.puc-rio.br>
Envia= das: Quinta-feira, 6 de Dezembro de 2007 17:01:58
Assunto: [obm-l] boa d= e combinatoria

=0A
Caros colegas...
=0A
 
=0A=
 
=0A
Seja In =3D {1,2,...,n}, analogamente Im, determin= ar o n=C3=BAmero de fun=C3=A7=C3=B5es f: In --> Im tais que:
=0A 
=0A
 
=0A
a) f seja crescente
=0A
=  
=0A
b) f seja n=C3=A3o-decrescente
=0A
 =0A
desde j=C3=A1 grato....
=0A
= =0A

=0A
=0A
=0AAbra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazena= mento!

=0A


=0A= =0A=0A
Abra sua conta no Yahoo! Mail, o =C3=BAn= ico sem limite de espa=C3=A7o para armazenamento! =0A --0-2049830293-1197138494=:31124-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 8 15:28:53 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB8HRp8l021891 for ; Sat, 8 Dec 2007 15:27:51 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB8HRpPC021889 for obm-l-MllGbsmmN; Sat, 8 Dec 2007 15:27:51 -0200 Received: from web33707.mail.mud.yahoo.com (web33707.mail.mud.yahoo.com [68.142.201.204]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB8HRm8l021886 for ; Sat, 8 Dec 2007 15:27:49 -0200 Received: (qmail 11439 invoked by uid 60001); 8 Dec 2007 18:22:31 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=NxPEhbz04irYJDZJ00C16yXy+fpuqlVjoMSbJcml14jkAU27h6lr8vi/HdKAqj6KV4sKSvBoOOUT0kIjFAlAvPSTXEbM25hI6dDChWi0gwb5vG8VDNZw+BM+JvMO9IMHWwQwa9U/WVDAD11PPo5QcCQydTxVwqMCCKQNJJB4xHo=; X-YMail-OSG: PiernY0VM1msRIy5WFQ0HM_e8VrtqsQKY0ozHLaKOm3P_50GV5reK8P8Vuq7cRW69NVlyJmc9gf9nqTAsGl9euHrUR63VegFufy2Ndl3EMQ.CFmrVGmKfyCTRVwdag-- Received: from [201.68.127.127] by web33707.mail.mud.yahoo.com via HTTP; Sat, 08 Dec 2007 10:22:31 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Sat, 8 Dec 2007 10:22:31 -0800 (PST) From: Eduardo Estrada Subject: [SPAM] Res: Res: [obm-l] boa de combinatoria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <315639.9845.qm@web33707.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=8.2 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_EXCESSIVE_QP,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-436907697-1197138151=:9845" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 204.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 204.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-436907697-1197138151=:9845 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Ol=C3=A1, Vit=C3=B3rio,=0A=0ASinto dizer, mas foi s=C3=B3 clicar em enviar,= ontem, que percebi que minha resposta estava errada! Para o n=C3=BAmero de= fun=C3=A7=C3=B5es crescentes e decrescentes, de fato o resultado =C3=A9 Cm= ,n. Mas para a contagem de fun=C3=A7=C3=B5es n=C3=A3o decrescentes, o resul= tado que exibi n=C3=A3o est=C3=A1 correto. De fato, isso ocorre porque uma = fun=C3=A7=C3=A3o n=C3=A3o decrescente n=C3=A3o =C3=A9 uma fun=C3=A7=C3=A3o = que n=C3=A3o =C3=A9 decrescente. Na verdade, uma fun=C3=A7=C3=A3o =C3=A9 di= ta n=C3=A3o decrescente se, de um termo para outro (maior), obtemos uma ima= gem igual ou maior. Ainda n=C3=A3o consegui pensar numa solu=C3=A7=C3=A3o, = mas consegui pensar numa rela=C3=A7=C3=A3o com contagem de seq=C3=BC=C3=AAn= cias:=0A=0ASeja f : {1,2,3,...,n} -> {1,2,3,...,m}. Contar o n=C3=BAmero de= fun=C3=A7=C3=B5es n=C3=A3o decrescentes f equivale a contar o n=C3=BAmero = de n-seq=C3=BC=C3=AAncias (seq=C3=BC=C3=AAncias de n d=C3=ADgitos) formadas= por algarismos compreendidos entre 1 e m, tais que o algarismo de uma dada= posi=C3=A7=C3=A3o da seq=C3=BC=C3=AAncia =C3=A9 sempre maior do que ou igu= al aos algarismos das posi=C3=A7=C3=B5es precedentes. Por exemplo, se m=3D2= e n=3D3, podemos pensar na seq=C3=BC=C3=AAncia 122, que leva 1 em 1, 2 em = 2 e 3 em 2. Al=C3=A9m desta, temos: 111, 112 e 222, ou seja, 4 fun=C3=A7=C3= =B5es, nesse caso. E isso n=C3=A3o bate com a f=C3=B3rmula exibida.=0A=0AAb= ra=C3=A7o,=0AEduardo=0A=0A----- Mensagem original ----=0ADe: vitoriogauss <= vitoriogauss@uol.com.br>=0APara: obm-l =0AEnviadas: S= exta-feira, 7 de Dezembro de 2007 15:17:56=0AAssunto: Re:Res: [obm-l] boa d= e combinatoria=0A=0A=0AT=C3=A3o simples asimm !!!!!=0A=0A =0A=0AEu pensei n= isso... mas n=C3=A3o acreditei...=0A=0A =0A=0AObrigado=0A=0A =0A=0A =0A=0A = =0A=0A =0A=0A Ol=C3=A1, Vit=C3=B3rio, =0A=0A> =0A=0A> Me parece que a resol= u=C3=A7=C3=A3o =C3=A9 a seguinte: =0A=0A> =0A=0A> a) Fun=C3=A7=C3=B5es cres= centes; =0A=0A> =0A=0A> Basta que, do contradom=C3=ADnio com m elementos, s= elecionem-se n. A cada sele=C3=A7=C3=A3o, associa-se uma =C3=BAnica fun=C3= =A7=C3=A3o crescente, e vice-versa. Asim, a resposta =C3=A9 Cm,n. Observe q= ue, quando m =0A> =0A=0A> b) Fun=C3=A7=C3=B5es n=C3=A3o decrescentes; =0A= =0A> =0A=0A> Analogamente, o total de fun=C3=A7=C3=B5es decrescentes =C3=A9= Cm,n (de fato, observe que, a cada fun=C3=A7=C3=A3o crescente, associa-se = uma =C3=BAnica fun=C3=A7=C3=A3o decrescente, e vice-versa). Como o total de= fun=C3=A7=C3=B5es (de qualquer tipo) =C3=A9 m^n, temos que o valor procura= do =C3=A9 m^n - Cm,n. =0A=0A> =0A=0A> Espero ter ajudado, um abra=C3=A7o! = =0A=0A> Eduardo L. Estrada =0A=0A> =0A=0A> ----- Mensagem original ---- =0A= =0A> De: vitoriogauss =0A =0A> Para: obm-l =0A =0A> Enviadas: Quinta-feira,= 6 de Dezembro de 2007 17:01:58 =0A=0A> Assunto: [obm-l] boa de combinatori= a =0A=0A> =0A=0A> Caros colegas... =0A=0A> =0A=0A> =0A=0A> =0A=0A> =0A=0A> = =0A=0A> Seja In =3D {1,2,...,n}, analogamente Im, determinar o n=C3=BAmero = de fun=C3=A7=C3=B5es f: In --> Im tais que: =0A=0A> =0A=0A> =0A=0A> =0A=0A>= =0A=0A> =0A=0A> a) f seja crescente =0A=0A> =0A=0A> =0A=0A> =0A=0A> b) f s= eja n=C3=A3o-decrescente =0A=0A> =0A=0A> =0A=0A> =0A=0A> desde j=C3=A1 grat= o.... =0A=0A> =0A=0A> =0A=0A> =0A=0A> =0A=0A> =0A=0A> =0A=0A> =0A=0A> Abra = sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armaz= enamento! =0A=0A> http://br.mail.yahoo.com/ =0A=0A=0A=0AVit=C3=B3rio Gauss= =0A=0A=0A=0A=0A=0A=0A=0A=0A=0A Abra sua conta no Yahoo! Mail, o =C3=BA= nico sem limite de espa=C3=A7o para armazenamento!=0Ahttp://br.mail.yahoo.c= om/ --0-436907697-1197138151=:9845 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Ol=C3=A1, Vit=C3=B3rio,

Sinto dizer, mas foi s= =C3=B3 clicar em enviar, ontem, que percebi que minha resposta estava errad= a! Para o n=C3=BAmero de fun=C3=A7=C3=B5es crescentes e decrescentes, de fa= to o resultado =C3=A9 Cm,n. Mas para a contagem de fun=C3=A7=C3=B5es n=C3= =A3o decrescentes, o resultado que exibi n=C3=A3o est=C3=A1 correto. De fat= o, isso ocorre porque uma fun=C3=A7=C3= =A3o n=C3=A3o decrescente n=C3=A3o =C3=A9 uma= fun=C3=A7=C3=A3o que n=C3=A3o =C3=A9 decrescente. Na verdade, uma fun=C3= =A7=C3=A3o =C3=A9 dita n=C3=A3o decrescente se, de um termo para outro (mai= or), obtemos uma imagem igual ou maior. Ainda n=C3=A3o consegui pens= ar numa solu=C3=A7=C3=A3o, mas consegui pensar numa rela=C3=A7=C3=A3o com contagem de seq=C3=BC=C3=AAncias:

Seja f= : {1,2,3,...,n} -> {1,2,3,...,m}. Contar o n=C3=BAmero de fun=C3=A7=C3= =B5es n=C3=A3o decrescentes f equivale a contar o n=C3=BAmero de n-seq=C3= =BC=C3=AAncias (seq=C3=BC=C3=AAncias de n d=C3=ADgitos) formadas por algari= smos compreendidos entre 1 e m, tais que o algarismo de uma dada posi=C3=A7= =C3=A3o da seq=C3=BC=C3=AAncia =C3=A9 sempre maior do que ou igual aos alga= rismos das posi=C3=A7=C3=B5es precedentes. Por exemplo, se m=3D2 e n=3D3, p= odemos pensar na seq=C3=BC=C3=AAncia 122, que leva 1 em 1, 2 em 2 e 3 em 2.= Al=C3=A9m desta, temos: 111, 112 e 222, ou seja, 4 fun=C3=A7=C3=B5es, ness= e caso. E isso n=C3=A3o bate com a f=C3=B3rmula exibida.

Abra=C3=A7o= ,
Eduardo

----- Mensagem original ----
De: vitoriogaus= s <vitoriogauss@uol.com.br>
Para: obm-l <obm-l@mat.puc-rio.br&g= t;
Enviadas: Sexta-feira, 7 de Dezembro de 2007 15:17:56
Assunto: Re:= Res: [obm-l] boa de combinatoria

=0A
T=C3=A3o simples asimm !!!!!
=0A 
=0A
Eu pensei nisso... mas n=C3=A3o acreditei...
=0A<= div> 
=0A
Obrigado
=0A
 
=0A
 =0A
 
=0A
 
=0A
 Ol=C3=A1, Vit=C3= =B3rio,
=0A
>
=0A
> Me parece que a resolu=C3=A7= =C3=A3o =C3=A9 a seguinte:
=0A
>
=0A
> a) Fun=C3= =A7=C3=B5es crescentes;
=0A
>
=0A
> Basta que, do= contradom=C3=ADnio com m elementos, selecionem-se n. A cada sele=C3=A7=C3= =A3o, associa-se uma =C3=BAnica fun=C3=A7=C3=A3o crescente, e vice-versa. A= sim, a resposta =C3=A9 Cm,n. Observe que, quando m =0A
>
=0A> b) Fun=C3=A7=C3=B5es n=C3=A3o decrescentes;
=0A
> =0A
> Analogamente, o total de fun=C3=A7=C3=B5es decrescentes =C3= =A9 Cm,n (de fato, observe que, a cada fun=C3=A7=C3=A3o crescente, associa-= se uma =C3=BAnica fun=C3=A7=C3=A3o decrescente, e vice-versa). Como o total= de fun=C3=A7=C3=B5es (de qualquer tipo) =C3=A9 m^n, temos que o valor proc= urado =C3=A9 m^n - Cm,n.
=0A
>
=0A
> Espero ter a= judado, um abra=C3=A7o!
=0A
> Eduardo L. Estrada
=0A>
=0A
> ----- Mensagem original ----
=0A
> De= : vitoriogauss
=0A
> Para: obm-l
=0A
> Enviadas= : Quinta-feira, 6 de Dezembro de 2007 17:01:58
=0A
> Assunto: = [obm-l] boa de combinatoria
=0A
>
=0A
> Caros col= egas...
=0A
>
=0A
>
=0A
>
=0A<= div>>
=0A
>
=0A
> Seja In =3D {1,2,...,n}, ana= logamente Im, determinar o n=C3=BAmero de fun=C3=A7=C3=B5es f: In --> Im= tais que:
=0A
>
=0A
>
=0A
>
= =0A
>
=0A
>
=0A
> a) f seja crescente =0A
>
=0A
>
=0A
>
=0A
> b) = f seja n=C3=A3o-decrescente
=0A
>
=0A
>
=0A=
>
=0A
> desde j=C3=A1 grato....
=0A
> =0A
>
=0A
>
=0A
>
=0A
> =0A
>
=0A
>
=0A
> Abra sua conta no Ya= hoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento! =0A=0A
=0A
Vit=C3=B3= rio Gauss
=0A


=0A=0A=0A
Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite d= e espa=C3=A7o para armazenamento! =0A --0-436907697-1197138151=:9845-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 8 19:11:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB8L9j8l013501 for ; Sat, 8 Dec 2007 19:09:45 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB8L9jfW013499 for obm-l-MllGbsmmN; Sat, 8 Dec 2007 19:09:45 -0200 Received: from web56608.mail.re3.yahoo.com (web56608.mail.re3.yahoo.com [66.196.97.52]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB8L9i8l013489 for ; Sat, 8 Dec 2007 19:09:44 -0200 Received: (qmail 58178 invoked by uid 60001); 8 Dec 2007 22:11:09 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=quSPp75DWeKJh6O4ARD4uzZzd4BNqazTUp2ODSCLv1Vquvz7OoK9RJSg+lvW/hBU/xVY+UPle18eyLz2cZd1c7kfUrztK2Cs3uCWsmIuL6VljeD9mNkq/Ru9FpCvtpezeUEgW2e1PmSLW8m3xyN+Yu8p3bjlt3z1JMcwaYxqiZE=; X-YMail-OSG: kh4AS18VM1k1J0sO6AemO6TPBm._IVumjHl4IcTXkKX.NALLleEOMcfreqnmjuq4n6TK_UNM22P1otzEx7zicCB.jVt1cRP7PGRzBQ.DflvUNXyKSDQj7LvbEcaeL4DQVdYw2CV3XLDYlVM- Received: from [201.13.11.194] by web56608.mail.re3.yahoo.com via HTTP; Sat, 08 Dec 2007 19:11:08 ART Date: Sat, 8 Dec 2007 19:11:08 -0300 (ART) From: Gustavo Souza Subject: [SPAM] [obm-l] Geometria Plana To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <223141.57801.qm@web56608.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Gustavo Souza X-Spam-Status: Yes, hits=9.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2065453231-1197151868=:57801" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 194.11.13.201.list.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 52.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 52.97.196.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2065453231-1197151868=:57801 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Seja o triângulo ABC e o ponto D contido na reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD = 40º calcule o valor do angulo B^CD, sabendo que AB=CD ... Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar uma força... Estou enviando um link com a foto do triangulo nela, kem kiser ver pra fikar melhor... Obrigado http://img155.imageshack.us/my.php?image=triangulonw3.jpg --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2065453231-1197151868=:57801 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Seja o triângulo ABC e o ponto D contido na reta AB. Seja tambem o valor de  BÂC = 100º e o valor e o valor de A^CD = 40º calcule o valor do angulo B^CD, sabendo que AB=CD ...
 
Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar uma força...
 
Estou enviando um link com a foto do triangulo nela, kem kiser ver pra fikar melhor...
 
Obrigado
 
 

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<3bd00efc0712082050l12423fb0r9b8d95d2b7dc4e0c@mail.gmail.com> Date: Sun, 9 Dec 2007 02:50:04 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?UTF-8?Q?Re:_[obm-l]_segunda_fase_-_n=C3=ADvel_universit=C3=A1rio_2007?= In-Reply-To: <921472.64705.qm@web50606.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1247_59431.1197175804624" References: <921472.64705.qm@web50606.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=2.4 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_1247_59431.1197175804624 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline 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========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 01:50:24 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB93nK8l013639 for ; Sun, 9 Dec 2007 01:49:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB93nKYY013637 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 01:49:20 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB93nH8l013621 for ; Sun, 9 Dec 2007 01:49:18 -0200 Received: by wa-out-1112.google.com with SMTP id m28so2650522wag for ; Sat, 08 Dec 2007 20:50:43 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=BfRoKri9Sw9MpLQ1iHsHg3gyuHXmzDjmGkUboqkRBK0=; b=KWJ4F/LZoBsrldgiuXlJXzDPBEFMoElNQzRSbSXaIuV8j51c4AA+S3SdYG1S3HHPtu3rt3rHStObg5L+RPc0rsiNzdu+tg+4tbV/iSCPSvcKUE1x2RthhERIuL2sb3INhJIeCKFW735TC7jK2q7HDF5U7tTzrrBruwwolMq2ER0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Hwg2L14guGUJoGHOv6B40EihaqkVXhgEbwTDZI8WLhe04f2r9Ktu60aDBRP9om48Z8/+veAdEQORVhDr4PBx8tTbWOejxGffYypt5prLvITZ5bF4M3W3/YvpEnMyLIZWzCi5blCC3KSV/luG6Cw3dZwwRNJaA0jQBvRjifPVTLI= Received: by 10.114.156.1 with SMTP id d1mr5089111wae.1197175842471; Sat, 08 Dec 2007 20:50:42 -0800 (PST) Received: by 10.114.136.9 with HTTP; Sat, 8 Dec 2007 20:50:42 -0800 (PST) Message-ID: <3bd00efc0712082050v7d6c15dcx251adcd1732bdbb3@mail.gmail.com> Date: Sun, 9 Dec 2007 02:50:42 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?UTF-8?Q?Re:_[obm-l]_segunda_fase_-_n=C3=ADvel_universit=C3=A1rio_2007?= In-Reply-To: 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owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 10:58:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9CuO8l030476 for ; Sun, 9 Dec 2007 10:56:24 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB9CuNdQ030473 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 10:56:23 -0200 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.169]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9CuH8l030384 for ; Sun, 9 Dec 2007 10:56:18 -0200 Received: by ug-out-1314.google.com with SMTP id q7so1437452uge for ; Sun, 09 Dec 2007 05:57:43 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=55zL0MPTSgd9aF0HYFAF9zJ2S027znhglTiLbwOQEe4=; b=bptfzPM0YZkmD8O0CTHDtDt8ys+bWcpvezwKG/QK64m67L7aO6tWBtYms+IW8/fjt503C8ccZ2GH6Xn+hXYN0swphVcKYn3TlmCS+JlzruWrXkT4zw3Mj6O1KfrWWVsRv3T50as6uvJrnf2To1FvtYNIwnvqjzGXq0gaWxO1vfQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=e4+wnnjZCsa5Gn/JYDD58fmEpjrdW37+jBBw0pnr9SqNIFD+1OMoaV0ufMfhQt/1W0hMUejipWRIYsqoBIb2tS43PeaTLf5EcCigTWTCyw4TKYedT53tSar2W1/i/5v65W4Hq5Ny9XePMFxpULrTmcv63N5crmoJ4BAcg+OIDno= Received: by 10.66.249.8 with SMTP id w8mr5083886ugh.1197208662827; Sun, 09 Dec 2007 05:57:42 -0800 (PST) Received: by 10.66.218.12 with HTTP; Sun, 9 Dec 2007 05:57:42 -0800 (PST) Message-ID: Date: Sun, 9 Dec 2007 11:57:42 -0200 From: jose To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_ahlfors_-_an=E1lise_complexa?= In-Reply-To: <2eaf8c650712070420q68e318c4n1c4c820769c0c61a@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_8256_7570993.1197208662814" References: <2eaf8c650712070420q68e318c4n1c4c820769c0c61a@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: jose X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_8256_7570993.1197208662814 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Jones, Me desculpe esqueci uma v=EDrgula.. "prove that in any region A the family of analytic functions, with positive real part, is normal. Under what added condition is it locally bounded? Hint: consider the funtin exp(*-f*)." N=E3o queria traduzir, mas vai l=E1 Se F =E9 uma fam=EDlia de fun=E7=F5es com *parte real =E9 positiva*, ent=E3= o toda sequ=EAncia de em F admite uma subsequ=EAncia convergente.(i.e. *F =E9 norm= al*). Acho que =E9 isso que diz o exerc=EDcio. Agradece pela aten=E7=E3o J. Gondin Em 07/12/07, colombo escreveu: > > J. Gordon, o que significa dizer que a: parte real =E9 normal? Tem alg= uma > outra defini=E7=E3o al=E9m do prosaico "normal"? Pois se for somente ist= o, n=E3o > sei exatamente o que precisa ser verificado. > Fico aguardando. > Jones > On Dec 7, 2007 5:02 AM, jose wrote: > > > Caros amigo, > > > > Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise > > complexa do livro do Ahlfors. > > N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja > > estudou o cap. 5 e 6 desse livro, ent=E3o pe=E7o que me ajude. > > > > Uma das quest=F5es =E9: > > > > "prove that in any region A the family of analytic functions with > > positive real part is normal. Under what added condition is it locally > > bounded? Hint: consider the funtin exp(*-f*)." > > > > desde j=E1 agrade=E7o > > > > J. Gondin > > > > ------=_Part_8256_7570993.1197208662814 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Jones,
Me desculpe esqueci uma v=EDrgula..
"prove that in any region A  the family of analytic function= s, with positive real part, is normal. Under what added condition is it loc= ally bounded? Hint: consider the funtin exp(-f)."
 
N=E3o queria traduzir, mas vai l=E1
Se F =E9 uma fam=EDlia de fun=E7=F5es com parte real =E9 posit= iva, ent=E3o toda sequ=EAncia de em F admite uma subsequ=EAncia co= nvergente.(i.e. F =E9 normal).
 
Acho que =E9 isso que diz o exerc=EDcio.
 
Agradece pela aten=E7=E3o
 
J. Gondin
 
 
 

 
Em 07/12/07, colombo <jones.colombo@g= mail.com> escreveu:
  J. Gordon, o que signific= a dizer que a:  parte real =E9 normal? Tem alguma outra defini=E7=E3o = al=E9m do prosaico "normal"?  Pois se for somente isto, n=E3= o sei exatamente o que precisa ser verificado.=20
Fico aguardando.
Jones=20

On Dec 7, 2007 5:02 AM, jose <gondintw@gmail.com> wrote:
Caros amigo,
 
Gostaria de uma ajuda para resolver alguns exerc=EDcios de analise com= plexa do livro do Ahlfors.
N=E3o encontrei os exercicios em outros livros, por isso, se alguem ja= estudou o cap. 5 e 6 desse  livro, ent=E3o  pe=E7o que me a= jude.
 
Uma das quest=F5es =E9:
 
"prove that in any region A  the family of analytic function= s with positive real part is normal. Under what added condition is it local= ly bounded? Hint: consider the funtin exp(-f)."
 
desde j=E1 agrade=E7o
 
J. Gondin

=
------=_Part_8256_7570993.1197208662814-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 14:43:09 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9GfR8l005000 for ; Sun, 9 Dec 2007 14:41:27 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB9GfR1H004998 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 14:41:27 -0200 Received: from sc2.he.tucows.com (mail07.sc2.he.tucows.com [64.97.154.85]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9GfP8l004995 for ; Sun, 9 Dec 2007 14:41:26 -0200 Received: from [201.50.240.91] by sc2.he.tucows.com with HTTP; Sun, 9 Dec 2007 17:22:19 +0000 Date: Sun, 9 Dec 2007 15:22:19 -0200 Message-ID: <47587BD30000499B@mail07.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] trigonometria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 201.50.240.91 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lB9GfQ8l004996 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.1 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 85.154.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 85.154.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Encontre o valor da soma S=(tg1º)^2+(tg3°)^2+(tg5°)^2+...+(tg89°)^2. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 16:30:01 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9ISe8l013935 for ; Sun, 9 Dec 2007 16:28:40 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB9ISdIE013930 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 16:28:39 -0200 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9ISZ8l013873 for ; Sun, 9 Dec 2007 16:28:36 -0200 Received: by py-out-1112.google.com with SMTP id a29so4121300pyi for ; Sun, 09 Dec 2007 11:30:01 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=GfMNT2r9H+bHENohmjMgr4wwK229k72pkWy4cbvAj4o=; b=C0eQecC4OYqXvHMFuz7C5Cj4T2RQ33ARTmAWJZCkJYRM2storrC5Lbj6G/47w1Q72FWuf4O9wKK4lMS5Y1isSswk7y+bKAzSFwY6CNLqSI5wpKHQfnqFEmRSAIujJQ3uvfcL+jFstuGsOK/eziLo2o9yKq0dIE4iT8qy8LTpMyw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=OQzOeVHOK2lF/Ie5Jf8kZghTkFSxK/CzkB1TwKZQLAHl5A93atQO3w/gBvW5JF8eaTcEzLBwQI9aTToWoBCgU6M1aG7PEO/h1Jo9yQZ+CksRDqYZpXlJ5TM52/z62ykxwxFe6hhPAF7w/UWmaCqUGElw6dtJirhxt+5Bgrzn3F0= Received: by 10.142.109.16 with SMTP id h16mr2721912wfc.1197228173810; Sun, 09 Dec 2007 11:22:53 -0800 (PST) Received: from ?201.20.195.180? ( [201.20.195.180]) by mx.google.com with ESMTPS id h14sm4710280wxd.2007.12.09.11.22.51 (version=SSLv3 cipher=RC4-MD5); Sun, 09 Dec 2007 11:22:52 -0800 (PST) Message-ID: <475C4088.3000203@gmail.com> Date: Sun, 09 Dec 2007 17:22:48 -0200 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Geometria Plana References: <223141.57801.qm@web56608.mail.re3.yahoo.com> In-Reply-To: <223141.57801.qm@web56608.mail.re3.yahoo.com> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: No, hits=4.8 required=5.0 tests=CTYPE_JUST_HTML,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Gustavo Souza escreveu:
Seja o triângulo ABC e o ponto D contido na reta AB. Seja tambem o valor de  BÂC = 100º e o valor e o valor de A^CD = 40º calcule o valor do angulo B^CD, sabendo que AB=CD ...
 
Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar uma força...
 
Estou enviando um link com a foto do triangulo nela, kem kiser ver pra fikar melhor...
 
Obrigado
 
 

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!
Olá gustavo.
Se chamarmos de y o ângulo  D^BC, teremos que como soma total dos ângulos do triângulo é de 180°, então

100 + ( 40 + x ) + y = 180

ou seja

y = 40 - x

Usando agora a lei dos senos, temos que

CD/sen(100) = AD/sen(40)

ou

AD = [ sen(40)/sen(100) ] CD

e tambem temos que

CD/sen(y) = DB/sen(x)

ou

DB =  [ sen(x)/sen(y) ] CD

como AD + DB = AB = CD, então

          AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD  =>

=> [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] =  1

Mas y= 40 - x, portanto

sen(y) = sen( 40 - x ) = sen(40) cos(x)  +  sen(x) cos(100)

logo, teremos

[ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] } =  1 =>

sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] =  1 - [ sen(40)/sen(100) ]  =>

sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] =  [ sen(100) -  sen(40) ]/sen(100)  =>

[ sen(40) cos(x)  +  sen(x) cos(100) ]/sen(x) =  sen(100)/[ sen(100) -  sen(40) ]  =>

sen(40) cotg(x)  +  cos(100)  =  sen(100)/[ sen(100) -  sen(40) ]  =>

cotg(x) =  { sen(100)/[ sen(100) -  sen(40) ] - cos(100)  }/sen(40) =
= { sen(100) - cos(100)[ sen(100) -  sen(40) ]  }/{ sen(40)[ sen(100) -  sen(40) ] }

ou ainda

tg(x) =  { sen(40) [ sen(100) -  sen(40) ] }/{ sen(100)[ 1 - cos(100) ]  - sen(40) ] }

e assim

x = arctg({ sen(40) [ sen(100) -  sen(40) ] }/{ sen(100)[ 1 - cos(100) ]  - sen(40) ] })

Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos que simplificar o último termo para ser uma tangente.
Qualquer dúvida, pode mandar.
Até mais.


========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 21:50:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lB9Nmv8l006421 for ; Sun, 9 Dec 2007 21:48:57 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lB9Nmtuh006419 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 21:48:55 -0200 Received: from smtp110.mail.mud.yahoo.com (smtp110.mail.mud.yahoo.com [209.191.85.220]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lB9NmT8l006409 for ; Sun, 9 Dec 2007 21:48:30 -0200 Received: (qmail 43266 invoked from network); 10 Dec 2007 00:49:52 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=RvDfISuEE4B0dOWORG3mdOHZezRc5NMOYVUVKV86lxmCrDqePkkK25WsjtGR78k3TZJ8LmPdtoi+V5wifn1CIPLQ816fiUTjIRib4phxCLkWuomwpLLPC40uR0OUR6wrc88AiryAll0qJbUNOpuSxgS/aL3KdX+IzJZaMbDmcuw= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp110.mail.mud.yahoo.com with SMTP; 10 Dec 2007 00:49:49 -0000 X-YMail-OSG: yWAN3nsVM1nzyj4BK5RBCqga49st1IuLJX0hTNuyyiPyomC8tX0dIwAm3YFulUTqLBniJ3IxTXgA7taniEHT46L1vbn6cWMiTnXLrz6bdaOuGcarmLk- Message-ID: <004901c83a05$e52f02d0$02270269@rodrigo7a25356> From: To: References: <921472.64705.qm@web50606.mail.re2.yahoo.com> <3bd00efc0712082050l12423fb0r9b8d95d2b7dc4e0c@mail.gmail.com> <3bd00efc0712082050v7d6c15dcx251adcd1732bdbb3@mail.gmail.com> Subject: [SPAM] [obm-l] =?UTF-8?Q?Re:_=5Bobm-l=5D_segunda_fase_-_n=C3=ADvel?= =?UTF-8?Q?_universit=C3=A1rio_2007?= Date: Sat, 8 Dec 2007 22:50:31 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=8.4 required=5.0 tests=AWL,DATE_IN_PAST_12_24,FORGED_YAHOO_RCVD,MAILTO_LINK, MIME_EXCESSIVE_QP,NO_REAL_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0046_01C839EC.BC105070" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (8.40 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: DATE_IN_PAST_12_24 (0.2 points) Date: is 12 to 24 hours before Received: date SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 220.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 220.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0046_01C839EC.BC105070 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Ol=C3=A1 Marcelo, voc=C3=AA leu a demonstra=C3=A7=C3=A3o abaixo?gostaria de saber se ela = cont=C3=A9m algum erro abra=C3=A7os ----- Original Message -----=20 From: Marcelo Salhab Brogliato=20 To: obm-l@mat.puc-rio.br=20 Sent: Sunday, December 09, 2007 1:50 AM Subject: Re: [obm-l] segunda fase - n=C3=ADvel universit=C3=A1rio 2007 eita... desculpe! tava pensando e sem querer apertei um atalho e = enviou... hehe ;) abra=C3=A7os, Salhab On Dec 9, 2007 2:50 AM, Marcelo Salhab Brogliato < msbrogli@gmail.com> = wrote: Ol=C3=A1 Rodrigo, Dado um inteiro positivo n, mostre que existe um inteiro positivo N = com a seguinte propriedade: se A =C3=A9 um subconjunto de {1,2,...,N} = com pelo menos N/2 elementos, ent=C3=A3o existe um inteiro positivo = m<=3D N - n tal que |A interse=C3=A7=C3=A3o com {m+1, m+2,..., = m+k}|>=3Dk/2 para todo k =3D 1, 2, =E2=80=A6, n. =20 |AUB| =3D |A| + |B| - |AinterB| |A inter {m+1, m+2, ..., m+k}| =3D |A| + |{m+1, m+2, ..., m+k}| - |A = uniao {m+1, m+2, ..., m+k}|=20 |A inter {m+1, m+2, ..., m+k}| =3D |A| + k - |A uniao {m+1, m+2, = ..., m+k}|=20 On Dec 6, 2007 6:19 PM, Rodrigo Cientista = wrote: PROBLEMA 2: Dado um inteiro positivo n, mostre que existe um inteiro positivo = N com a seguinte propriedade: se A =C3=A9 um subconjunto de {1,2,...,N} = com pelo menos N/2 elementos, ent=C3=A3o existe um inteiro positivo = m<=3D N - n tal que |A interse=C3=A7=C3=A3o com {m+1, m+2,..., = m+k}|>=3Dk/2=20 para todo k =3D 1, 2, =E2=80=A6, n. = *************************************************************************= ************************************************* (gostaria de coment=C3=A1rios sobre esta demonstra=C3=A7=C3=A3o, = falhas, se conhecem alguma demonstra=C3=A7=C3=A3o pra esse problema, = pois ainda n=C3=A3o tem o gabarito)=20 suponha existir x > N - n tal que |A interse=C3=A7=C3=A3o com = {x+1, x+2,..., x+k}|>=3Dk/2 como x + n > N, pelo menos um elemento de {x+1, x+2,..., x+k} = ser=C3=A1 maior que qualquer elemento de A; escolhendo-se um n =3D 1, a = afirma=C3=A7=C3=A3o acima =C3=A9 falsa=20 assim, se |A interse=C3=A7=C3=A3o com {m+1, m+2,..., m+k}|>=3Dk/2 = =3D=3D> existe m <=3D N - n chamemos S =3D {m+1, m+2,..., m+k} m + n <=3D N =3D=3D> m + k <=3D N para todo k =3D 1, 2, =E2=80=A6, = n =3D=3D> =3D=3D> S =C3=A9 subconjunto de {1,2,...,N}, ou =C3=A9 o = pr=C3=B3prio conjunto {1,2,...,N} na hip=C3=B3tese em que N =3D n=20 quando N =3D n =C3=A9 trivial que |A interse=C3=A7=C3=A3o com = {m+1, m+2,..., m+k}|>=3Dk/2 (=3D k/2 na verdade) suponha N > n =3D=3D> N/2 > n/2 =3D=3D> |{1,2,...,N}| > |S| = =3D=3D> |A| > |S|/2 =3D n/2 como S est=C3=A1 contido em {1,2,...,N} =3D=3D> =C3=A9 sempre = poss=C3=ADvel tomar-se um subconjunto A de {1,2,...,N} tal que S/2 = esteja contido em A=20 Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de = espa=C3=A7o para armazenamento! http://br.mail.yahoo.com/ = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=20 Instru=EF=BF=BD=C3=B5es para entrar na lista, sair da lista e usar = a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=20 ------=_NextPart_000_0046_01C839EC.BC105070 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable =EF=BB=BF
Ol=C3=A1 Marcelo,
 
voc=C3=AA leu a = demonstra=C3=A7=C3=A3o abaixo?gostaria de=20 saber se ela cont=C3=A9m algum erro
abra=C3=A7os
----- Original Message -----
From:=20 Marcelo Salhab=20 Brogliato
Sent: Sunday, December 09, 2007 = 1:50=20 AM
Subject: Re: [obm-l] segunda = fase - n=C3=ADvel=20 universit=C3=A1rio 2007

eita... desculpe! tava pensando e sem querer apertei um = atalho=20 e enviou... hehe ;)

abra=C3=A7os,
Salhab


On Dec 9, 2007 2:50 AM, Marcelo Salhab = Brogliato < msbrogli@gmail.com> = wrote:
Ol=C3=A1=20 Rodrigo,


Dado um inteiro positivo n, mostre que = existe um=20 inteiro positivo N com a seguinte propriedade: se A =C3=A9 um = subconjunto de=20 {1,2,...,N}  com pelo menos N/2 elementos, ent=C3=A3o existe um = inteiro=20 positivo m<=3D N - n   tal que  |A interse=C3=A7=C3=A3o = com {m+1, m+2,...,=20 m+k}|>=3Dk/2 para todo k =3D 1, 2, =E2=80=A6,=20 n.

 




|AUB| =3D |A| + |B| -=20 |AinterB|

|A inter {m+1, m+2, ..., m+k}| =3D |A| + |{m+1, = m+2, ...,=20 m+k}| - |A uniao {m+1, m+2, ..., m+k}|
|A inter {m+1, m+2, ..., = m+k}| =3D=20 |A| + k - |A uniao {m+1, m+2, ..., m+k}|=20







On Dec 6, 2007 6:19 PM, Rodrigo Cientista = <rodrigocientista@yahoo.com.br > wrote:
PROBLEMA=20 2:
Dado um inteiro positivo n, mostre que existe um inteiro = positivo N=20 com a seguinte propriedade: se A =C3=A9 um subconjunto de = {1,2,...,N}  com=20 pelo menos N/2 elementos, ent=C3=A3o existe um inteiro positivo = m<=3D N - n=20   tal que  |A interse=C3=A7=C3=A3o com {m+1, m+2,..., = m+k}|>=3Dk/2=20

para todo k =3D 1, 2, =E2=80=A6,=20 = n.

***************************************************************= ***********************************************************
(gostaria = de coment=C3=A1rios sobre esta demonstra=C3=A7=C3=A3o, falhas, se = conhecem alguma=20 demonstra=C3=A7=C3=A3o pra esse problema, pois ainda n=C3=A3o tem = o gabarito)=20

suponha existir x > N - n tal que  |A = interse=C3=A7=C3=A3o com {x+1,=20 x+2,..., x+k}|>=3Dk/2

como x + n > N, pelo menos um = elemento de=20  {x+1, x+2,..., x+k} ser=C3=A1 maior que qualquer elemento de = A;=20 escolhendo-se um n =3D 1, a afirma=C3=A7=C3=A3o acima =C3=A9 falsa =

assim, se=20  |A interse=C3=A7=C3=A3o com {m+1, m+2,..., m+k}|>=3Dk/2 = =3D=3D> existe m <=3D=20 N - n

chamemos S =3D {m+1, m+2,..., m+k}

m + n = <=3D N =3D=3D>=20 m + k <=3D N para todo k =3D 1, 2, =E2=80=A6, n = =3D=3D>

 =3D=3D> S =C3=A9=20 subconjunto de {1,2,...,N}, ou =C3=A9 o pr=C3=B3prio conjunto = {1,2,...,N} na=20 hip=C3=B3tese em que  N =3D n

quando N =3D n =C3=A9 = trivial que |A=20 interse=C3=A7=C3=A3o com {m+1, m+2,..., m+k}|>=3Dk/2 (=3D k/2 = na=20 verdade)

suponha N > n =3D=3D> N/2 > n/2 = =3D=3D> |{1,2,...,N}|=20 > |S| =3D=3D> |A| > |S|/2 =3D n/2

como S est=C3=A1 = contido em=20 {1,2,...,N} =3D=3D> =C3=A9 sempre poss=C3=ADvel tomar-se um = subconjunto A de=20 {1,2,...,N} tal que S/2 esteja contido em A


  =  =20  Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de = espa=C3=A7o para=20 armazenamento!
http://br.mail.yahoo.com/

=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=20
Instru=EF=BF=BD=C3=B5es para entrar na lista, sair da lista e = usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=20 =


------=_NextPart_000_0046_01C839EC.BC105070-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 22:54:02 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBA0qZ8l016777 for ; Sun, 9 Dec 2007 22:52:35 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBA0qZwF016775 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 22:52:35 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBA0qV8l016735 for ; Sun, 9 Dec 2007 22:52:32 -0200 Received: by wa-out-1112.google.com with SMTP id m28so3239114wag for ; Sun, 09 Dec 2007 17:53:57 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=SdNYoBBm/4XrFClB+uhSKSsBsJkyvCwOmyoByawe4iw=; b=StAlBZbwsyvlQiiCQj8cmXp2Kz4WQ8N9d/3NOD0FyRSlMuZLEDHxF+xEIx6x4ELmPWGvI/rHjrLEazNMIovMzvPrX4vpev2ElULizvd5Os33w2lho5XukhzaPjPCAtLZjQwtKViL1ESaGddkKi+EycHgp/mOYqMwysYNRB0KyLM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=GiLBDZLGbGGFe636Hk2siPP1HtouJsF18/LD8A07PFHVbsw4unep6fXv0M0aiKgYbXOyaZaZ34c23H1woFEuyFpQ+XDWnl3G4wkBBuLtjc/h/yBODypkTWcJW1kMizjRRC8WXnuQU1fjJKZn5W+gT9Uf1/DgNp1o77ZdzSZSb/I= Received: by 10.115.23.12 with SMTP id a12mr2187712waj.1197251633017; Sun, 09 Dec 2007 17:53:53 -0800 (PST) Received: by 10.114.136.9 with HTTP; Sun, 9 Dec 2007 17:53:52 -0800 (PST) Message-ID: <3bd00efc0712091753k21a0fc83x52659d64b380df7b@mail.gmail.com> Date: Sun, 9 Dec 2007 23:53:52 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Geometria Plana In-Reply-To: <223141.57801.qm@web56608.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4453_6487201.1197251633008" References: <223141.57801.qm@web56608.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=2.7 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_4453_6487201.1197251633008 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Gustavo, vamos dar os seguintes nomes aos lados: AB =3D CD =3D b AC =3D AD =3D l [calma, ja vamos provar que AC =3D AD] BC =3D r A^DC =3D 40 .. pois a soma dos angulos neste triangulo =E9 180... logo, o triangulo ADC =E9 isosceles e AD =3D AC no triangulo ADC, fazemos: cos(40) =3D b/2 * 1/l ... logo: b =3D 2lcos(40) mas b =3D k + l .... assim: k =3D l [2cos(40) - 1] usando lei dos senos no triangulo BDC, temos: k/sen(x) =3D b/sen(40-x) abrindo, temos: ksen(40) - kcos(40)tg(x) =3D btg(x) ... isando, temos: tg(x= ) =3D (k/b) * sen(40) / (1 + k/b * cos(40)) das relacoes acima, temos: k/b =3D [2cos(40) - 1]/(2cos(40)) substituindo e simplificando, obtemos: tg(x) =3D [2cos(40)-1]/[2cos(40)+1] * tg(40) abra=E7os, Salhab On Dec 8, 2007 8:11 PM, Gustavo Souza wrote: > Seja o tri=E2ngulo ABC e o ponto D contido na reta AB. Seja tambem o valo= r > de B=C2C =3D 100=BA e o valor e o valor de A^CD =3D 40=BA calcule o valo= r do angulo > B^CD, sabendo que AB=3DCD ... > > Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar > uma for=E7a... > > Estou enviando um link com a foto do triangulo nela, kem kiser ver pra > fikar melhor... > > Obrigado > > http://img155.imageshack.us/my.php?image=3Dtriangulonw3.jpg > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_4453_6487201.1197251633008 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Gustavo,

vamos dar os seguintes nomes aos lados:
AB =3D CD = =3D b
AC =3D AD =3D l   [calma, ja vamos provar que AC =3D AD]=
BC =3D r

A^DC =3D 40 .. pois a soma dos angulos neste triangulo = =E9 180... logo, o triangulo ADC =E9 isosceles e AD =3D AC
no triangulo ADC, fazemos: cos(40) =3D b/2 * 1/l ... logo: b =3D 2lcos(= 40)
mas b =3D k + l .... assim: k =3D l [2cos(40) - 1]

usando lei= dos senos no triangulo BDC, temos:
k/sen(x) =3D b/sen(40-x)
abrindo,= temos: ksen(40) - kcos(40)tg(x) =3D btg(x) ... isando, temos: tg(x) =3D (k= /b) * sen(40) / (1 + k/b * cos(40))

das relacoes acima, temos: k/b =3D [2cos(40) - 1]/(2cos(40))
sub= stituindo e simplificando, obtemos:

tg(x) =3D [2cos(40)-1]/[2cos(40)= +1] * tg(40)

abra=E7os,
Salhab






On Dec 8, 2007 8:11 PM, Gustavo Souza <gustavoandre2006site@yahoo.com.br> wrote:
Seja o tri=E2ngulo ABC e o ponto D contido na reta AB. Seja tambem o v= alor de  B=C2C =3D 100=BA e o valor e o valor de A^CD =3D 40=BA calcul= e o valor do angulo B^CD, sabendo que AB=3DCD ...
 
=
Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder d= ar uma for=E7a...
 
Estou enviando um link com a foto do triang= ulo nela, kem kiser ver pra fikar melhor...
 
= Obrigado
 
 

=20

Abra sua conta no Yahoo! M= ail, o =FAnico sem limite de espa=E7o para armazenamento!=20

------=_Part_4453_6487201.1197251633008-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 9 23:13:37 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBA1CX8l022713 for ; Sun, 9 Dec 2007 23:12:33 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBA1CXs1022710 for obm-l-MllGbsmmN; Sun, 9 Dec 2007 23:12:33 -0200 Received: from web56603.mail.re3.yahoo.com (web56603.mail.re3.yahoo.com [66.196.97.47]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBA1CU8l022668 for ; Sun, 9 Dec 2007 23:12:31 -0200 Received: (qmail 27170 invoked by uid 60001); 10 Dec 2007 02:13:56 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=PH9YlBG3/N/q1kZWbNz24Gb1L1pMlRA1wY4VxOdPnfdC8xi5nHd25nQzRqPnnWhRvIafmAgN3pKQu/dbWX7okQgNoPc45dDjr8x7YRS/HVUJMNLfcQAmByjEzK388iVrSL+isLVwuQm7+v85MlMrhihZUsRKPmdMJSIoQUZaV/s=; X-YMail-OSG: KaOCth4VM1ljqIRMSQjO7hEvw0Y9fF6iVtbL.zjgvpEmN9In9lhEHE4kbmy3_IPKzA-- Received: from [200.232.192.216] by web56603.mail.re3.yahoo.com via HTTP; Sun, 09 Dec 2007 23:13:56 ART Date: Sun, 9 Dec 2007 23:13:56 -0300 (ART) From: Gustavo Souza Subject: [SPAM] Re: [obm-l] Geometria Plana To: obm-l@mat.puc-rio.br In-Reply-To: <475C4088.3000203@gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <824486.26917.qm@web56603.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Gustavo Souza X-Spam-Status: Yes, hits=8.5 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,MIME_BOUND_DIGITS_5, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-398251969-1197252836=:26917" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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"arcguede@gmail.com" escreveu: Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD = 40º calcule o valor do angulo B^CD, sabendo que AB=CD ... Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar uma força... Estou enviando um link com a foto do triangulo nela, kem kiser ver pra fikar melhor... Obrigado http://img155.imageshack.us/my.php?image=triangulonw3.jpg --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! Olá gustavo. Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do triângulo é de 180°, então 100 + ( 40 + x ) + y = 180 ou seja y = 40 - x Usando agora a lei dos senos, temos que CD/sen(100) = AD/sen(40) ou AD = [ sen(40)/sen(100) ] CD e tambem temos que CD/sen(y) = DB/sen(x) ou DB = [ sen(x)/sen(y) ] CD como AD + DB = AB = CD, então AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD => => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1 Mas y= 40 - x, portanto sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100) logo, teremos [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } = 1 => sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ] => sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40) ]/sen(100) => [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) - sen(40) ] => sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] => cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) = = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) - sen(40) ] } ou ainda tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - sen(40) ] } e assim x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - sen(40) ] }) Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos que simplificar o último termo para ser uma tangente. Qualquer dúvida, pode mandar. Até mais. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-398251969-1197252836=:26917 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
como saber o seno de 40 e seno de 100???
 
 
 


"arcguede@gmail.com" <arcguede@gmail.com> escreveu:
Gustavo Souza escreveu:
Seja o triângulo ABC e o ponto D contido na reta AB. Seja tambem o valor de  BÂC = 100º e o valor e o valor de A^CD = 40º calcule o valor do angulo B^CD, sabendo que AB=CD ...
 
Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar uma força...
 
Estou enviando um link com a foto do triangulo nela, kem kiser ver pra fikar melhor...
 
Obrigado
 
 
Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!
Olá gustavo.
Se chamarmos de y o ângulo  D^BC, teremos que como soma total dos ângulos do triângulo é de 180°, então

100 + ( 40 + x ) + y = 180

ou seja

y = 40 - x

Usando agora a lei dos senos, temos que

CD/sen(100) = AD/sen(40)

ou

AD = [ sen(40)/sen(100) ] CD

e tambem temos que

CD/sen(y) = DB/sen(x)

ou

DB =  [ sen(x)/sen(y) ] CD

como AD + DB = AB = CD, então

          AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD  =>

=> [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] =  1

Mas y= 40 - x, portanto

sen(y) = sen( 40 - x ) = sen(40) cos(x)  +  sen(x) cos(100)

logo, teremos

[ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] } =  1 =>

sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] =  1 - [ sen(40)/sen(100) ]  =>

sen(x)/[ sen(40) cos(x)  +  sen(x) cos(100) ] =  [ sen(100) -  sen(40) ]/sen(100)  =>

[ sen(40) cos(x)  +  sen(x) cos(100) ]/sen(x) =  sen(100)/[ sen(100) -  sen(40) ]  =>

sen(40) cotg(x)  +  cos(100)  =  sen(100)/[ sen(100) -  sen(40) ]  =>

cotg(x) =  { sen(100)/[ sen(100) -  sen(40) ] - cos(100)  }/sen(40) =
= { sen(100) - cos(100)[ sen(100) -  sen(40) ]  }/{ sen(40)[ sen(100) -  sen(40) ] }

ou ainda

tg(x) =  { sen(40) [ sen(100) -  sen(40) ] }/{ sen(100)[ 1 - cos(100) ]  - sen(40) ] }

e assim

x = arctg({ sen(40) [ sen(100) -  sen(40) ] }/{ sen(100)[ 1 - cos(100) ]  - sen(40) ] })

Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos que simplificar o último termo para ser uma tangente.
Qualquer dúvida, pode mandar.
Até mais.


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Mail, o único sem limite de espaço para armazenamento! --0-489483153-1197324398=:81805 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Alguem poderia postar uma solução para a questão 6 da OBM 2007 universitaria???

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-489483153-1197324398=:81805-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 10 20:20:26 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBAMIo8l026372 for ; Mon, 10 Dec 2007 20:18:50 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBAMIgO5026362 for obm-l-MllGbsmmN; Mon, 10 Dec 2007 20:18:45 -0200 Received: from web56314.mail.re3.yahoo.com (web56314.mail.re3.yahoo.com [216.252.110.238]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBAMIO8l026350 for ; Mon, 10 Dec 2007 20:18:25 -0200 Received: (qmail 54160 invoked by uid 60001); 10 Dec 2007 23:19:51 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=e1sR/dTFFzsmsr6i3sMpHXOKZSUaAvKrHalLZArZBp8TwyiuNsFqnlAcmyi0BTnAAVUB76YJankFoBK7bodCohXDlFjD+45BhGT2y3Bq1O/onz0MKn3aniHi/sCAaIiypQr5zXSY7xzejQ4IQeL7niKnlJixrTiZWPW+Lld3+mI=; X-YMail-OSG: _4TFMr4VM1kdlBA4tHhXjfqnnGF18g_7jLO9mfT69bSu0h.TFHecVqRhqiIIx_sjHZp8gi9c2p23TehcUaEeTgzZ5t3HVxfYTY4hdETxU8bVD0fzBMk- Received: from [201.69.139.2] by web56314.mail.re3.yahoo.com via HTTP; Mon, 10 Dec 2007 20:19:51 ART Date: Mon, 10 Dec 2007 20:19:51 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] Re: [obm-l] Exercicio olimpico To: obm-l@mat.puc-rio.br In-Reply-To: <009501c83781$deac6cd0$02270269@rodrigo7a25356> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <506885.52708.qm@web56314.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=6.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (6.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 238.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 238.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Achei legal as sugestões e as idéias que vocês deram. Obrigado! Entretanto, não posso deixar de ponderar que um aluno de sétima ou oitava série aprendam , mesmo em treinos para olimpíadas, o teorema do resto chinês. Pra ser sincero, nem conguências modulo m eu imaginava que eles aprendiam. Nesse sentido, gostaria de saber o que seria uma solução desse problema com os argumentos de um garoto, talentoso, mas estudando no nível fundamental. Sem alguém souber agradeço antecipadamente. Abraço --- rodrigocientista@yahoo.com.br escreveu: > rust escreveu: > > se p divide (a^29 - 1)/(a - 1), com p>29, então p == > 1 mod 29 e para todo primo p == 1 mod 29 existe pelo > menos um a_p incongruente a 1 mod p tal que p divide > [(a + lp)^29 - 1]/(a + lp - 1). Assim, pelo teorema > do resto chinês, podemos escolher um a tal que a == > a_p mod p_i, i = 1,2,3,...,n >= 2007 > ----- Original Message ----- > From: Fernando Oliveira > To: obm-l@mat.puc-rio.br > Sent: Wednesday, December 05, 2007 10:03 AM > Subject: Re: [obm-l] Exercicio olimpico > > > Se alguém souber inglês, pode tentar decifrar o > que escreveram aqui: > http://www.mathlinks.ro/viewtopic.php?t=173020 > > -- > Fernando Oliveira Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 11 13:09:46 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBBF7p8l016663 for ; Tue, 11 Dec 2007 13:07:51 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBBF7oe9016659 for obm-l-MllGbsmmN; Tue, 11 Dec 2007 13:07:50 -0200 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.171]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBBF7k8l016598 for ; Tue, 11 Dec 2007 13:07:47 -0200 Received: by ug-out-1314.google.com with SMTP id q7so338406uge.0 for ; Tue, 11 Dec 2007 08:09:14 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=w4fpngU9WJe1jPs3T6rqQDHQwsEnqBH5xKH7acoQ4lE=; b=GbUTwb8CuPUPdgduVhG70GIYOPLOZdeajeH4GvIPIlkYqdZ4uxyO9h9W31W/ISxElzMdD4mH4JQ0/PgpXpxL0EnSO4wE5/uDlkqKUgsaIHpPG9Up/Ujni0/xPOXLc/jeW19p0J6xumCN2BS9awjxd5XO/gYesJCKfqWITLeHDVs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=oIKFJge8cZAinbmdP3/ZkAOv22DcX6ReAG+iCcKEPVSW84yUu+pjd9PcDSY3oMUWTTC/1uawTbi7OIyE57m0C4CjHjO5eH6OnRbW6r5SA+pFdpYIPta0GTCLQkjavhtdsRYVd6XGAfh4jX0uhhasUCXAfZZZw/qnOXl9ZyRVwOU= Received: by 10.78.201.2 with SMTP id y2mr8797234huf.1197389353666; Tue, 11 Dec 2007 08:09:13 -0800 (PST) Received: by 10.78.138.10 with HTTP; Tue, 11 Dec 2007 08:09:13 -0800 (PST) Message-ID: <71c5e1520712110809w7d30327ay89df5f8c2086d96a@mail.gmail.com> Date: Tue, 11 Dec 2007 14:09:13 -0200 From: "Nicolau C. Saldanha" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Resultado da OBM In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: X-Google-Sender-Auth: 1f2c784358ecb032 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBBF7n8l016646 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Nicolau C. Saldanha" X-Spam-Status: No, hits=3.2 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Deve sair hoje no final da tarde. N. On Dec 7, 2007 12:42 PM, Fernando Oliveira wrote: > Leitores da lista, > > Me parece que li em algum lugar uma data para a divulgação dos resultados da > OBM de 2008. Estou ficando doido ou há mesmo uma estimativa para a > divulgação? > > -- > Fernando Oliveira ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 11 15:36:01 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBBHJYH1008484 for ; Tue, 11 Dec 2007 15:34:29 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBBGs16B007104 for obm-l-MllGbsmmN; Tue, 11 Dec 2007 14:54:01 -0200 Received: from mobius.impa.br (mobius.impa.br [147.65.1.81]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBBGqo8l007058; Tue, 11 Dec 2007 14:52:58 -0200 Received: from [147.65.2.170] (obm-01.impa.br [147.65.2.170]) (authenticated bits=0) by mobius.impa.br (8.13.8/8.13.8) with ESMTP id lBBHsJ2i011233 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Tue, 11 Dec 2007 15:54:19 -0200 Message-ID: <475ECEF8.6090100@impa.br> Date: Tue, 11 Dec 2007 15:55:04 -0200 From: Olimpiada Brasileira de Matematica User-Agent: Thunderbird 1.5.0.13 (Windows/20070809) MIME-Version: 1.0 To: Lista de discussao , aobm-l@mat.puc-rio.br Subject: [obm-l] Premiados 2007 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Greylist: Sender succeeded SMTP AUTH authentication, not delayed by milter-greylist-3.0 (mobius.impa.br [147.65.1.27]); Tue, 11 Dec 2007 15:54:19 -0200 (BRST) Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Olimpiada Brasileira de Matematica X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caros(as) amigos(as) da OBM: A listagem de premiados da OBM-2007 já está publicada no endereço: http://www.obm.org.br/frameset-premiosobm.htm Abraços, Nelly ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 11 22:33:06 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC0UV8l007891 for ; Tue, 11 Dec 2007 22:30:31 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBC0UVNO007889 for obm-l-MllGbsmmN; Tue, 11 Dec 2007 22:30:31 -0200 Received: from smtp109.mail.mud.yahoo.com (smtp109.mail.mud.yahoo.com [209.191.85.219]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBC0US8l007881 for ; Tue, 11 Dec 2007 22:30:29 -0200 Received: (qmail 79608 invoked from network); 11 Dec 2007 21:59:29 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:Subject:Date:MIME-Version:Content-Type:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=fFi9Fbj9Se1xnwA/zCk9EVLpYm/nTxS/77MkCg+xSyqNpkYTGkxQUttEEgNtGSNQn4+3cIgAJWSdKdJeL5gRuEHMGGAZnRP1DToJyr7s/yXhZMc4bFh7PWa7Ba3VLh+GgDUDF3jJXLSfdLKcwSb6dRCxrfYc3sbTtxs3jr+Wnro= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp109.mail.mud.yahoo.com with SMTP; 11 Dec 2007 21:59:27 -0000 X-YMail-OSG: 2JIhP1QVM1l.pkNxGtEaDgUhaQJUCZa.c6uSesVP.T8d5SqUmriXCcjRe2oT2IQkNtJHHAbBDQ-- Message-ID: <004501c83c49$96c52200$02270269@rodrigo7a25356> From: To: Subject: [SPAM] [obm-l] prova de impossibilidade Date: Tue, 11 Dec 2007 19:48:03 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=8.0 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,NO_REAL_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_003B_01C83C2E.BDC6E570" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 219.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 219.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_003B_01C83C2E.BDC6E570 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1, Gostaria de saber se algu=E9m conhece algum problema como exemplo em que = se prova ser imposs=EDvel a uma certa s=E9rie possuir uma f=F3rmula = fechada, ou de recorr=EAncia. Exemplo: eu estava tentando achar uma f=F3rmula de recorr=EAncia para um = produto que o colega Albert colocou aqui na lista: P =3D (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2) E imaginei que se caso este produto n=E3o possua uma f=F3rmula fechada = eu poderia prov=E1-lo, ao inv=E9s de continuar com as tentativas de = achar a f=F3rmula. ------=_NextPart_000_003B_01C83C2E.BDC6E570 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1,
 
 
Gostaria de saber se algu=E9m conhece = algum problema=20 como exemplo em que se prova ser imposs=EDvel a uma certa s=E9rie = possuir uma=20 f=F3rmula fechada, ou de recorr=EAncia.
 
Exemplo: eu estava tentando achar uma = f=F3rmula de=20 recorr=EAncia para um produto que o colega Albert colocou aqui na=20 lista:
 
P =3D (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 = +=20 n^2)
 
E imaginei que se caso este produto = n=E3o possua uma=20 f=F3rmula fechada eu poderia prov=E1-lo, ao inv=E9s de continuar com as = tentativas de=20 achar a f=F3rmula.
------=_NextPart_000_003B_01C83C2E.BDC6E570-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 11 23:18:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC1GP8l009577 for ; Tue, 11 Dec 2007 23:16:25 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBC1GOFX009575 for obm-l-MllGbsmmN; Tue, 11 Dec 2007 23:16:24 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.244]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC1GM8l009569 for ; Tue, 11 Dec 2007 23:16:23 -0200 Received: by hs-out-2122.google.com with SMTP id 4so53062hsl.13 for ; Tue, 11 Dec 2007 18:17:51 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=breGEjR1yTojCXqXouCVX/JKDdrVoH0fCunZFD5NV20=; b=eVPn6JJ1cYFT7KwJVtwr+nRWPNUG1s7u5E7V12blQ7yXwucEhcpc+wC2EH+hHQQd+XIsT420J9PPU+8fAYcgzePrBaX7BUIb5EReJY1sMYCG+/Wr8xls9IqFcshsZg6UFX1FSk7CWt/Finxv3Cdnz9zwSYhEgNr70pcbp7IdFaM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=eSdBR18NoY3FWId5yEf81VN2/MOg3d4qqhSx5z790lMxvQMZ3XmUcKhUfSi6oaLnD5DLAgc2Wud+WMLpIrB993tYi9BbL+OYQqBfGHPjvCia871r+BcNYWww7F9hpQLFJMAE6DPZe2zzOPorE58L9diefxmSvMoQOhaUEckiy3g= Received: by 10.70.108.18 with SMTP id g18mr217533wxc.26.1197425870849; Tue, 11 Dec 2007 18:17:50 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.192.55]) by mx.google.com with ESMTPS id i15sm10635285wxd.2007.12.11.18.17.46 (version=TLSv1/SSLv3 cipher=RC4-MD5); Tue, 11 Dec 2007 18:17:47 -0800 (PST) Message-ID: <475F44C8.8090406@gmail.com> Date: Wed, 12 Dec 2007 00:17:44 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] prova de impossibilidade References: <004501c83c49$96c52200$02270269@rodrigo7a25356> In-Reply-To: <004501c83c49$96c52200$02270269@rodrigo7a25356> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBC1GO8l009573 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=3.2 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** rodrigocientista@yahoo.com.br escreveu: > Olá, > > > Gostaria de saber se alguém conhece algum problema como exemplo em que > se prova ser impossível a uma certa série possuir uma fórmula fechada, > ou de recorrência. > > Exemplo: eu estava tentando achar uma fórmula de recorrência para um > produto que o colega Albert colocou aqui na lista: > > P = (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2) > > E imaginei que se caso este produto não possua uma fórmula fechada eu > poderia prová-lo, ao invés de continuar com as tentativas de achar a > fórmula. Belo ponto de vista Rodrigo. E se formos verificar, todo produto finito se reduz a uma somatória de logaritmos ln( Prod^N_{n=0} a_n ) = Sum^N_{n=0} ln(a_n) Se der pra provar que esta soma tem fórmula fechada, então dá pra provar que o produto tambêm têm. Como ln(a_n) = 2. Sum^Infty_{k=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 ) ]^{2k+1} Assim fica o problema de resolver a soma b_k = Sum^N_{n=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 ) ]^{2k+1} e depois a soma S = 2. Sum^Infty_{k=0} b_k Não sei se trocar um problema por dois resolve, mas acho que somatóriass são mais tratáveis do que produtos. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 00:42:18 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC2eC8l017523 for ; Wed, 12 Dec 2007 00:40:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBC2eCel017521 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 00:40:12 -0200 Received: from smtp102.mail.mud.yahoo.com (smtp102.mail.mud.yahoo.com [209.191.85.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBC2e98l017517 for ; Wed, 12 Dec 2007 00:40:10 -0200 Received: (qmail 56201 invoked from network); 12 Dec 2007 03:25:03 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:Content-Transfer-Encoding:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=Y8NeEmAgebrjz5I74Tb73p+RvIca4ppOivBN4VArr/bwnQmsk1S2pcWn5gClqtfnFAXAlWsD1RA3LdlUV527XOsFmfjnXhaCxkpl9ejKqSYhCHlUi48qF6H79tIM+iLX1cWMAD2Yg2zOevRgc3dvE8I+hh0oZrOcCI+KTSr7a6w= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp102.mail.mud.yahoo.com with SMTP; 12 Dec 2007 03:25:02 -0000 X-YMail-OSG: Rd8.SrYVM1n90oNRi_l._mxAnJv7WgDgETsFkstZp4ZY5jtkctmpghW9ToA8nsYV9C4DRI8MXkx37TwofxXpQdUg3y_L67UWAa_It9enl.5DAUtW2ig- Message-ID: <001201c83c77$12636de0$02270269@rodrigo7a25356> From: To: References: <004501c83c49$96c52200$02270269@rodrigo7a25356> <475F44C8.8090406@gmail.com> Subject: [SPAM] Re: [obm-l] prova de impossibilidade Date: Wed, 12 Dec 2007 01:25:44 -0300 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=response Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,NO_REAL_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 212.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 212.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- è verdade Albert, Somatórias são mais tratáveis, na verdade eu posso realizar a multiplicação e notar que os diversos fatores formam certos padrões de soma, mas sem sucesso em expor que padrões são esses numa fórmula fechada. Para n = 4, por exemplo, notei que P = 2 + (1^2 + 2^2 + 3^2 + 4^2)^2 + 2*(4!)^2 - (1^4 + 2^4 + 3^4 + 4^4), o que falha para n> 4... por ter encontrado tal fórmula, talvez tenha me passado algum detalhe despercebido que alguém da lista possa completar. quanto aos logaritmos, log (ab) = log a + log b, mas log (abc) = log a + log b + log c? ou mais geralmente, log (abc...n) = log a + log b + log c +...+ log n? ----- Original Message ----- From: "albert richerd carnier guedes" To: Sent: Tuesday, December 11, 2007 11:17 PM Subject: Re: [obm-l] prova de impossibilidade > rodrigocientista@yahoo.com.br escreveu: >> Olá, >> Gostaria de saber se alguém conhece algum problema como exemplo em que >> se prova ser impossível a uma certa série possuir uma fórmula fechada, ou >> de recorrência. >> Exemplo: eu estava tentando achar uma fórmula de recorrência para um >> produto que o colega Albert colocou aqui na lista: >> P = (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2) >> E imaginei que se caso este produto não possua uma fórmula fechada eu >> poderia prová-lo, ao invés de continuar com as tentativas de achar a >> fórmula. > Belo ponto de vista Rodrigo. > E se formos verificar, todo produto finito se reduz a uma somatória de > logaritmos > > > ln( Prod^N_{n=0} a_n ) = Sum^N_{n=0} ln(a_n) > > > Se der pra provar que esta soma tem fórmula fechada, então dá pra provar > que o produto tambêm têm. > Como > > > ln(a_n) = 2. Sum^Infty_{k=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + > ) ]^{2k+1} > > > Assim fica o problema de resolver a soma > > > b_k = Sum^N_{n=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 ) ]^{2k+1} > > > e depois a soma > > > S = 2. Sum^Infty_{k=0} b_k > > > Não sei se trocar um problema por dois resolve, mas acho que somatóriass > são mais tratáveis do que produtos. > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 01:37:04 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC3YG8l021213 for ; Wed, 12 Dec 2007 01:34:16 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBC3YFPB021211 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 01:34:15 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.241]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBC3YD8l021204 for ; Wed, 12 Dec 2007 01:34:14 -0200 Received: by hs-out-2122.google.com with SMTP id 4so91766hsl.13 for ; Tue, 11 Dec 2007 20:35:42 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=K99KhQpDvKHIQKzoYMcmU1ebZxf0fQFrvAVksJwmR98=; b=hpptGxJahG7x0RKys/nedHC6T1OdVM/0MZOxJhqYEfG7BpKBcSfb/q/siG3NBkKjKlrtvRdjuyx2/L+hb4UYkStvDOX+Dp595WI0N46KW3z2mn5K+0Pfg135kyubjiaQoxyo8am+Wfjz42GB8gOii2O/qd5MOf5aQVQwZLhYM8k= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=VbqjGJRJtxFoATEO1uBIfT6SkKJ0AITlmfZQWNRSC4VpMorPFw2uwMTBMxcsJ9pxSCjC5ZITwU+zvKoegJoPHPyZMdz6dJyIs/iRyzPDAucBdIzqwV7CzsaQxUQ0z6mvqm3NBr2G3Nf52CRLy+uQvMDemOhhLjyB2cP7IZsbWBk= Received: by 10.70.50.3 with SMTP id x3mr358558wxx.72.1197434142062; Tue, 11 Dec 2007 20:35:42 -0800 (PST) Received: from ?192.168.99.198? ( [201.20.192.55]) by mx.google.com with ESMTPS id h14sm10817400wxd.2007.12.11.20.35.39 (version=TLSv1/SSLv3 cipher=RC4-MD5); Tue, 11 Dec 2007 20:35:40 -0800 (PST) Message-ID: <475F6518.2070707@gmail.com> Date: Wed, 12 Dec 2007 02:35:36 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] prova de impossibilidade References: <004501c83c49$96c52200$02270269@rodrigo7a25356> <475F44C8.8090406@gmail.com> <001201c83c77$12636de0$02270269@rodrigo7a25356> In-Reply-To: <001201c83c77$12636de0$02270269@rodrigo7a25356> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBC3YF8l021208 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=3.2 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** rodrigocientista@yahoo.com.br escreveu: > è verdade Albert, > > Somatórias são mais tratáveis, na verdade eu posso realizar a > multiplicação e notar que os diversos fatores formam certos padrões de > soma, mas sem sucesso em expor que padrões são esses numa fórmula > fechada. > > Para n = 4, por exemplo, notei que P = 2 + (1^2 + 2^2 + 3^2 + 4^2)^2 + > 2*(4!)^2 - (1^4 + 2^4 + 3^4 + 4^4), o que falha para n> 4... por ter > encontrado tal fórmula, talvez tenha me passado algum detalhe > despercebido que alguém da lista possa completar. > > quanto aos logaritmos, log (ab) = log a + log b, mas log (abc) = log a > + log b + log c? ou mais geralmente, log (abc...n) = log a + log b + > log c +...+ log n? > > ----- Original Message ----- From: "albert richerd carnier guedes" > > To: > Sent: Tuesday, December 11, 2007 11:17 PM > Subject: Re: [obm-l] prova de impossibilidade > > >> rodrigocientista@yahoo.com.br escreveu: >>> Olá, >>> Gostaria de saber se alguém conhece algum problema como exemplo em >>> que se prova ser impossível a uma certa série possuir uma fórmula >>> fechada, ou de recorrência. >>> Exemplo: eu estava tentando achar uma fórmula de recorrência para >>> um produto que o colega Albert colocou aqui na lista: >>> P = (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2) >>> E imaginei que se caso este produto não possua uma fórmula fechada >>> eu poderia prová-lo, ao invés de continuar com as tentativas de >>> achar a fórmula. >> Belo ponto de vista Rodrigo. >> E se formos verificar, todo produto finito se reduz a uma somatória >> de logaritmos >> >> >> ln( Prod^N_{n=0} a_n ) = Sum^N_{n=0} ln(a_n) >> >> >> Se der pra provar que esta soma tem fórmula fechada, então dá pra >> provar que o produto tambêm têm. >> Como >> >> >> ln(a_n) = 2. Sum^Infty_{k=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + ) >> ]^{2k+1} >> >> >> Assim fica o problema de resolver a soma >> >> >> b_k = Sum^N_{n=0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 ) ]^{2k+1} >> >> >> e depois a soma >> >> >> S = 2. Sum^Infty_{k=0} b_k >> >> >> Não sei se trocar um problema por dois resolve, mas acho que >> somatóriass são mais tratáveis do que produtos. >> >> >> ========================================================================= >> >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> ========================================================================= > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > Não entendi esta sua última pergunta "quanto aos logaritmos, log (ab) = log a + log b, mas log (abc) = log a + log b + log c? ou mais geralmente, log (abc...n) = log a + log b + log c +...+ log n? " ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 10:13:20 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCCBW8l010787 for ; Wed, 12 Dec 2007 10:11:32 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCCBW2l010785 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 10:11:32 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCCBT8l010778 for ; Wed, 12 Dec 2007 10:11:30 -0200 Received: by wa-out-1112.google.com with SMTP id m28so408772wag.13 for ; Wed, 12 Dec 2007 05:12:57 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=hI/vNieeWuMcwowe2g8LlVylN0CcKKIeghPpicseD/g=; b=Ckri90g6hlELAyZ1JbBa2hphAez82vihRk/Junw81jLoKoFX+d5n5r7mD43egV1zSMNVmgFA76peFbfoXaT3yeKGCfso5dzF2u2LAiaATxAQoRtubo43v9EKRUEbQ7rxBlIJT2Q5qvHl8hdXdUyc7syBu1ufizqVy7qcc7BoDy8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=kprm9OjoRYnDZaUcR4XyFBLLum53NXz20a2Vg3uPe/wCxN2sSr66er4Jg/2GQgxQ4/0TpEI/k8GufGT6q9bsbpjzifc5oonO4z6bBQa/VwBSlm9MoZQYofQ5WExQSwTU1YAuHc4bDqKVBCF4fnvB9UwX2CcaUuW98BfiT1/vWfE= Received: by 10.114.210.2 with SMTP id i2mr766612wag.36.1197465177757; Wed, 12 Dec 2007 05:12:57 -0800 (PST) Received: by 10.114.136.9 with HTTP; Wed, 12 Dec 2007 05:12:57 -0800 (PST) Message-ID: <3bd00efc0712120512x75daea64m48660f0862d7aecb@mail.gmail.com> Date: Wed, 12 Dec 2007 11:12:57 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] prova de impossibilidade In-Reply-To: <001201c83c77$12636de0$02270269@rodrigo7a25356> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_13009_17623961.1197465177717" References: <004501c83c49$96c52200$02270269@rodrigo7a25356> <475F44C8.8090406@gmail.com> <001201c83c77$12636de0$02270269@rodrigo7a25356> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=3.0 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_13009_17623961.1197465177717 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Rodrigo, sim, log(abc) =3D log(a) + log(b) + log(c) .... veja: log(abc) =3D log(a(bc)) =3D log(a) + log(bc) =3D log(a) + log(b) + lo= g(c) facilmente prova-se por inducao que: log(abc...z) =3D log(a) + log(b) + log= (c) + ... + log(z) abra=E7os, Salhab On Dec 12, 2007 2:25 AM, wrote: > =E8 verdade Albert, > > Somat=F3rias s=E3o mais trat=E1veis, na verdade eu posso realizar a > multiplica=E7=E3o > e notar que os diversos fatores formam certos padr=F5es de soma, mas sem > sucesso em expor que padr=F5es s=E3o esses numa f=F3rmula fechada. > > Para n =3D 4, por exemplo, notei que P =3D 2 + (1^2 + 2^2 + 3^2 + 4^2)^2 = + > 2*(4!)^2 - (1^4 + 2^4 + 3^4 + 4^4), o que falha para n> 4... por ter > encontrado tal f=F3rmula, talvez tenha me passado algum detalhe desperceb= ido > que algu=E9m da lista possa completar. > > quanto aos logaritmos, log (ab) =3D log a + log b, mas log (abc) =3D log = a + > log > b + log c? ou mais geralmente, log (abc...n) =3D log a + log b + log c +.= ..+ > log n? > > ----- Original Message ----- > From: "albert richerd carnier guedes" > To: > Sent: Tuesday, December 11, 2007 11:17 PM > Subject: Re: [obm-l] prova de impossibilidade > > > > rodrigocientista@yahoo.com.br escreveu: > >> Ol=E1, > >> Gostaria de saber se algu=E9m conhece algum problema como exemplo em = que > >> se prova ser imposs=EDvel a uma certa s=E9rie possuir uma f=F3rmula fe= chada, > ou > >> de recorr=EAncia. > >> Exemplo: eu estava tentando achar uma f=F3rmula de recorr=EAncia para= um > >> produto que o colega Albert colocou aqui na lista: > >> P =3D (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2) > >> E imaginei que se caso este produto n=E3o possua uma f=F3rmula fechad= a eu > >> poderia prov=E1-lo, ao inv=E9s de continuar com as tentativas de achar= a > >> f=F3rmula. > > Belo ponto de vista Rodrigo. > > E se formos verificar, todo produto finito se reduz a uma somat=F3ria d= e > > logaritmos > > > > > > ln( Prod^N_{n=3D0} a_n ) =3D Sum^N_{n=3D0} ln(a_n) > > > > > > Se der pra provar que esta soma tem f=F3rmula fechada, ent=E3o d=E1 pra= provar > > que o produto tamb=EAm t=EAm. > > Como > > > > > > ln(a_n) =3D 2. Sum^Infty_{k=3D0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + > > ) ]^{2k+1} > > > > > > Assim fica o problema de resolver a soma > > > > > > b_k =3D Sum^N_{n=3D0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 ) ]^{2k+1} > > > > > > e depois a soma > > > > > > S =3D 2. Sum^Infty_{k=3D0} b_k > > > > > > N=E3o sei se trocar um problema por dois resolve, mas acho que somat=F3= riass > > s=E3o mais trat=E1veis do que produtos. > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_13009_17623961.1197465177717 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Rodrigo,

sim, log(abc) =3D log(a) + log(b) + log(c) ....
ve= ja: log(abc) =3D log(a(bc)) =3D log(a) + log(bc) =3D log(a) + log(b) + log(= c)
facilmente prova-se por inducao que: log(abc...z) =3D log(a) + log(b)= + log(c) + ... + log(z)

abra=E7os,
Salhab

On Dec 12, 2= 007 2:25 AM, <rodrigoc= ientista@yahoo.com.br> wrote:
=E8 verdade Albert,

Somat=F3rias s=E3o mais trat=E1veis, na verdade = eu posso realizar a multiplica=E7=E3o
e notar que os diversos fatores fo= rmam certos padr=F5es de soma, mas sem
sucesso em expor que padr=F5es s= =E3o esses numa f=F3rmula fechada.

Para n =3D 4, por exemplo, notei que P =3D 2 + (1^2 + 2^2 + 3^2 + 4= ^2)^2 +
2*(4!)^2 - (1^4 + 2^4 + 3^4 + 4^4), o que falha para n> 4... = por ter
encontrado tal f=F3rmula, talvez tenha me passado algum detalhe = despercebido
que algu=E9m da lista possa completar.

quanto aos logaritmos, lo= g (ab) =3D log a + log b, mas log (abc) =3D log a + log
b + log c? ou ma= is geralmente, log (abc...n) =3D log a + log b + log c +...+
log n?
<= div class=3D"Ih2E3d">
----- Original Message -----
From: "albert richerd carnier gued= es" <arcguede@gmail.com&g= t;
To: <obm-l@mat.puc-rio.br<= /a> >
Sent: Tuesday, December 11, 2007 11:17 PM
Subject: Re: [obm-l] p= rova de impossibilidade


> rodrigocientista@yahoo.com.br escreveu:
>> Ol=E1= ,
>>  Gostaria de saber se algu=E9m conhece algum problema com= o exemplo em que
>> se prova ser imposs=EDvel a uma certa s=E9rie = possuir uma f=F3rmula fechada, ou
>> de recorr=EAncia.
>>=  Exemplo: eu estava tentando achar uma f=F3rmula de recorr=EAncia par= a um
>> produto que o colega Albert colocou aqui na lista:
>>=  P =3D (1 + 1^2)(1 + 2^2)(1 + 3^2)...(1 + n^2)
>>  E im= aginei que se caso este produto n=E3o possua uma f=F3rmula fechada eu
&g= t;> poderia prov=E1-lo, ao inv=E9s de continuar com as tentativas de ach= ar a
>> f=F3rmula.
> Belo ponto de vista Rodrigo.
> E se f= ormos verificar, todo produto finito se reduz a uma somat=F3ria de
> = logaritmos
>
>
> ln( Prod^N_{n=3D0} a_n ) =3D Sum^N_{n=3D= 0} ln(a_n)
>
>
> Se der pra provar que esta soma tem f=F3rmula fech= ada, ent=E3o d=E1 pra provar
> que o produto tamb=EAm t=EAm.
> = Como
>
>
> ln(a_n) =3D 2. Sum^Infty_{k=3D0} [ 1/( 2k+1 ) = ][ ( a_n - 1 )/( a_n +
>  )  ]^{2k+1}=
>
>
> Assim fica o problema de resolver a soma
>>
> b_k =3D Sum^N_{n=3D0} [ 1/( 2k+1 ) ][ ( a_n - 1 )/( a_n + 1 = )  ]^{2k+1}
>
>
> e depois a soma
>
>
> S =3D 2. Sum^I= nfty_{k=3D0} b_k
>
>
> N=E3o sei se trocar um problema po= r dois resolve, mas acho que somat=F3riass
> s=E3o mais trat=E1veis d= o que produtos.
>
>
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D
> Instru=E7=F5es para entrar na lista, sair da = lista e usar a lista em
> http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> =3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es= para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_13009_17623961.1197465177717-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 12:05:06 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCE3L8l018585 for ; Wed, 12 Dec 2007 12:03:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCE3LbQ018583 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 12:03:21 -0200 Received: from venus.ccet.ufrn.br (venus.ccet.ufrn.br [200.19.174.45]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCE3J8l018580 for ; Wed, 12 Dec 2007 12:03:19 -0200 Received: from olivina (olivina.ccet.ufrn.br [10.9.0.153]) by venus.ccet.ufrn.br (Postfix) with SMTP id B742814332 for ; Wed, 12 Dec 2007 12:04:47 -0300 (GMT+3) Message-ID: <001501c83cd0$558d5910$9900090a@ccet.ufrn.br> From: "Benedito" To: Subject: [SPAM] [obm-l] =?iso-8859-1?B?SW5kaWNh5+Nv?= Date: Wed, 12 Dec 2007 13:04:45 -0200 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Benedito" X-Spam-Status: Yes, hits=5.2 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0012_01C83CBF.918FA730" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 45.174.19.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 45.174.19.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0012_01C83CBF.918FA730 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Prezado Senhores, Consultamos a Coordena=E7=E3o da OBM sobre a possibilidade do estudante = RAFAEL ALVES PINHEIRO fazer a Olimp=EDada de Maio 2008.=20 Ele nasceu em : 17/02/1995, =E9 aluno do Col=E9gio Contempor=E2neo, em = Natal, e j=E1 obteve as seguintes medalhas: Medalha de ouro na XVII Olimp=EDada de Matem=E1tica do Estado do RN - = 2006 - n=EDvel I Medalha de ouro na XVIII Olimp=EDada de Matem=E1tica do Estado do RN - = 2007 - n=EDvel II Medalha de Prata na XIII Olimp=EDada de Maio - 2007 - n=EDvel I Medalha de Prata na X OBA - 2007 - n=EDvel 3 Atenciosamente Benedito Tadeu V. Freire Coordenador Regional da OBM ------=_NextPart_000_0012_01C83CBF.918FA730 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Prezado Senhores,
 
Consultamos a Coordena=E7=E3o da OBM  sobre a = possibilidade do=20 estudante=20
RAFAEL ALVES PINHEIRO fazer a Olimp=EDada de Maio 2008.
Ele nasceu em : 17/02/1995, =E9 aluno do Col=E9gio = Contempor=E2neo, em=20 Natal, e j=E1 obteve as seguintes medalhas:
 
Medalha de ouro na XVII Olimp=EDada de Matem=E1tica do Estado do RN = - 2006 -=20 n=EDvel I
 
Medalha de ouro na XVIII Olimp=EDada de Matem=E1tica do Estado do = RN - 2007 -=20 n=EDvel II
 
Medalha de Prata na XIII Olimp=EDada de Maio - 2007 - n=EDvel = I
 
Medalha de Prata na X OBA - 2007 - n=EDvel 3
 
Atenciosamente
 
Benedito Tadeu V. Freire
Coordenador Regional da OBM
------=_NextPart_000_0012_01C83CBF.918FA730-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 12:36:10 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCEZ48l021638 for ; Wed, 12 Dec 2007 12:35:05 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCEZ4xW021636 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 12:35:04 -0200 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCEZ28l021628 for ; Wed, 12 Dec 2007 12:35:03 -0200 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 4AAA6E0074A9 for ; Wed, 12 Dec 2007 13:36:32 -0200 (BRST) Received: from bol.com.br (whisper1.mail.sys.intranet [172.26.5.136]) by salsa3.bol.com.br (Postfix) with ESMTP id 113DAE0065AF for ; Wed, 12 Dec 2007 13:36:31 -0200 (BRST) Date: Wed, 12 Dec 2007 13:36:31 -0200 Message-Id: Subject: [obm-l] =?iso-8859-1?b?RE9NzU5JTyBEQSBGVU7Hw08=?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197473791.2A.851300.42.27760.52.42.007.1185348362" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.72 X-SIG5: 4aa12ebbb5df7926bf6a045b6eef0261 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.4 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,LINES_OF_YELLING_3,SPAM_PHRASE_00_01, TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1197473791.2A.851300.42.27760.52.42.007.1185348362 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA: (UFPB-71) O dom=EDnio da fun=E7=E3o definida por f(x) =3D log (log x) =E9= : a) O conjunto dos n=FAmeros reais maiores que zero e menores que um. b) O conjunto dos n=FAmeros reais menores que um. c) O conjunto dos n=FAmeros inteiros positivos. d) O conjunto dos n=FAmeros reais maiores que um. e) O conjunto dos n=FAmeros irracionais. DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1197473791.2A.851300.42.27760.52.42.007.1185348362 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:<= /FONT>

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">(UFPB-71) O dom=EDnio da fun=E7=E3o definida por f(x) =3D l= og (log x) =E9:

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">a) O conjunto dos n=FAmeros reais maiores que zero e menore= s que um.

<= B style=3D"mso-bidi-font-weight: normal">b) O conjunto dos n=FAmeros reais menores que um.

<= B style=3D"mso-bidi-font-weight: normal">c) O conjunto dos n=FAmeros inteiros positivos.<= /FONT>

<= B style=3D"mso-bidi-font-weight: normal">d) O conjunto dos n=FAmeros reais maiores que um.

<= B style=3D"mso-bidi-font-weight: normal">e) O conjunto dos n=FAmeros irracionais.<= /FONT>

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">DESDE J=C1 MUITO OBRIGADO

<= B style=3D"mso-bidi-font-weight: normal"> 

--_=__=_XaM3_.1197473791.2A.851300.42.27760.52.42.007.1185348362-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 13:42:36 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCFbW8l003093 for ; Wed, 12 Dec 2007 13:37:32 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCFbVbM003085 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 13:37:31 -0200 Received: from web50612.mail.re2.yahoo.com (web50612.mail.re2.yahoo.com [206.190.38.158]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBCFbQ8l003007 for ; Wed, 12 Dec 2007 13:37:26 -0200 Received: (qmail 36468 invoked by uid 60001); 12 Dec 2007 16:38:54 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=jZurv8c04lRd+cG8fxbarW9Fe0jGb2czIO+L85mqBJToEiZ6LoMjVQpCivK3+eRTMXnFYICJqwT3NOsCheGi2uKg229MPAYgKoGgwtzLqCmXFibIzM48uWm4n1j+wlY12M0v8xOhMkaOMlJ2YeoyRL39C4l4oNrh5CUnr7M0FRI=; Received: from [161.148.198.135] by web50612.mail.re2.yahoo.com via HTTP; Wed, 12 Dec 2007 08:38:54 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Wed, 12 Dec 2007 08:38:54 -0800 (PST) From: Rodrigo Cientista Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Res=3A_=5Bobm-l=5D_DOM=CDNIO_DA_FUN=C7=C3O?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <566191.35354.qm@web50612.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Rodrigo Cientista X-Spam-Status: Yes, hits=8.3 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,LINES_OF_YELLING_3,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1681450225-1197477534=:35354" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: LINES_OF_YELLING_3 (0.3 points) BODY: 3 WHOLE LINES OF YELLING DETECTED SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: LINES_OF_YELLING_2 (0.2 points) BODY: 2 WHOLE LINES OF YELLING DETECTED SPAM: LINES_OF_YELLING (0.2 points) BODY: A WHOLE LINE OF YELLING DETECTED SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 158.38.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 158.38.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1681450225-1197477534=:35354 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable a fun=E7=E3o y=3Dlog(x) s=F3 est=E1 definida para valores de x > 0=0A=0Acom= o log 1 =3D 0 =3D=3D> log(log1) =3D n=E3o definido, assim letra D =0A=0A=0A= ----- Mensagem original ----=0ADe: arkon =0APara: obm-l <= obm-l@mat.puc-rio.br>=0AEnviadas: Quarta-feira, 12 de Dezembro de 2007 13:3= 6:31=0AAssunto: [obm-l] DOM=CDNIO DA FUN=C7=C3O=0A=0A=0AALGU=C9M PODE, POR = FAVOR, RESOLVER ESTA:=0A =0A(UFPB-71) O dom=EDnio da fun=E7=E3o definida po= r f(x) =3D log (log x) =E9:=0A =0Aa) O conjunto dos n=FAmeros reais maiores= que zero e menores que um.=0Ab) O conjunto dos n=FAmeros reais menores que= um.=0Ac) O conjunto dos n=FAmeros inteiros positivos.=0Ad) O conjunto dos = n=FAmeros reais maiores que um.=0Ae) O conjunto dos n=FAmeros irracionais.= =0A =0ADESDE J=C1 MUITO OBRIGADO=0A=0A=0A Abra sua conta no Yahoo! Mai= l, o =FAnico sem limite de espa=E7o para armazenamento!=0Ahttp://br.mail.ya= hoo.com/ --0-1681450225-1197477534=:35354 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
a fun=E7=E3o y=3Dlog(x) s=F3 est=E1 definida para= valores de x > 0
=0A
 
=0A
como log 1 = =3D 0 =3D=3D> log(log1) =3D n=E3o definido, assim letra D 

<= /DIV>=0A
----- Mensagem original ----
De: arkon <arkon@bol.c= om.br>
Para: obm-l <obm-l@mat.puc-rio.br>
Enviadas: Quarta-f= eira, 12 de Dezembro de 2007 13:36:31
Assunto: [obm-l] DOM=CDNIO DA FUN= =C7=C3O

=0A
=0A
=0A

ALGU=C9M PODE, = POR FAVOR, RESOLVER ESTA:

=0A

 

=0A

(UFPB-71) O dom=EDnio da fun=E7=E3o definida por f(x) =3D log (lo= g x) =E9:

=0A

&= nbsp;

=0A

a) O c= onjunto dos n=FAmeros reais maiores que zero e menores que um.

=0A

b) O conjunto dos= n=FAmeros reais menores que um.

=0A

c) O conjunto dos n=FAmeros inteiros positivos.=

=0A

d) O= conjunto dos n=FAmeros reais maiores que um.

=0A

e) O conjunto dos n=FAmeros irraci= onais.

=0A

&nbs= p;

=0A

DESDE J= =C1 MUITO OBRIGADO

=0A

 

=0A


=0A=0A=0A
Abra sua conta no Yahoo! Mail, o= =FAnico sem limite de espa=E7o para armazenamento! =0A --0-1681450225-1197477534=:35354-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 13:48:37 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCFic8l005769 for ; Wed, 12 Dec 2007 13:44:38 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCFibvL005766 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 13:44:37 -0200 Received: from web30109.mail.mud.yahoo.com (web30109.mail.mud.yahoo.com [209.191.69.41]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBCFiW8l005705 for ; Wed, 12 Dec 2007 13:44:33 -0200 Received: (qmail 41513 invoked by uid 60001); 12 Dec 2007 16:46:00 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=gWFwn1SyGkphJE9um2dcXP5g4UqNGUeAfCRkBoZa3ejsxCFZYUhHfr42fS8KEaH5RmrfDxJ0xOvhDLtqqGn/FxcWhfcwLHBN8Cyz3Cgwi7vnrmATFG/GdoEBDj9OMUaAKk56gCZ8yY4Fatpf00azeAyGj1Q+kFochfItJv2YppM=; X-YMail-OSG: MbuwXGcVM1mwHds8xe0gaj6pP08rr5zS8Dm3ks5YncAa59MYEQWHsDXosxWtX0al6WCoM4zDSLKd_9tG3vsauQ18SfgE4qObTVVmvtU3ybdxysLo.Ew- Received: from [201.63.131.82] by web30109.mail.mud.yahoo.com via HTTP; Wed, 12 Dec 2007 13:46:00 ART Date: Wed, 12 Dec 2007 13:46:00 -0300 (ART) From: Angelo Schranko Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20DOM=CDNIO=20DA=20FUN=C7=C3O?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <367511.38605.qm@web30109.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Angelo Schranko X-Spam-Status: Yes, hits=7.2 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,HTML_50_70,IN_REP_TO, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1407404149-1197477960=:38605" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 41.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 41.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1407404149-1197477960=:38605 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit O domínio de y = log(x) é x pertencente a ]0, 1[ U ]1, +infinito[ A imagem de y = log(x) é y pertencente ]-infinito, +infinito[ Dessa forma log[log(x)] = log(y). Ou seja, o domínio de log(y) é y > 0 e diferente de 1. Isso ocorre quando x > 1 arkon escreveu: ALGUÉM PODE, POR FAVOR, RESOLVER ESTA: (UFPB-71) O domínio da função definida por f(x) = log (log x) é: a) O conjunto dos números reais maiores que zero e menores que um. b) O conjunto dos números reais menores que um. c) O conjunto dos números inteiros positivos. d) O conjunto dos números reais maiores que um. e) O conjunto dos números irracionais. DESDE JÁ MUITO OBRIGADO --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1407404149-1197477960=:38605 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
O domínio de y = log(x) é x pertencente a ]0, 1[ U ]1, +infinito[
A imagem de y = log(x) é y pertencente ]-infinito, +infinito[
 
Dessa forma log[log(x)] = log(y).
 
Ou seja, o domínio de log(y) é y > 0 e diferente de 1.
Isso ocorre quando x > 1

arkon <arkon@bol.com.br> escreveu:
ALGUÉM PODE, POR FAVOR, RESOLVER ESTA:
 
(UFPB-71) O domínio da função definida por f(x) = log (log x) é:
 
a) O conjunto dos números reais maiores que zero e menores que um.
b) O conjunto dos números reais menores que um.
c) O conjunto dos números inteiros positivos.
d) O conjunto dos números reais maiores que um.
e) O conjunto dos números irracionais.
 
DESDE JÁ MUITO OBRIGADO
 

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1407404149-1197477960=:38605-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 12 14:11:29 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBCG5X8l013369 for ; Wed, 12 Dec 2007 14:05:41 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBCG5RWg013363 for obm-l-MllGbsmmN; Wed, 12 Dec 2007 14:05:27 -0200 Received: from web30104.mail.mud.yahoo.com (web30104.mail.mud.yahoo.com [209.191.69.36]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBCG4m8l013316 for ; Wed, 12 Dec 2007 14:04:48 -0200 Received: (qmail 59134 invoked by uid 60001); 12 Dec 2007 17:06:16 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=H5bD3JTSudIWOTlqesHIEI5hhtCMRYNSG79eRCvULWRIaakMg8JmQWrXS1f2nE4ZhqVKvbC6bCehkPUfUZxS6MBfAQ1RkW3iMQdQ32kGTHC8i6KmzJxOlocMlubLGFSAX0MFn6dmp1j+lDATrR6VXe1t0M2Wb1ah42BvffPKbxg=; X-YMail-OSG: lb7Pd4kVM1lg6i8QjNaPyB2bQ9Uf_7aHxfgPy2ZxNlhbU4Ha_3YKTLH98eEvNRY.KdPrkQkHooJHwKHptlLv5wqMtyaxV3zT0x802uiGqrzAv6rG27XA9aUgsAw_hg-- Received: from [201.63.131.82] by web30104.mail.mud.yahoo.com via HTTP; Wed, 12 Dec 2007 14:06:15 ART Date: Wed, 12 Dec 2007 14:06:15 -0300 (ART) From: Angelo Schranko Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20DOM=CDNIO=20DA=20FUN=C7=C3O?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <958222.58364.qm@web30104.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Angelo Schranko X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,HTML_50_70,IN_REP_TO, MIME_BOUND_DIGITS_5,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-397354936-1197479175=:58364" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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De forma mais prática, pense assim: considere f:R->R \ f(x) = log[log(x)] Se x <= 0, log(x) não está definida. Se 0 < x <= 1, log(x) <= 0, portanto log[log(x)] não está definida. Se x > 1, log(x) > 0 e portanto log[log(x)] existe. Logo x > 1 arkon escreveu: ALGUÉM PODE, POR FAVOR, RESOLVER ESTA: (UFPB-71) O domínio da função definida por f(x) = log (log x) é: a) O conjunto dos números reais maiores que zero e menores que um. b) O conjunto dos números reais menores que um. c) O conjunto dos números inteiros positivos. d) O conjunto dos números reais maiores que um. e) O conjunto dos números irracionais. DESDE JÁ MUITO OBRIGADO --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-397354936-1197479175=:58364 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Desculpe, cometi um erro nas condições da última resposta ...

De forma mais prática, pense assim: considere f:R->R \ f(x) = log[log(x)]
Se x <= 0, log(x) não está definida.
Se 0 < x <= 1, log(x) <= 0, portanto log[log(x)] não está definida.
Se x > 1, log(x) > 0 e portanto log[log(x)] existe.
Logo x > 1

arkon <arkon@bol.com.br> escreveu:
ALGUÉM PODE, POR FAVOR, RESOLVER ESTA:
 
(UFPB-71) O domínio da função definida por f(x) = log (log x) é:
 
a) O conjunto dos números reais maiores que zero e menores que um.
b) O conjunto dos números reais menores que um.
c) O conjunto dos números inteiros positivos.
d) O conjunto dos números reais maiores que um.
e) O conjunto dos números irracionais.
 
DESDE JÁ MUITO OBRIGADO
 

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-397354936-1197479175=:58364-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 04:48:06 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBD6hW8l009151 for ; Thu, 13 Dec 2007 04:43:32 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBD6hV0M009149 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 04:43:31 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.245]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBD6hM8l009056 for ; Thu, 13 Dec 2007 04:43:24 -0200 Received: by hs-out-2122.google.com with SMTP id 4so574640hsl.13 for ; Wed, 12 Dec 2007 23:44:51 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=zS4vJxlWAxlUSvQcfloGIGY5GXIFXyPh2C8rEswDovk=; b=JaYiI9mqME6TqxH4OA+jIuNnW8XQ7BB/Mcxp4u9bJlFw+fSFR5N58ZqRJlacF5S9ynLn6SfiZYMh1i2vWVbrYQGz0IypeCdJfuYj/Snb3HEWxJ9R55il2mFpnRRaE1NBv+34571w+AIRus1poQAcFm7TKjIG5CTLZmoZN1FQf0w= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=JKbQIZrBsHYCxxGHqTDRnM9W01OxmxkmqSaeCSLSWpUI63eSH9N+oflNyzImsGYwapaiELmBMF/jRv+eliOSXl0hsFnXHhXSEhogSGZWb/Xpej7QV+sRT6qt8FH/yQFOya1XRi/R9eXyMf9R3uebcdD5gu8F5DLYK6HpO+YGYxE= Received: by 10.150.225.14 with SMTP id x14mr529972ybg.153.1197531890765; Wed, 12 Dec 2007 23:44:50 -0800 (PST) Received: by 10.150.158.20 with HTTP; Wed, 12 Dec 2007 23:44:50 -0800 (PST) Message-ID: <5bb472220712122344h3a07ef0av2a3dff6270a1e5e7@mail.gmail.com> Date: Thu, 13 Dec 2007 05:44:50 -0200 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Geometria Plana In-Reply-To: <824486.26917.qm@web56603.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <475C4088.3000203@gmail.com> <824486.26917.qm@web56603.mail.re3.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBD6hR8l009119 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Você pode usar um ponto auxiliar P e tentar forma um Triângulo Equilátero ACP. Observando os ângulos e os lados, verificamos que os triangulos ABP e ACD são congruentes e o ânuglo BPC tem 160º e é o angulo do vértice do Triangulo Isosceles BPC. Logo BCD tem 10º. JVB. On 12/10/07, Gustavo Souza wrote: > como saber o seno de 40 e seno de 100??? > > > > > > "arcguede@gmail.com" escreveu: > Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na > reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD = > 40º calcule o valor do angulo B^CD, sabendo que AB=CD ... > > Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar > uma força... > > Estou enviando um link com a foto do triangulo nela, kem kiser ver pra > fikar melhor... > > Obrigado > > http://img155.imageshack.us/my.php?image=triangulonw3.jpg > > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! Olá gustavo. > Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do > triângulo é de 180°, então > > 100 + ( 40 + x ) + y = 180 > > ou seja > > y = 40 - x > > Usando agora a lei dos senos, temos que > > CD/sen(100) = AD/sen(40) > > ou > > AD = [ sen(40)/sen(100) ] CD > > e tambem temos que > > CD/sen(y) = DB/sen(x) > > ou > > DB = [ sen(x)/sen(y) ] CD > > como AD + DB = AB = CD, então > > AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD => > > => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1 > > Mas y= 40 - x, portanto > > sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100) > > logo, teremos > > [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } = > 1 => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ] > => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40) > ]/sen(100) => > > [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) - > sen(40) ] => > > sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] => > > cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) = > = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) - > sen(40) ] } > > ou ainda > > tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] } > > e assim > > x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] }) > > Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado > de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos > que simplificar o último termo para ser uma tangente. > Qualquer dúvida, pode mandar. > Até mais. > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 09:06:14 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDB4A8l024052 for ; Thu, 13 Dec 2007 09:04:10 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDB49ic024049 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 09:04:09 -0200 Received: from web56610.mail.re3.yahoo.com (web56610.mail.re3.yahoo.com [66.196.97.54]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBDB448l023995 for ; Thu, 13 Dec 2007 09:04:05 -0200 Received: (qmail 92361 invoked by uid 60001); 13 Dec 2007 12:05:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=3W0b9KB8nHdiIFEyXV94VcraUIOvdw2UHcFvgtZaMRP1VVBTA6yICpRI4u7dy5igiQpilDjPOoU9mKNrWj8n5Kes/3jyfFVB2+883AYrUOQT66NCrgN9Tw1SL4BenAe3X9yOFKHWvYtvq4NL6yDQmOPAY4/K7H64RZttPrt9AHk=; X-YMail-OSG: MowU98YVM1nD7y9MyDNK_Z_u8.XdwhWTBd0vRTZbPPHSd_JUHxlxhNt1X2HpuJZgkKM1aLMWQk8rwLuUCTus0lOozQNvuzxYORST6jT7_dS_lopvfDGbxBCA7xjbZ9VX_UggUkgDuC3pHMg- Received: from [201.20.206.79] by web56610.mail.re3.yahoo.com via HTTP; Thu, 13 Dec 2007 09:05:33 ART Date: Thu, 13 Dec 2007 09:05:33 -0300 (ART) From: Gustavo Souza Subject: [SPAM] Re: [obm-l] Geometria Plana To: obm-l@mat.puc-rio.br In-Reply-To: <5bb472220712122344h3a07ef0av2a3dff6270a1e5e7@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <991167.91728.qm@web56610.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Gustavo Souza X-Spam-Status: Yes, hits=7.7 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,MIME_BOUND_DIGITS_5, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-249885928-1197547533=:91728" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 54.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 54.97.196.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-249885928-1197547533=:91728 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Achei muito interessante a sua resolução, obrigado pela ajuda... Porem tentei desenhar e ver como que acontece e não consigo achar a congruencia entre o triangulos ABP e ACD, tambem não consigo achar onde irá ficar o ponto P... E vlw a TODOS pela ajuda... Joao Victor Brasil escreveu: Você pode usar um ponto auxiliar P e tentar forma um Triângulo Equilátero ACP. Observando os ângulos e os lados, verificamos que os triangulos ABP e ACD são congruentes e o ânuglo BPC tem 160º e é o angulo do vértice do Triangulo Isosceles BPC. Logo BCD tem 10º. JVB. On 12/10/07, Gustavo Souza wrote: > como saber o seno de 40 e seno de 100??? > > > > > > "arcguede@gmail.com" escreveu: > Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na > reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD = > 40º calcule o valor do angulo B^CD, sabendo que AB=CD ... > > Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar > uma força... > > Estou enviando um link com a foto do triangulo nela, kem kiser ver pra > fikar melhor... > > Obrigado > > http://img155.imageshack.us/my.php?image=triangulonw3.jpg > > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! Olá gustavo. > Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do > triângulo é de 180°, então > > 100 + ( 40 + x ) + y = 180 > > ou seja > > y = 40 - x > > Usando agora a lei dos senos, temos que > > CD/sen(100) = AD/sen(40) > > ou > > AD = [ sen(40)/sen(100) ] CD > > e tambem temos que > > CD/sen(y) = DB/sen(x) > > ou > > DB = [ sen(x)/sen(y) ] CD > > como AD + DB = AB = CD, então > > AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD => > > => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1 > > Mas y= 40 - x, portanto > > sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100) > > logo, teremos > > [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } = > 1 => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ] > => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40) > ]/sen(100) => > > [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) - > sen(40) ] => > > sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] => > > cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) = > = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) - > sen(40) ] } > > ou ainda > > tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] } > > e assim > > x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] }) > > Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado > de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos > que simplificar o último termo para ser uma tangente. > Qualquer dúvida, pode mandar. > Até mais. > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-249885928-1197547533=:91728 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Achei muito interessante a sua resolução, obrigado pela ajuda...
 
Porem tentei desenhar e ver como que acontece e não consigo achar a congruencia entre o triangulos ABP e ACD, tambem não consigo achar onde irá ficar o ponto P...
 
E vlw a TODOS pela ajuda...
 


Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Você pode usar um ponto auxiliar P e tentar forma um Triângulo
Equilátero ACP. Observando os ângulos e os lados, verificamos que os
triangulos ABP e ACD são congruentes e o ânuglo BPC tem 160º e é o
angulo do vértice do Triangulo Isosceles BPC.

Logo BCD tem 10º.

JVB.


On 12/10/07, Gustavo Souza wrote:
> como saber o seno de 40 e seno de 100???
>
>
>
>
>
> "arcguede@gmail.com" escreveu:
> Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na
> reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD =
> 40º calcule o valor do angulo B^CD, sabendo que AB=CD ...
>
> Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar
> uma força...
>
> Estou enviando um link com a foto do triangulo nela, kem kiser ver pra
> fikar melhor...
>
> Obrigado
>
> http://img155.imageshack.us/my.php?image=triangulonw3.jpg
>
>
>
> ---------------------------------
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento! Olá gustavo.
> Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do
> triângulo é de 180°, então
>
> 100 + ( 40 + x ) + y = 180
>
> ou seja
>
> y = 40 - x
>
> Usando agora a lei dos senos, temos que
>
> CD/sen(100) = AD/sen(40)
>
> ou
>
> AD = [ sen(40)/sen(100) ] CD
>
> e tambem temos que
>
> CD/sen(y) = DB/sen(x)
>
> ou
>
> DB = [ sen(x)/sen(y) ] CD
>
> como AD + DB = AB = CD, então
>
> AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD =>
>
> => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1
>
> Mas y= 40 - x, portanto
>
> sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100)
>
> logo, teremos
>
> [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } =
> 1 =>
>
> sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ]
> =>
>
> sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40)
> ]/sen(100) =>
>
> [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) -
> sen(40) ] =>
>
> sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] =>
>
> cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) =
> = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) -
> sen(40) ] }
>
> ou ainda
>
> tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] -
> sen(40) ] }
>
> e assim
>
> x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] -
> sen(40) ] })
>
> Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado
> de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos
> que simplificar o último termo para ser uma tangente.
> Qualquer dúvida, pode mandar.
> Até mais.
>
>
> =========================================================================
> Instruções para entrar na lista, sair da lista e usar a lista em
> http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> =========================================================================
>
>
> ---------------------------------
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento!

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-249885928-1197547533=:91728-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 10:06:54 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDC5b8l003029 for ; Thu, 13 Dec 2007 10:05:37 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDC5bck003027 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 10:05:37 -0200 Received: from web56608.mail.re3.yahoo.com (web56608.mail.re3.yahoo.com [66.196.97.52]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBDC5Y8l003023 for ; Thu, 13 Dec 2007 10:05:35 -0200 Received: (qmail 4055 invoked by uid 60001); 13 Dec 2007 13:07:03 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=OcnjH7hUGhUrvWmJKFmnBtkox+9QhSY+KVlH1ZZBo4lMpiE342ex23Z++zDZeTTv/wtY94QFxzme1XDWHPYlzqjuGn9GvSrZl1IZvJg6GJEiM/z5zpN+8t4jZkcZAMO4pPu/F3ZpGNtHGED3bLRodMotp4BbECwo7l41/WKv8uA=; X-YMail-OSG: xrL2GiYVM1kGdAvzjSRxU2LaoxJiDfnIr_AKVsDC9K6PR6KZZoZhm6fWfuWT695bL9kIG4jtpetHtWneH9UoLPMYoAAAwhxFyNASA.LprdW35DqfrzBY_b.mnb7tXyY9KWQT0Kfp_57egvk- Received: from [201.20.206.79] by web56608.mail.re3.yahoo.com via HTTP; Thu, 13 Dec 2007 10:07:02 ART Date: Thu, 13 Dec 2007 10:07:02 -0300 (ART) From: Gustavo Souza Subject: [SPAM] Re: [obm-l] Geometria Plana To: obm-l@mat.puc-rio.br In-Reply-To: <991167.91728.qm@web56610.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <594873.4017.qm@web56608.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Gustavo Souza X-Spam-Status: Yes, hits=6.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-767038869-1197551222=:4017" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.90 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 52.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 52.97.196.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-767038869-1197551222=:4017 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit =P Dexa queto, já achei a congruencia e todo o resto... Brigadão + uma vez Gustavo Souza escreveu: Achei muito interessante a sua resolução, obrigado pela ajuda... Porem tentei desenhar e ver como que acontece e não consigo achar a congruencia entre o triangulos ABP e ACD, tambem não consigo achar onde irá ficar o ponto P... E vlw a TODOS pela ajuda... Joao Victor Brasil escreveu: Você pode usar um ponto auxiliar P e tentar forma um Triângulo Equilátero ACP. Observando os ângulos e os lados, verificamos que os triangulos ABP e ACD são congruentes e o ânuglo BPC tem 160º e é o angulo do vértice do Triangulo Isosceles BPC. Logo BCD tem 10º. JVB. On 12/10/07, Gustavo Souza wrote: > como saber o seno de 40 e seno de 100??? > > > > > > "arcguede@gmail.com" escreveu: > Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na > reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD = > 40º calcule o valor do angulo B^CD, sabendo que AB=CD ... > > Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar > uma força... > > Estou enviando um link com a foto do triangulo nela, kem kiser ver pra > fikar melhor... > > Obrigado > > http://img155.imageshack.us/my.php?image=triangulonw3.jpg > > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! Olá gustavo. > Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do > triângulo é de 180°, então > > 100 + ( 40 + x ) + y = 180 > > ou seja > > y = 40 - x > > Usando agora a lei dos senos, temos que > > CD/sen(100) = AD/sen(40) > > ou > > AD = [ sen(40)/sen(100) ] CD > > e tambem temos que > > CD/sen(y) = DB/sen(x) > > ou > > DB = [ sen(x)/sen(y) ] CD > > como AD + DB = AB = CD, então > > AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD => > > => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1 > > Mas y= 40 - x, portanto > > sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100) > > logo, teremos > > [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } = > 1 => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ] > => > > sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40) > ]/sen(100) => > > [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) - > sen(40) ] => > > sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] => > > cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) = > = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) - > sen(40) ] } > > ou ainda > > tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] } > > e assim > > x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] - > sen(40) ] }) > > Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado > de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos > que simplificar o último termo para ser uma tangente. > Qualquer dúvida, pode mandar. > Até mais. > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-767038869-1197551222=:4017 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
=P
Dexa queto, já achei a congruencia e todo o resto...
Brigadão + uma vez


Gustavo Souza <gustavoandre2006site@yahoo.com.br> escreveu:
Achei muito interessante a sua resolução, obrigado pela ajuda...
 
Porem tentei desenhar e ver como que acontece e não consigo achar a congruencia entre o triangulos ABP e ACD, tambem não consigo achar onde irá ficar o ponto P...
 
E vlw a TODOS pela ajuda...
 


Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Você pode usar um ponto auxiliar P e tentar forma um Triângulo
Equilátero ACP. Observando os ângulos e os lados, verificamos que os
triangulos ABP e ACD são congruentes e o ânuglo BPC tem 160º e é o
angulo do vértice do Triangulo Isosceles BPC.

Logo BCD tem 10º.

JVB.


On 12/10/07, Gustavo Souza wrote:
> como saber o seno de 40 e seno de 100???
>
>
>
>
>
> "arcguede@gmail.com" escreveu:
> Gustavo Souza escreveu: Seja o triângulo ABC e o ponto D contido na
> reta AB. Seja tambem o valor de BÂC = 100º e o valor e o valor de A^CD =
> 40º calcule o valor do angulo B^CD, sabendo que AB=CD ...
>
> Ae gente, tentei pra caramba resolver esse + naum rolou, quem puder dar
> uma força...
>
> Estou enviando um link com a foto do triangulo nela, kem kiser ver pra
> fikar melhor...
>
> Obrigado
>
> http://img155.imageshack.us/my.php?image=triangulonw3.jpg
>
>
>
> ---------------------------------
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento! Olá gustavo.
> Se chamarmos de y o ângulo D^BC, teremos que como soma total dos ângulos do
> triângulo é de 180°, então
>
> 100 + ( 40 + x ) + y = 180
>
> ou seja
>
> y = 40 - x
>
> Usando agora a lei dos senos, temos que
>
> CD/sen(100) = AD/sen(40)
>
> ou
>
> AD = [ sen(40)/sen(100) ] CD
>
> e tambem temos que
>
> CD/sen(y) = DB/sen(x)
>
> ou
>
> DB = [ sen(x)/sen(y) ] CD
>
> como AD + DB = AB = CD, então
>
> AD + DB = [ sen(40)/sen(100) ] CD + [ sen(x)/sen(y) ] CD = CD =>
>
> => [ sen(40)/sen(100) ] + [ sen(x)/sen(y) ] = 1
>
> Mas y= 40 - x, portanto
>
> sen(y) = sen( 40 - x ) = sen(40) cos(x) + sen(x) cos(100)
>
> logo, teremos
>
> [ sen(40)/sen(100) ] + { sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] } =
> 1 =>
>
> sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = 1 - [ sen(40)/sen(100) ]
> =>
>
> sen(x)/[ sen(40) cos(x) + sen(x) cos(100) ] = [ sen(100) - sen(40)
> ]/sen(100) =>
>
> [ sen(40) cos(x) + sen(x) cos(100) ]/sen(x) = sen(100)/[ sen(100) -
> sen(40) ] =>
>
> sen(40) cotg(x) + cos(100) = sen(100)/[ sen(100) - sen(40) ] =>
>
> cotg(x) = { sen(100)/[ sen(100) - sen(40) ] - cos(100) }/sen(40) =
> = { sen(100) - cos(100)[ sen(100) - sen(40) ] }/{ sen(40)[ sen(100) -
> sen(40) ] }
>
> ou ainda
>
> tg(x) = { sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] -
> sen(40) ] }
>
> e assim
>
> x = arctg({ sen(40) [ sen(100) - sen(40) ] }/{ sen(100)[ 1 - cos(100) ] -
> sen(40) ] })
>
> Eu tô meio sem tempo, se esperar eu envio a simplificação deste emaranhado
> de senos e cossenos, mas para resumir a opera, o valor de x é esse, só temos
> que simplificar o último termo para ser uma tangente.
> Qualquer dúvida, pode mandar.
> Até mais.
>
>
> =========================================================================
> Instruções para entrar na lista, sair da lista e usar a lista em
> http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> =========================================================================
>
>
> ---------------------------------
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento!

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-767038869-1197551222=:4017-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 10:37:24 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDCaH8l006355 for ; Thu, 13 Dec 2007 10:36:17 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDCaHsn006352 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 10:36:17 -0200 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDCaF8l006345 for ; Thu, 13 Dec 2007 10:36:15 -0200 Received: by nf-out-0910.google.com with SMTP id k4so747535nfd.19 for ; Thu, 13 Dec 2007 05:37:40 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=aTvinCuPIFyjBKWvMNp2mqGMyqmcXLPiCKUnJb5vLvc=; b=WvCuXze/E2E2pr37UUeVl+Cm+urcSS8lQSFye6oTkkhl5BkGvAIYtaiQ57QYBU/L5Tss8SRWceqDa7phfMrblthDg7zLM1okofiAVlCBF0lElr8AJS79ZagCPVP1JZ/UBQqZYX3PSB6VSSbF1bzdgi0AdKNfABsjauHMlOlXyKU= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=I3yUnC0fbyIdvBJxqCoA92/Q9MaJyyoTXA2snayMlz35W0E5rqmEmZB5ZYHaACdsu25lc0wmLxQots1YP+dUKAXkwSUoOFjdfUf175VIUSM3gzJpEfs7BHuIxqz4DVseM0qjAoCAnfk2og9964UTNHR/1SC3X0LvogBexFIFO18= Received: by 10.78.81.20 with SMTP id e20mr2307865hub.60.1197553060473; Thu, 13 Dec 2007 05:37:40 -0800 (PST) Received: by 10.78.134.12 with HTTP; Thu, 13 Dec 2007 05:37:40 -0800 (PST) Message-ID: <71c5e1520712130537k3df371f2o4d344b0d85bda894@mail.gmail.com> Date: Thu, 13 Dec 2007 11:37:40 -0200 From: "Nicolau C. Saldanha" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Um_problema_de_c=F4nicas?= In-Reply-To: <267706.20647.qm@web63303.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <267706.20647.qm@web63303.mail.re1.yahoo.com> X-Google-Sender-Auth: b29c7d7e27951f6c Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBDCaG8l006349 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Nicolau C. Saldanha" X-Spam-Status: No, hits=3.2 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** On Dec 6, 2007 4:06 PM, João Pedro de Gusmão Silva wrote: > Amigos me ajudem nos seguintes exercícios: > > 1) Por um ponto J exterior a uma elipse tracemos as retas tangentes à > elipse, JM e JN, onde M e N são os pontos de tangência. Seja P o ponto > médio de MN, mostre que a reta JP passa pelo centro dessa cônica. Aplique uma transformação afim para transformar a elipse em um círculo. Note que retas tangentes são levadas em retas tangentes, centro em centro e ponto médio em ponto médio. Note também que para um círculo o problema é trivial. > 2) Análogo ao anterior para hipérbole. Dá para provar por argumentos abstratos que se a coisa dá certo para toda elipse deve necessariamente dar certo para uma hipérbole também. Mas acho que o mais fácil é fazer por analítica. Aplique uma transformação afim para que a hipérbole seja xy = 1. Se o ponto J = (a,b) estiver no primeiro quadrante devemos ter ab < 1. Aplique transformação linear da forma diagonal(c,1/c) para ver que você pode supor que o ponto J tenha a forma (d,d), 0 < d < 1. O resultado segue por simetria em relação à reta y=x. Se o ponto J estiver no segundo quadrante a transformação linear diz que podemos supor J = (-d,d) e agora o resultado segue por simetria em relação à reta y=-x. O terceiro quadrante é análogo ao primeiro e o quarto é análogo ao segundo. Se o ponto J estiver em um dos eixos a situação é um pouco degenerada pois uma das tangentes vira uma assíntota e o correspondente ponto de tangência foge para infinito. Mesmo assim dá certo. > 3) O aconteceria se a cônica fosse uma parábola? A reta JP fica paralela ao eixo da parábola. N. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 11:06:26 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDD5K8l007803 for ; Thu, 13 Dec 2007 11:05:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDD5KOw007801 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 11:05:20 -0200 Received: from relay2.uol.com.br (relay2.uol.com.br [200.221.4.109]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDD5J8l007796 for ; Thu, 13 Dec 2007 11:05:19 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper2.uol.com.br (Postfix) with ESMTP id A2957E014455 for ; Thu, 13 Dec 2007 12:06:49 -0200 (BRST) Received: from uol.com.br (whisky1.mail.sys.intranet [172.26.5.85]) by sniper2.uol.com.br (Postfix) with ESMTP id 7D49FE0144FE for ; Thu, 13 Dec 2007 12:06:49 -0200 (BRST) Date: Thu, 13 Dec 2007 12:06:49 -0200 Message-Id: Subject: [obm-l] =?iso-8859-1?b?cXVlc3TjbyBkYSBPQk0gN6ogLSBUZXJjZWlyYSA=?= =?iso-8859-1?b?RmFzZQ==?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197554809.2A.420560.42.2378.52.42.007.2002286711" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.1.10.93 X-SIG5: 8e5eed7e6e5f2cc1cf4f9084c0bdfea6 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197554809.2A.420560.42.2378.52.42.007.2002286711 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Colegas.... A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM, mas para = um aluno de 7=AA e 8=AA parece-me complicada... N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia, que infel= izmente n=E3o ensinei profundamente aos meus alunos. Vou ter que ensinar melhor em 2008, creio que at=E9 invari=E2ncia. Grato --_=__=_XaM3_.1197554809.2A.420560.42.2378.52.42.007.2002286711 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Colegas....
 
A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM, mas= para um aluno de 7=AA e 8=AA parece-me complicada...
 
N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia, que= infelizmente n=E3o ensinei profundamente aos meus alunos.
 
Vou ter que ensinar melhor em 2008, creio que at=E9 invari=E2ncia.<= /DIV>
 
 
Grato
--_=__=_XaM3_.1197554809.2A.420560.42.2378.52.42.007.2002286711-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 12:53:08 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDEpL8l025614 for ; Thu, 13 Dec 2007 12:51:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDEpLdx025612 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 12:51:21 -0200 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDEpK8l025608 for ; Thu, 13 Dec 2007 12:51:20 -0200 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 75B9AE006BC3 for ; Thu, 13 Dec 2007 13:52:50 -0200 (BRST) Received: from bol.com.br (whisper5.mail.sys.intranet [172.26.5.77]) by salsa3.bol.com.br (Postfix) with ESMTP id 4533CE005D21 for ; Thu, 13 Dec 2007 13:52:50 -0200 (BRST) Date: Thu, 13 Dec 2007 13:52:50 -0200 Message-Id: Subject: [obm-l] VALOR DO DETERMINANTE MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197561170.2A.144066.42.4101.52.42.007.501953999" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 640aba0ab5474d467d87a958b459590c Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.2 required=5.0 tests=AWL,BIG_FONT,GAPPY_TEXT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1197561170.2A.144066.42.4101.52.42.007.501953999 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Algu=E9m pode, por favor, resolver esta (EEAR) Se n e p s=E3o n=FAmeros inteiros e positivos, com n > p > 1, e C,= A e P s=E3o, respectivamente, combina=E7=E3o, arranjo e permuta=E7=E3o, = ent=E3o o valor do determinante |Cn,p An,p | |1 Pp | , =E9: a) 1. b) 0. c) n. d) p. DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1197561170.2A.144066.42.4101.52.42.007.501953999 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">Algu=E9m pode, por favor, r= esolver esta

<= B style=3D"mso-bidi-font-weight: normal"> 

=

<= B style=3D"mso-bidi-font-weight: normal">(EEAR) Se n e p s=E3o n=FAmeros inteiros e po= sitivos, com n > p > 1, e C, A e P s=E3o, respectivamente, combina=E7= =E3o, arranjo e permuta=E7=E3o, ent=E3o o valor do determinante

<= B style=3D"mso-bidi-font-weight: normal">    |Cn,p    An,p  |

<= B style=3D"mso-bidi-font-weight: normal">    |1      =        Pp  | , =E9:

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">a) 1.   &n= bsp;  b) 0.  &nbs= p; c) n.    d) p.

<= B style=3D"mso-bidi-font-weight: normal"> 

DESDE J= =C1 MUITO OBRIGADO

--_=__=_XaM3_.1197561170.2A.144066.42.4101.52.42.007.501953999-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 13:33:21 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDFVF8l029068 for ; Thu, 13 Dec 2007 13:31:15 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDFVEd6029066 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 13:31:14 -0200 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDFVC8l029059 for ; Thu, 13 Dec 2007 13:31:12 -0200 Received: by nf-out-0910.google.com with SMTP id k4so813937nfd.19 for ; Thu, 13 Dec 2007 08:32:42 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=83i2W5lmKgNjdBcJEB4vlBk/oeBe61CQxVihlx2TNP8=; b=SRcGlGwwmwBCRtIVq7tAIdySQ6+W2zD9eDylT/Zp/reZ+vi+1bTuNF3d3n56MraIPBAhWb6utyjFA8krID52usLJjVZG+o9axteC33PleNyMSSp0qIJfJjFMDoPhKmrauN+wKcp0Hz5wodbYlcu2ptNPkrX4ssS2TmUcijzAxMM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=MYomNyuLm7kQ36/68E9WbzzxInfkvn7FkQGrbACnGsLIlwnKS488jwHFyWLegWBZw7ILDF2JVvVUUcXaf+c7wsPU1ap1x/fu8Jf2vV3lFn8yLrw5OAJfFP0QXVkTGfdM07N3bd61l+XroEHxzNAnNGmWMxwUHBaOpDz31x3/4rw= Received: by 10.82.138.6 with SMTP id l6mr5729166bud.20.1197563146613; Thu, 13 Dec 2007 08:25:46 -0800 (PST) Received: by 10.82.154.3 with HTTP; Thu, 13 Dec 2007 08:25:46 -0800 (PST) Message-ID: Date: Thu, 13 Dec 2007 14:25:46 -0200 From: "=?ISO-8859-1?Q?Sim=E3o_Pedro?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] VALOR DO DETERMINANTE In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_33172_2013476.1197563146611" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Sim=E3o_Pedro?=" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,BIG_FONT,GAPPY_TEXT,HTML_50_70,IN_REP_TO, LINES_OF_YELLING,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_33172_2013476.1197563146611 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Resposta: b) 0. Em 13/12/07, arkon escreveu: > > * > > Algu=E9m pode, por favor, resolver esta > > > * > > *(EEAR) Se n e p s=E3o n=FAmeros inteiros e positivos, com n > p > 1, e C= , A e > P s=E3o, respectivamente, combina=E7=E3o, arranjo e permuta=E7=E3o, ent= =E3o o valor do > determinante* > > * |Cn,p An,p |* > > * |1 Pp | , =E9:* > > * * > > *a) 1. b) 0. c) n. d) p.* > > * * > > *DESDE J=C1 MUITO OBRIGADO* > --=20 Publicidade obrigat=F3ria: www.flogao.com.br/simaopedro Fiquem na paz! ------=_Part_33172_2013476.1197563146611 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
 
Resposta: b) 0.
 
 


 
Em 13/12/07, arkon <arkon@bol.com.br>= escreveu:

Algu=E9m pode,&nbs= p;por favor, resolver esta

 

<= font face=3D"Times New Roman">(EEAR) Se n e p s=E3o n=FAmeros= inteiros e positivos, com n > p > 1, e C, A e P s=E3o, respectivamen= te, combina=E7=E3o, arranjo e permuta=E7=E3o, ent=E3o o valor do determinan= te

<= font face=3D"Times New Roman">    |Cn,p&n= bsp;   An,p  |

<= font face=3D"Times New Roman">    |1 = ;            = Pp  | , =E9:

 

<= font face=3D"Times New Roman">a) 1.      b) 0.    c) n.    d) p.

 

DESDE J=C1 MUITO OBRIGADO




--
Publicidade obrigat=F3ria: www.flogao.com.br/simaopedro
Fiquem na paz!=20 ------=_Part_33172_2013476.1197563146611-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 13:45:28 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDFhs8l029660 for ; Thu, 13 Dec 2007 13:43:54 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDFhs7C029658 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 13:43:54 -0200 Received: from sc2.he.tucows.com (smtpout2009.sc2.he.tucows.com [64.97.155.9]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDFhr8l029650 for ; Thu, 13 Dec 2007 13:43:53 -0200 Received: from [201.9.227.15] by sc2.he.tucows.com with HTTP; Thu, 13 Dec 2007 16:45:17 +0000 Date: Thu, 13 Dec 2007 14:45:17 -0200 Message-ID: <4758778F0000FC1A@mail05.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] soma de quadrados - trigonometria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 201.9.227.15 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBDFhs8l029656 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.1 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 9.155.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 9.155.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Encontre o valor da soma S=(tg1º)^2+(tg3°)^2+(tg5°)^2+...+(tg89°)^2. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 15:00:44 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDGxP8l003178 for ; Thu, 13 Dec 2007 14:59:25 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDGxPnj003176 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 14:59:25 -0200 Received: from web30115.mail.mud.yahoo.com (web30115.mail.mud.yahoo.com [209.191.69.47]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBDGxM8l003172 for ; Thu, 13 Dec 2007 14:59:23 -0200 Received: (qmail 81268 invoked by uid 60001); 13 Dec 2007 18:00:51 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=25jKAAk/itqMLK17EIfnyREv9AsQo2JNlSiJFYJfWAWWu1M0AHqcoT/o22wZR2SLKDKiqzO4AQScpxzlLir1ZPCOOgaIASP2B/uBez58a/XAxfCxHVrcPU/hvAmhw3gt4D797kod8IuECoY2zTkXSZomFkchig5hFxWPQ0nomFw=; X-YMail-OSG: c.Ufz08VM1kBljVl0ur.HZYYbOuOIq8nGf0btO3OKbc2xEnc3xx97pTnTXRCsNWXP6Uiu_LbaCHMFlu9jRW26xjsHnUJ0bBKLMo5ZF7nS_VqQ_g3tQY- Received: from [201.63.131.82] by web30115.mail.mud.yahoo.com via HTTP; Thu, 13 Dec 2007 15:00:44 ART Date: Thu, 13 Dec 2007 15:00:44 -0300 (ART) From: Angelo Schranko Subject: [SPAM] Re: [obm-l] VALOR DO DETERMINANTE To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <2391.80340.qm@web30115.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Angelo Schranko X-Spam-Status: Yes, hits=7.5 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,GAPPY_TEXT,HTML_50_70, IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2038183982-1197568844=:80340" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 47.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 47.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2038183982-1197568844=:80340 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Pp.Cn,p = An,p, logo a resposta é 0 Simão Pedro escreveu: Resposta: b) 0. Em 13/12/07, arkon escreveu: Alguém pode, por favor, resolver esta (EEAR) Se n e p são números inteiros e positivos, com n > p > 1, e C, A e P são, respectivamente, combinação, arranjo e permutação, então o valor do determinante |Cn,p An,p | |1 Pp | , é: a) 1. b) 0. c) n. d) p. DESDE JÁ MUITO OBRIGADO -- Publicidade obrigatória: www.flogao.com.br/simaopedro Fiquem na paz! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2038183982-1197568844=:80340 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Pp.Cn,p = An,p, logo a resposta é 0

Simão Pedro <sp.eureka@gmail.com> escreveu:
 
Resposta: b) 0.
 
 


 
Em 13/12/07, arkon <arkon@bol.com.br> escreveu:
Alguém pode, por favor, resolver esta
 
(EEAR) Se n e p são números inteiros e positivos, com n > p > 1, e C, A e P são, respectivamente, combinação, arranjo e permutação, então o valor do determinante
    |Cn,p    An,p  |
    |1             Pp  | , é:
 
a) 1.      b) 0.    c) n.    d) p.
 
DESDE JÁ MUITO OBRIGADO



--
Publicidade obrigatória: www.flogao.com.br/simaopedro
Fiquem na paz!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2038183982-1197568844=:80340-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 18:41:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDKcZ8l012184 for ; Thu, 13 Dec 2007 18:38:35 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDKcZJn012182 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 18:38:35 -0200 Received: from smtp107.mail.mud.yahoo.com (smtp107.mail.mud.yahoo.com [209.191.85.217]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBDKcW8l012178 for ; Thu, 13 Dec 2007 18:38:33 -0200 Received: (qmail 1781 invoked from network); 13 Dec 2007 21:04:59 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:Content-Transfer-Encoding:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=D9ERwzIXokrnip+op+pATCTmOfBeUb3/MdRd3tVKpwtlGsBnd2/+VtgrxzjzJfvH8FfL96VjueUJRb7ZDTClLHyxi0lC7xSX15v7xWu3IGRp+BRNhBNq6v07Y5o3LCZzh83PvLQhte+00fYsbK4VDBKOScFV9tRIckBrd5Q8peA= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp107.mail.mud.yahoo.com with SMTP; 13 Dec 2007 21:04:56 -0000 X-YMail-OSG: wVvA1VEVM1lGDLjADV2q5LSgFgyyElYJZqErrSlDS5DfS2j5OMz7N9KuVBoOlTIZ1.SBAPO0MFVqdiFMLdinwclholujnOQOdL4NF4bjpq6cTlAdIxI- Message-ID: <005c01c83dd4$4d59c8f0$02270269@rodrigo7a25356> From: To: References: <4758778F0000FC1A@mail05.sc2.he.tucows.com> Subject: [SPAM] Re: [obm-l] soma de quadrados - trigonometria Date: Thu, 13 Dec 2007 19:05:29 -0300 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="ISO-8859-15"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,NO_REAL_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 217.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 217.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Eu não sei se a sua soma requer alguma propriedade trigonométrica diferente das usuais encontradas em qualquer livro... se não requer, realmente, não consegui avançar muito nela até agora... ----- Original Message ----- From: To: Sent: Thursday, December 13, 2007 1:45 PM Subject: [obm-l] soma de quadrados - trigonometria > Encontre o valor da soma S=(tg1º)^2+(tg3°)^2+(tg5°)^2+...+(tg89°)^2. > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 13 20:02:27 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDM0C8l025553 for ; Thu, 13 Dec 2007 20:00:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBDM0C8C025548 for obm-l-MllGbsmmN; Thu, 13 Dec 2007 20:00:12 -0200 Received: from nz-out-0506.google.com (nz-out-0506.google.com [64.233.162.224]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBDM098l025508 for ; Thu, 13 Dec 2007 20:00:10 -0200 Received: by nz-out-0506.google.com with SMTP id z6so482703nzd.9 for ; Thu, 13 Dec 2007 15:01:39 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=o40TNKHeaQffZ7X6e0sVWXCzDVUOKCVGMe64SG8tLe8=; b=qyRx1lFTyzCqPsI1bcu18bwfXKX6YQdhjjkQV+jZBHLu9JtXM5fu/tc3BjSX4NXxPeyj5v2JsoiprlLBqk7fyTFNnposbXpTWbSI+MwRRLXj8giRLfz/0aleNwvc9lbuUV9xARYNeZGI5Z3TBcg6tKfCjoCp7+bEH9wMy9HqPI4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=fQ85YmZqini5L78BG+G2d6i7kPf1VYtqza+FBRjGIsci0evPuTFYainnwCzIjXdgD0YjCqIzCn5UxLiX9rWSKeWkUnJoQtVzPpezrmoojv2RSpsodJJbOO6HLzWLoeD32uVO5dEHReAmxbd9jt1dWqiwRiU8Pxq1AVyH3DeChiU= Received: by 10.142.98.18 with SMTP id v18mr1262531wfb.61.1197586898176; Thu, 13 Dec 2007 15:01:38 -0800 (PST) Received: by 10.142.108.14 with HTTP; Thu, 13 Dec 2007 15:01:38 -0800 (PST) Message-ID: Date: Thu, 13 Dec 2007 21:01:38 -0200 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] soma de quadrados - trigonometria In-Reply-To: <4758778F0000FC1A@mail05.sc2.he.tucows.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_36652_2895537.1197586898171" References: <4758778F0000FC1A@mail05.sc2.he.tucows.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_36652_2895537.1197586898171 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline S=3Dsomatg(2n+1)^2(n=3D0,44) z=3Dcos(2n+1)+isen(2n+1) senx=3Di(z-cosx) -(z-cosx)^2+cosx^2=3D1 -z^2+2zcosx-1=3D0 cosx=3D(z^2+1)/2z tgx=3Di(z-(z^2+1)/2z)=3Di(z^2-1)/2z=3Di(z-1/z) tgx^2=3D-(z^2-2+1/z^2)=3D-2cos2(2n+1) +2 S=3Dsoma(2-2cos2(2n+1))(n=3D0,44) =3D88-2soma(cos2(2n+1))(n=3D0,44)=3D =3D88-soma((1+cos(2n+1)) -(1-cos(2n+1))=3D =3D88-2somacos(2n+1)(n=3D0,44) que e uma soma de cossenos em PA, que e tabelada. On 12/13/07, cauchy@globo.com wrote: > > Encontre o valor da soma S=3D(tg1=BA)^2+(tg3=B0)^2+(tg5=B0)^2+...+(tg89= =B0)^2. > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_36652_2895537.1197586898171 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
S=3Dsomatg(2n+1)^2(n=3D0,44)
z=3Dcos(2n+1)+isen(2n+1)
senx=3Di(z-cosx)
-(z-cosx)^2+cosx^2=3D1
-z^2+2zcosx-1=3D0
cosx=3D(z^2+1)/2z
tgx=3Di(z-(z^2+1)/2z)=3Di(z^2-1)/2z=3Di(z-1/z)
tgx^2=3D-(z^2-2+1/z^2)=3D-2cos2(2n+1) +2
S=3Dsoma(2-2cos2(2n+1))(n=3D0,44)
=3D88-2soma(cos2(2n+1))(n=3D0,44)=3D
=3D88-soma((1+cos(2n+1)) -(1-cos(2n+1))=3D
=3D88-2somacos(2n+1)(n=3D0,44)
que e uma soma de cossenos em PA, que e tabelada.
 
On 12/13/07, cauchy@globo.com <cauchy@globo.com> wrote:
Encontre o valor da soma S=3D(tg= 1=BA)^2+(tg3=B0)^2+(tg5=B0)^2+...+(tg89=B0)^2.



=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista emhttp://www.mat= .puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_36652_2895537.1197586898171-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 13:35:42 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEFWe8l008321 for ; Fri, 14 Dec 2007 13:32:40 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEFWed2008318 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 13:32:40 -0200 Received: from relay2.uol.com.br (relay2.uol.com.br [200.221.4.109]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEFWc8l008312 for ; Fri, 14 Dec 2007 13:32:38 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper2.uol.com.br (Postfix) with ESMTP id 17192E013B3A for ; Fri, 14 Dec 2007 14:34:10 -0200 (BRST) Received: from uol.com.br (whisky10.mail.sys.intranet [172.26.5.21]) by sniper2.uol.com.br (Postfix) with ESMTP id C46B7E0138E9 for ; Fri, 14 Dec 2007 14:34:07 -0200 (BRST) Date: Fri, 14 Dec 2007 14:34:07 -0200 Message-Id: Subject: [obm-l] =?iso-8859-1?b?W29ibS1sXSBxdWVzdONvIGRhIE9CTQ==?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197650047.2A.987632.42.17482.52.42.007.1141967369" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.70.135.138 X-SIG5: 2b110da856296f222858cef16054718c Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197650047.2A.987632.42.17482.52.42.007.1141967369 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable > Colegas.... > > A respeito da quest=E3o (a^29 - 1)/a-1... para provar que h=E1 2007 fat= ores primos s=F3 por congru=EAncia??? > Grato > Vit=F3rio Gauss --_=__=_XaM3_.1197650047.2A.987632.42.17482.52.42.007.1141967369 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
> Colegas....
>
> A respeito da quest=E3o (a^29 - 1)/a-1... para provar que h=E1 = 2007 fatores primos
 
s=F3 por congru=EAncia???
 
> Grato
>
Vit=F3rio Gauss
--_=__=_XaM3_.1197650047.2A.987632.42.17482.52.42.007.1141967369-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 13:37:34 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEFZi8l008412 for ; Fri, 14 Dec 2007 13:35:44 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEFZiBY008410 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 13:35:44 -0200 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEFZh8l008393 for ; Fri, 14 Dec 2007 13:35:43 -0200 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 47CD2E006FE9 for ; Fri, 14 Dec 2007 14:37:14 -0200 (BRST) Received: from bol.com.br (whisper2.mail.sys.intranet [172.26.5.137]) by salsa3.bol.com.br (Postfix) with ESMTP id 180D7E006DA7 for ; Fri, 14 Dec 2007 14:37:14 -0200 (BRST) Date: Fri, 14 Dec 2007 14:37:14 -0200 Message-Id: Subject: [obm-l] ALGARISMO Z MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197650234.2A.83828.42.31501.52.42.007.1469955140" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.73 X-SIG5: bcf5f2e8461022158ef83712607fcf33 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.4 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,LINES_OF_YELLING_3,SPAM_PHRASE_00_01, SUPERLONG_LINE,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1197650234.2A.83828.42.31501.52.42.007.1469955140 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA: Em uma empresa, o acesso a uma =E1rea restrita =E9 feito digitando uma s= enha que =E9 mudada diariamente. Para a obten=E7=E3o da senha, utiliza-se= uma opera=E7=E3o matem=E1tica =93#=94 definida por a#b =3D 4a (a+2b). A senha a ser digitada =E9 o resultado da convers=E3o de um c=F3digo form= ado por tr=EAs algarismos, xyz, atrav=E9s da express=E3o x#(y#z). Sabendo= que a senha a ser digitada =E9 2660, e o c=F3digo correspondente =E9 52z= , ent=E3o o algarismo z =E9 a) 1. b) 3. c) 5. d) 7. e) 9. GABARITO LETRA B DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1197650234.2A.83828.42.31501.52.42.007.1469955140 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:<= /FONT>

 

 Em uma empresa, o acesso= a uma =E1rea restrita =E9 feito digitando uma senha que =E9 mudada diari= amente. Para a obten=E7=E3o da senha, utiliza-se uma opera=E7=E3o matem=E1= tica =93#=94 definida por a#b =3D 4a (a+2b).=

A senha a ser digitada =E9 o r= esultado da convers=E3o de um c=F3digo formado por tr=EAs algarismos, xyz= , atrav=E9s da express=E3o x#(y#z). Sabendo que a senha a ser digitada =E9= 2660, e o c=F3digo correspondente =E9 52z, ent=E3o o algarismo z =E9

 

a) 1.     b) 3.      = c) 5.    &n= bsp; d) 7.   &nbs= p;  e) 9.

 

GA= BARITO LETRA B

 

DESDE J=C1 MUITO OBRIGADO

--_=__=_XaM3_.1197650234.2A.83828.42.31501.52.42.007.1469955140-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 14:02:54 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEG0T8l009444 for ; Fri, 14 Dec 2007 14:00:29 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEG0TMA009442 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 14:00:29 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEG0P8l009438 for ; Fri, 14 Dec 2007 14:00:27 -0200 Received: by rv-out-0910.google.com with SMTP id c27so913480rvf.9 for ; Fri, 14 Dec 2007 09:01:56 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=un2eITpjRYn56QKaNdysjEKC46Q6j9hNEZHb1vj5HQs=; b=O6HPJAnheyZyuUI542Tif1ynPZl3OHi7gVn9lqYFeToybwN2/VisF2hoC8HHrUCWg/oSH/ayRtfuLX51QbXzF0l2jOO1eFOnh3FN9rDRz4Id6cw49FmwgwAV6iDICRra/WiDbCacwYqVTTvg8MUwS0Y1S2NkyVU24GW+8dGd0Mo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=UNy6xi8CEO0L2ri9cWIUdbZ0YTPjf5Fe8waDg9J1wgac86QNhJxv/Me0ItKLrqTK9hHXAmyKUxHWZOerHkeeeqDZtkzqrbtbPZKP1uLtyRtG19uFcTkwzpotsYiVWrQ2fi89IPGT1QGVt2hjvqydadwKBMhlJuG2zM1cEjPZW+w= Received: by 10.141.51.15 with SMTP id d15mr2022117rvk.118.1197651716099; Fri, 14 Dec 2007 09:01:56 -0800 (PST) Received: by 10.141.99.13 with HTTP; Fri, 14 Dec 2007 09:01:56 -0800 (PST) Message-ID: <99886d920712140901m20a6e117m277b50524554ddcd@mail.gmail.com> Date: Fri, 14 Dec 2007 18:01:56 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] ALGARISMO Z In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1658_31879408.1197651716065" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,BIG_FONT,IN_REP_TO,LINES_OF_YELLING,LINES_OF_YELLING_2, MAILTO_LINK,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_1658_31879408.1197651716065 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Basta resolver a equa=E7=E3o: 5#(2#z) =3D 2660. Ora, 5#(2#z) =3D 5#(4*2*(2+2*z)) =3D 5#(16 + 16z) =3D 4*5*(5+2*(16+16z)) =3D 740= + 640z Assim, temos 740 + 640z =3D 2660 <=3D=3D> z =3D 3 Abra=E7o Bruno 2007/12/14, arkon : > > *ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:* > > * * > > * Em uma empresa, o acesso a uma =E1rea restrita =E9 feito digitando uma = senha > que =E9 mudada diariamente. Para a obten=E7=E3o da senha, utiliza-se uma = opera=E7=E3o > matem=E1tica "#" definida por a#b =3D 4a (a+2b).* > > *A senha a ser digitada =E9 o resultado da convers=E3o de um c=F3digo for= mado > por tr=EAs algarismos, xyz, atrav=E9s da express=E3o x#(y#z). Sabendo que= a senha > a ser digitada =E9 2660, e o c=F3digo correspondente =E9 52z, ent=E3o o a= lgarismo z > =E9* > > * * > > *a) 1. b) 3. c) 5. d) 7. e) 9.* > > * * > > *GABARITO LETRA B* > > * * > > *DESDE J=C1 MUITO OBRIGADO* > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_1658_31879408.1197651716065 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Basta resolver a equa=E7=E3o: 5#(2#z) =3D 2660.

Ora,
5#(2#z) =3D = 5#(4*2*(2+2*z)) =3D 5#(16 + 16z) =3D 4*5*(5+2*(16+16z)) =3D 740 + 640z
<= br>Assim, temos
740 + 640z =3D 2660 <=3D=3D> z =3D 3

Abra= =E7o
Bruno

2007/12/14, arkon <arkon@bol.com.br>:

= ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:

 

=  Em uma empresa, o acesso a uma =E1rea = restrita =E9 feito digitando uma senha que =E9 mudada diariamente. Para a o= bten=E7=E3o da senha, utiliza-se uma opera=E7=E3o matem=E1tica "#" definida= por a#b =3D 4a (a+2b).

= A senha a ser digitada =E9 o resultado da co= nvers=E3o de um c=F3digo formado por tr=EAs algarismos, xyz, atrav=E9s da e= xpress=E3o x#(y#z). Sabendo que a senha a ser digitada =E9 2660, e o c=F3di= go correspondente =E9 52z, ent=E3o o algarismo z =E9

 

= a) 1. = ;    b) 3<= span style=3D"color: red;"> .       c) 5. =      d) 7.      <= /span>e) 9.

 

GABARITO LETRA = B

 

DESDE J=C1 MUITO OBRIGADO




--
Bruno FRAN=C7A DOS REIS=

msn: brunoreis666@hotma= il.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16

e^(pi= *i)+1=3D0 ------=_Part_1658_31879408.1197651716065-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 16:16:44 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEIDt8l022079 for ; Fri, 14 Dec 2007 16:13:55 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEIDtHE022077 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 16:13:55 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEIDs8l022072 for ; Fri, 14 Dec 2007 16:13:54 -0200 Received: from MAIL.mme.gov.br ([172.16.1.53] RDNS failed) by correio.mme.gov.br with Microsoft SMTPSVC(6.0.3790.3959); Fri, 14 Dec 2007 17:15:54 -0200 X-MimeOLE: Produced By Microsoft Exchange V6.5 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C83E85.BFA2561E" Subject: [obm-l] =?iso-8859-1?Q?Provar_que_esta_fun=E7=E3o_=E9_f_=E9_cont=EDnua?= Date: Fri, 14 Dec 2007 17:15:57 -0200 Message-ID: In-Reply-To: <99886d920712140901m20a6e117m277b50524554ddcd@mail.gmail.com> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: [obm-l] ALGARISMO Z Thread-Index: Acg+eMxVvIXhQxM6Sy+zZhz7m4+VRQADONTg From: "Artur Costa Steiner" To: X-OriginalArrivalTime: 14 Dec 2007 19:15:54.0457 (UTC) FILETIME=[BF818C90:01C83E85] X-TM-AS-Product-Ver: SMEX-8.0.0.1181-5.000.1023-15606.001 X-TM-AS-Result: No--0.919800-4.000000-31 X-TM-AS-User-Approved-Sender: No X-TM-AS-User-Blocked-Sender: No Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Artur Costa Steiner" X-Spam-Status: No, hits=4.9 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** This is a multi-part message in MIME format. ------_=_NextPart_001_01C83E85.BFA2561E Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Algu=E9m poderia me ajudar com este problema, ou indicar onde eu possa = achar ajuda? Tenho tentando resolver sem sucesso.=20 =20 Seja A um subconjunto de R^n com medida de Lebesgue m(A) < oo e seja x + = A a translacao de A pelo vetor x de R^n. Definamos f:R^n--> R por f(x) = =3D m(A Inter (x + A)). Mostre que f =E9 cont=EDnua. =20 Obrigado=20 Artur ------_=_NextPart_001_01C83E85.BFA2561E Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Algu=E9m poderia me=20 ajudar com este problema, ou indicar onde eu possa achar ajuda? Tenho = tentando=20 resolver sem sucesso. 
 
Seja A um=20 subconjunto de R^n com medida de Lebesgue m(A) < oo e seja x + A a = translacao=20 de A pelo vetor x de R^n. Definamos f:R^n--> R por f(x) =3D m(A Inter = (x + A)).=20 Mostre que f =E9 cont=EDnua.
 
Obrigado=20
Artur
------_=_NextPart_001_01C83E85.BFA2561E-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 16:45:58 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEIhk8l025508 for ; Fri, 14 Dec 2007 16:43:46 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEIhjLE025506 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 16:43:45 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEIhi8l025501 for ; Fri, 14 Dec 2007 16:43:45 -0200 Received: from MAIL.mme.gov.br ([172.16.1.53] RDNS failed) by correio.mme.gov.br with Microsoft SMTPSVC(6.0.3790.3959); Fri, 14 Dec 2007 17:45:44 -0200 X-MimeOLE: Produced By Microsoft Exchange V6.5 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" Subject: [obm-l] lim n --> oo x_n = a(1^a + 2^a +.....n^a)/[n^(a +1)] Date: Fri, 14 Dec 2007 17:45:51 -0200 Message-ID: In-Reply-To: <005c01c83dd4$4d59c8f0$02270269@rodrigo7a25356> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: [obm-l] soma de quadrados - trigonometria Thread-Index: Acg91mMApX3b5udoSCi7fDCxYDlyqgAr57zQ From: "Artur Costa Steiner" To: X-OriginalArrivalTime: 14 Dec 2007 19:45:44.0855 (UTC) FILETIME=[EAAA9A70:01C83E89] X-TM-AS-Product-Ver: SMEX-8.0.0.1181-5.000.1023-15606.001 X-TM-AS-Result: No--2.220300-4.000000-31 X-TM-AS-User-Approved-Sender: No X-TM-AS-User-Blocked-Sender: No Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBEIhj8l025504 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Artur Costa Steiner" X-Spam-Status: No, hits=4.9 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Se a <= -1, podemos mostrar, sem maiores dificuldades, que x_n --> oo Se a = 0, x_n --> 1 trivialmente Se a> 0, verificamos que x_n é uma sequencia de somas de Riemman da função x --> x^a, computadas sobre o intervalo [0,1], com relação a particoes cuja norma (comprimento do maior intervalo, no caso 1/n) tende a 0. Como x --> x^a é definida e contínua, logo integrável, em [0,1] para a >0, temos que x_n --> Integral (0 a 1) x^a dx = 1/(a + 1). Vemos, assim, que, para todo a >=0, x_n --> 1(a + 1). Minha duvida eh quando a esta em (-1, 0). A função x --> x^a continua tendo integral 1/(a +1) sobre [0,1], mas é integral impropria, pois a funcao nao eh definida e nao tem limite em x = 0 e nem mesmo eh limitada em (0,1]. Assim, o argumento das somas de Riemann nao eh mais valido. Mas acredito que o limite de x_n continua sendo 1/(a +1), embora nao tenha conseguido provar. Isto eh verdade? Se for, como podemos provar? No caso de a >0 (e, talvez, no caso a> -1), podemos ver x_n como uma sequencia de funcoes f_n de a que converge para funcao f(a) = 1/(a +1). Tentei analisar se a convergencia é uniforme, mas noa conclui. Alguma sugestao? Obrigado Artur ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 17:32:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEJUN8l030744 for ; Fri, 14 Dec 2007 17:30:23 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEJUM46030742 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 17:30:22 -0200 Received: from web53805.mail.re2.yahoo.com (web53805.mail.re2.yahoo.com [206.190.36.200]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBEJUK8l030695 for ; Fri, 14 Dec 2007 17:30:20 -0200 Received: (qmail 36741 invoked by uid 60001); 14 Dec 2007 20:25:06 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=wfpwj1xzQgq3xeNHQ70My8D+2EkWpIlTtZoY+FMGlzET3KDRqkQ1J9LjgRrKzy5wWhz+j9vtBBbZ9AMTzPTdo6oxzhMu6+XHYGh62jHmKMThWfh1hwouJOTrdC6/uBLGnybIN76waK+acKVE028+Yd+W/XjQzyNHE6j2R5mD194=; X-YMail-OSG: kDPHf5EVM1m0HLQWsSIpvvcWfVcwGp_FZVlu16e9tRrFwb2i_HVZBWevkDzxCMvbF9jSSTUYdri2d4QGginXugYnVrmhczsVQV2Cy1VC9F63Yd2ghp0iH2zhWhcgcwfmzhigq8skQyOqyXM- Received: from [200.148.246.234] by web53805.mail.re2.yahoo.com via HTTP; Fri, 14 Dec 2007 12:25:06 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Fri, 14 Dec 2007 12:25:06 -0800 (PST) From: Carlos Yuzo Shine Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re=3A_=5Bobm-l=5D_=5Bobm-l=5D_quest=E3o_da_OBM?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <272591.36332.qm@web53805.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Yuzo Shine X-Spam-Status: Yes, hits=9.0 required=5.0 tests=FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-476290008-1197663906=:36332" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 200.36.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 200.36.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-476290008-1197663906=:36332 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Na verdade, n=E3o. Uma id=E9ia =E9 fazer indutivamente: suponha que (a^29 -= 1)/(a - 1) tem k fatores primos distintos. Considere, ent=E3o, a^2 no luga= r de a: fatorando, obtemos=0A ((a^2)^29 - 1)/(a^2 - 1) =3D ((a^29 - 1)/(a = - 1))((a^29 + 1)/(a + 1))=0A=0AO mdc de a^29 + 1 com a^29 - 1 e a - 1 =E9 n= o m=E1ximo 2 (para observar isso, se d =E9 o mdc de a^29 + 1 e a - 1, basta= notar que se d divide a - 1 ent=E3o divide a^29 - 1 e, como d divide a^29 = + 1, d divide a diferen=E7a, que =E9 2), ent=E3o deve aparecer um fator pri= mo novo em (a^29 + 1)/(a + 1), que =E9 inteiro. Deste modo, ((a^2)^29 - 1)/= (a^2 - 1) tem mais um fator primo novo, tendo k+1 fatores primos.=0A=0AIsso= quser dizer que, digamos, ((2^(2^2007))^29 - 1)/(2^(2^2007) - 1) tem pelo = menos 2007 fatores primos (neste caso, a =3D 2^(2^2007)). Na =E9poca, t=EDn= hamos conseguido uma fatora=E7=E3o que mostra que h=E1 2007 primos distinto= s diretamente, mas n=E3o lembro exatamente como era. Algu=E9m se habilita?= =0A=0A[]'s=0AShine=0A=0A=0A----- Original Message ----=0AFrom: vitoriogauss= =0ATo: obm-l =0ASent: Frida= y, December 14, 2007 1:34:07 PM=0ASubject: [obm-l] [obm-l] quest=E3o da OBM= =0A=0A=0A> Colegas.... =0A> =0A> A respeito da quest=E3o (a^29 - 1)/a-1... = para provar que h=E1 2007 fatores primos=0A =0As=F3 por congru=EAncia???=0A= =0A> Grato =0A> =0AVit=F3rio Gauss=0A=0A=0A _________________________= ___________________________________________________________=0ANever miss a = thing. Make Yahoo your home page. =0Ahttp://www.yahoo.com/r/hs --0-476290008-1197663906=:36332 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Na verdade, n=E3o. Uma id=E9ia =E9 fazer indutiva= mente: suponha que (a^29 - 1)/(a - 1) tem k fatores primos distintos. Consi= dere, ent=E3o, a^2 no lugar de a: fatorando, obtemos
=0A
&nbs= p; ((a^2)^29 - 1)/(a^2 - 1) =3D ((a^29 - 1)/(a - 1))((a^29 + 1)/(a + 1= ))
=0A
 
=0A
O mdc de a^29 + 1 com a^29 - = 1 e a - 1 =E9 no m=E1ximo 2 (para observar isso, se d =E9 o mdc de a^29 + 1= e a - 1, basta notar que se d divide a - 1 ent=E3o divide a^29 - 1 e, como= d divide a^29 + 1, d divide a diferen=E7a, que =E9 2), ent=E3o deve aparec= er um fator primo novo em (a^29 + 1)/(a + 1), que =E9 inteiro. Deste modo, = ((a^2)^29 - 1)/(a^2 - 1) tem mais um fator primo novo, tendo k+1 fatores pr= imos.
=0A
 
=0A
Isso quser dizer que, diga= mos, ((2^(2^2007))^29 - 1)/(2^(2^2007) - 1) tem pelo menos 2007 fatores pri= mos (neste caso, a =3D 2^(2^2007)). Na =E9poca, t=EDnhamos conseguido uma f= atora=E7=E3o que mostra que h=E1 2007 primos distintos diretamente, mas n= =E3o lembro exatamente como era. Algu=E9m se habilita?
=0A
=  
=0A
[]'s
=0A
Shine

=0A
----- Original Message ----
From: vitoriogauss <vitoriogauss@uol= .com.br>
To: obm-l <obm-l@mat.puc-rio.br>
Sent: Friday, Dece= mber 14, 2007 1:34:07 PM
Subject: [obm-l] [obm-l] quest=E3o da OBM
=0A
=0A
> Colegas....
=0A
>
=0A
> A = respeito da quest=E3o (a^29 - 1)/a-1... para provar que h=E1 2007 fatores p= rimos
=0A
 
=0A
s=F3 por congru=EAncia???
=0A 
=0A
> Grato
=0A
>
=0A
= =0A
Vit=F3rio Gauss
=0A


= =0A
Be a better friend, newshound, and =0Aknow-it-all wit= h Yahoo! Mobile. Try it now.= --0-476290008-1197663906=:36332-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 18:06:56 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEK4e8l007709 for ; Fri, 14 Dec 2007 18:04:40 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEK4e4d007705 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 18:04:40 -0200 Received: from web53812.mail.re2.yahoo.com (web53812.mail.re2.yahoo.com [206.190.39.55]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBEK4c8l007667 for ; Fri, 14 Dec 2007 18:04:38 -0200 Received: (qmail 95494 invoked by uid 60001); 14 Dec 2007 21:06:08 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=I1YLpEK8/t0acx+QbUA5dbx4CvjUTDbhpV+F1jHYD56NnPdCZsPQ3nOaaEPjuvCuUxkPeJUt8wXmHmL14ManBKjCV/QD3H5NA2rerc9jGsZD0668QAibP/VqVxfLxY3fh/X90YHxxBw0OgemgO8WXHeIszl/oM+y08rv5WOn8KY=; X-YMail-OSG: ueGq2LEVM1mDPisiF_3G1IN5IACzJwofGCH0kO4_Bemc6cECrA34K4X8CDcvdKnH57ztWngqAK5aZK41yGM4d5TjMU2WGh0wmfq7X4YmWpTmgHudya7PsAih5kOCc5NklugUJgafiR5MS.E- Received: from [200.148.246.234] by web53812.mail.re2.yahoo.com via HTTP; Fri, 14 Dec 2007 13:06:08 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Fri, 14 Dec 2007 13:06:08 -0800 (PST) From: Carlos Yuzo Shine Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re=3A_=5Bobm-l=5D_=5Bobm-l=5D_quest=E3o_da_OBM?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <616142.94568.qm@web53812.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Yuzo Shine X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2095724980-1197666368=:94568" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 55.39.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 55.39.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2095724980-1197666368=:94568 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Ah, no e-mail anterior eu esqueci de provar que os primos de a^29 + 1 e a += 1 n=E3o se cortam todos. Mas =E9 s=F3 mais um trabalho de mdc (an=E1logo a= o anterior) provar que mdc(a + 1; (a^29 + 1)/(a + 1)) divide 29 e ver que a= ^29+1 =E9 muito maior do que a+1 para mostrar que n=E3o se cortam todos.=0A= =0ANesse =FAltimo mdc, eu admito que usar congru=EAncia =E9 mais r=E1pido; = todavia, n=E3o =E9 absolutamente necess=E1rio.=0A=0A[]'s=0AShine=0A=0A=0A--= --- Original Message ----=0AFrom: vitoriogauss =0A= To: obm-l =0ASent: Friday, December 14, 2007 1:34:07 = PM=0ASubject: [obm-l] [obm-l] quest=E3o da OBM=0A=0A=0A> Colegas.... =0A> = =0A> A respeito da quest=E3o (a^29 - 1)/a-1... para provar que h=E1 2007 fa= tores primos=0A =0As=F3 por congru=EAncia???=0A =0A> Grato =0A> =0AVit=F3ri= o Gauss=0A=0A=0A _____________________________________________________= _______________________________=0ANever miss a thing. Make Yahoo your home= page. =0Ahttp://www.yahoo.com/r/hs --0-2095724980-1197666368=:94568 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Ah, no e-mail anterior eu esqueci de provar que o= s primos de a^29 + 1 e a + 1 n=E3o se cortam todos. Mas =E9 s=F3 mais um tr= abalho de mdc (an=E1logo ao anterior) provar que mdc(a + 1; (a^29 + 1)/(a += 1)) divide 29 e ver que a^29+1 =E9 muito maior do que a+1 para mostrar que= n=E3o se cortam todos.
=0A
 
=0A
Nesse = =FAltimo mdc, eu admito que usar congru=EAncia =E9 mais r=E1pido; todavia, = n=E3o =E9 absolutamente necess=E1rio.
=0A
 
=0A[]'s
=0A
Shine

=0A
----- Original= Message ----
From: vitoriogauss <vitoriogauss@uol.com.br>
To: = obm-l <obm-l@mat.puc-rio.br>
Sent: Friday, December 14, 2007 1:34:= 07 PM
Subject: [obm-l] [obm-l] quest=E3o da OBM

=0A
=0A
&= gt; Colegas....
=0A
>
=0A
> A respeito da quest= =E3o (a^29 - 1)/a-1... para provar que h=E1 2007 fatores primos
=0A 
=0A
s=F3 por congru=EAncia???
=0A
 
= =0A
> Grato
=0A
>
=0A
=0A
Vit=F3rio= Gauss
=0A


=0A
Be a better friend, newshound, and =0Aknow-it-all with Yahoo! Mobile. = Try it now. --0-2095724980-1197666368=:94568-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 18:24:36 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBECNj8l025518 for ; Fri, 14 Dec 2007 10:23:46 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBECNiFv025512 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 10:23:44 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBECNb8l025427 for ; Fri, 14 Dec 2007 10:23:37 -0200 Received: from MAIL.mme.gov.br ([172.16.1.53] RDNS failed) by correio.mme.gov.br with Microsoft SMTPSVC(6.0.3790.3959); Fri, 14 Dec 2007 11:23:35 -0200 X-MimeOLE: Produced By Microsoft Exchange V6.5 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: text/plain Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Provar_que_esta_fun=E7=E3o_f_=E9_cont=EDnua?= Date: Fri, 14 Dec 2007 11:23:33 -0200 Message-ID: In-Reply-To: <2391.80340.qm@web30115.mail.mud.yahoo.com> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: [obm-l] VALOR DO DETERMINANTE Thread-Index: Acg9uO+7Su2g52e1Q/uTIhlnXJw7zwAmpULw From: "Artur Costa Steiner" To: X-OriginalArrivalTime: 14 Dec 2007 13:23:35.0558 (UTC) FILETIME=[87BD8A60:01C83E54] X-TM-AS-Product-Ver: SMEX-8.0.0.1181-5.000.1023-15604.003 X-TM-AS-Result: No--0.379500-4.000000-31 X-TM-AS-User-Approved-Sender: No X-TM-AS-User-Blocked-Sender: No Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Artur Costa Steiner" X-Spam-Status: Yes, hits=5.0 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C83E54.88065CD9" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.00 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 3959.3790.0.6.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 3959.3790.0.6.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------_=_NextPart_001_01C83E54.88065CD9 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Algu=E9m poderia me ajudar com este problema, ou indicar onde eu possa = achar ajuda? Tenho tentando resolver sem sucesso.=20 =20 Seja A um subconjunto de R^n com medida de Lebesgue m(A) < oo e seja x + = A a translacao de A pelo vetor x de R^n. Definamos f:R^n--> R por f(x) = =3D m(A Inter (x + A)). Mostre que f =E9 cont=EDnua. =20 Obrigado=20 Artur ------_=_NextPart_001_01C83E54.88065CD9 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Algu=E9m=20 poderia me ajudar com este problema, ou indicar onde eu possa achar = ajuda? Tenho=20 tentando resolver sem sucesso. 
 
Seja A um subconjunto de R^n com medida = de=20 Lebesgue m(A) < oo e seja x + A a translacao de A pelo vetor x de = R^n.=20 Definamos f:R^n--> R por f(x) =3D m(A Inter (x + A)). Mostre que f = =E9=20 cont=EDnua.
 
Obrigado
Artur
------_=_NextPart_001_01C83E54.88065CD9-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 19:37:16 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELZC8l018340 for ; Fri, 14 Dec 2007 19:35:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBELZCNv018338 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 19:35:12 -0200 Received: from relay3.uol.com.br (relay3.uol.com.br [200.221.4.110]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELZB8l018334 for ; Fri, 14 Dec 2007 19:35:11 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper3.uol.com.br (Postfix) with ESMTP id 089FAB000346 for ; Fri, 14 Dec 2007 20:36:43 -0200 (BRST) Received: from uol.com.br (whisky10.mail.sys.intranet [172.26.5.21]) by sniper3.uol.com.br (Postfix) with ESMTP id 7C634B00025A for ; Fri, 14 Dec 2007 20:36:40 -0200 (BRST) Date: Fri, 14 Dec 2007 20:36:40 -0200 Message-Id: Subject: [obm-l] email MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197671800.2A.754146.42.25414.52.42.007.391257429" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.70.135.138 X-SIG5: cffe7750f7da76db548294b523b7938d Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197671800.2A.754146.42.25414.52.42.007.391257429 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable >os email n=E3o estao aprecendo --_=__=_XaM3_.1197671800.2A.754146.42.25414.52.42.007.391257429 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
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--_=__=_XaM3_.1197671800.2A.754146.42.25414.52.42.007.391257429-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 19:37:16 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELZH8l018346 for ; Fri, 14 Dec 2007 19:35:17 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBELZHis018344 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 19:35:17 -0200 Received: from relay1.uol.com.br (relay1.uol.com.br [200.221.4.108]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELZG8l018335 for ; Fri, 14 Dec 2007 19:35:16 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper1.uol.com.br (Postfix) with ESMTP id A5A90F03F439 for ; Fri, 14 Dec 2007 20:36:47 -0200 (BRST) Received: from uol.com.br (whisky12.mail.sys.intranet [172.26.5.42]) by sniper1.uol.com.br (Postfix) with ESMTP id 7CD1CF05A4A4 for ; Fri, 14 Dec 2007 20:36:47 -0200 (BRST) Date: Fri, 14 Dec 2007 20:36:47 -0200 Message-Id: Subject: [obm-l] email MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197671807.2A.469153.42.25509.52.42.007.1742889446" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.70.135.138 X-SIG5: 95700648ce53a111fecccf558f166e98 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197671807.2A.469153.42.25509.52.42.007.1742889446 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable >os email n=E3o estao aprecendo --_=__=_XaM3_.1197671807.2A.469153.42.25509.52.42.007.1742889446 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
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--_=__=_XaM3_.1197671807.2A.469153.42.25509.52.42.007.1742889446-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 19:57:50 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELsi8l019393 for ; Fri, 14 Dec 2007 19:54:44 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBELsiD7019391 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 19:54:44 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBELsf8l019378 for ; Fri, 14 Dec 2007 19:54:42 -0200 Received: by rv-out-0910.google.com with SMTP id c27so998681rvf.9 for ; Fri, 14 Dec 2007 14:56:11 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=YaoLuHToJVf+NxbbU0/l1sAz9vAoFAmMtuzUtI8YSN0=; b=jz6DArZ42DHvod9xdyVHEZ0gWhco4f3WEu9ZIzxOEdtdLZvCtKPwtFzWiDxPvkLhH9QzKmWMB/wl2QAEsLdQQpf/0b7D9eP5u3oHDP/A2crg1HP9BUX0IntRbmFdSvO6beWu3pvmjLhFxYC2GWo1LHDbcvZGkc3ikCqvJbVb9bo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=MMEYdzHV+NSL1KEgXm2MslM7P82sCecUf9V0jixJuqyGhCxC8gDnAL6UEOGwFsNaMwO97k4EhJVjO57YVMYsfzVhF1A214LPlE+iizogke31YTDfsDHVPx91CvIUna3/cCezcndPbnQA85sHEP6cMZlJ1ABHjfATLRAOiAt2j00= Received: by 10.141.36.10 with SMTP id o10mr2278115rvj.176.1197672971942; Fri, 14 Dec 2007 14:56:11 -0800 (PST) Received: by 10.141.87.17 with HTTP; Fri, 14 Dec 2007 14:56:11 -0800 (PST) Message-ID: <2b5739960712141456p4075149cl8e456e2b2f7023ad@mail.gmail.com> Date: Fri, 14 Dec 2007 20:56:11 -0200 From: "Rogerio Ponce" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] lim n --> oo x_n = a(1^a + 2^a +.....n^a)/[n^(a +1)] In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <005c01c83dd4$4d59c8f0$02270269@rodrigo7a25356> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBELsh8l019381 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rogerio Ponce" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola' Artur, a expressao original era x_n = a(1^a + 2^a +.....n^a)/[n^(a +1)] Reescrevendo-a de outra forma temos: x_n = a [ (1/n)^a + (2/n)^a +.....(n/n)^a ] (1/n) Quando n-->oo , isso te lembra o que? []'s Rogerio Ponce PS: acho que voce esqueceu de computar o primeiro "a" no seu calculo. Em 14/12/07, Artur Costa Steiner escreveu: > Se a <= -1, podemos mostrar, sem maiores dificuldades, que x_n --> oo > > Se a = 0, x_n --> 1 trivialmente > > Se a> 0, verificamos que x_n é uma sequencia de somas de Riemman da função x --> x^a, computadas sobre o intervalo [0,1], com relação a particoes cuja norma (comprimento do maior intervalo, no caso 1/n) tende a 0. Como x --> x^a é definida e contínua, logo integrável, em [0,1] para a >0, temos que x_n --> Integral (0 a 1) x^a dx = 1/(a + 1). > > Vemos, assim, que, para todo a >=0, x_n --> 1(a + 1). > > Minha duvida eh quando a esta em (-1, 0). A função x --> x^a continua tendo integral 1/(a +1) sobre [0,1], mas é integral impropria, pois a funcao nao eh definida e nao tem limite em x = 0 e nem mesmo eh limitada em (0,1]. Assim, o argumento das somas de Riemann nao eh mais valido. Mas acredito que o limite de x_n continua sendo 1/(a +1), embora nao tenha conseguido provar. Isto eh verdade? Se for, como podemos provar? > > No caso de a >0 (e, talvez, no caso a> -1), podemos ver x_n como uma sequencia de funcoes f_n de a que converge para funcao f(a) = 1/(a +1). Tentei analisar se a convergencia é uniforme, mas noa conclui. Alguma sugestao? > > Obrigado > Artur > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 14 21:01:27 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBEMxF8l001771 for ; Fri, 14 Dec 2007 20:59:15 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBEMxFg9001768 for obm-l-MllGbsmmN; Fri, 14 Dec 2007 20:59:15 -0200 Received: from web36813.mail.mud.yahoo.com (web36813.mail.mud.yahoo.com [209.191.85.64]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBEMxB8l001721 for ; Fri, 14 Dec 2007 20:59:12 -0200 Received: (qmail 29176 invoked by uid 60001); 15 Dec 2007 00:00:41 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=VzEtKcR0gt3vTwOcjOxARrAqLJCRFz3wh0Y7cucx/biBJk7WFexrO4TNMkzeiHaJDYBiuuLBHTY65gPoV25WTuAlPfhl+crJFTjwy+qN6M+h/ICCpkM5ezdOAMV3qJkAWD+UR2WyjADj42yNzipBMvJEeqbAn5tr36f7NLi2EEI=; X-YMail-OSG: wqkVIdcVM1m2izv8fHu8Es18b8durc4PIc1krp_u.cV1HTa4YF90XPNDiLx76YnnEfm5pUZd2Weg6s_zUz16sqvYyj_lc1JVK7FTWEEU21RwcDH76anTusdTxPp6CQ-- Received: from [195.189.142.144] by web36813.mail.mud.yahoo.com via HTTP; Fri, 14 Dec 2007 16:00:40 PST Date: Fri, 14 Dec 2007 16:00:40 -0800 (PST) From: Artur Costa Steiner Subject: [SPAM] Re: [obm-l] lim n --> oo x_n = (1^a + 2^a +.....n^a)/[n^(a +1)] To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <974164.29061.qm@web36813.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: Yes, hits=5.6 required=5.0 tests=EMAIL_ATTRIBUTION,FORGED_YAHOO_RCVD,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: EMAIL_ATTRIBUTION (-1.6 points) BODY: Contains what looks like an email attribution SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 64.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 64.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Oh, foi um erro de digitacao. Nao tem aquele primeiro a.. Desculpe. Artur . --- Rogerio Ponce wrote: > Ola' Artur, > a expressao original era > x_n = a(1^a + 2^a +.....n^a)/[n^(a +1)] > > Reescrevendo-a de outra forma temos: > x_n = a [ (1/n)^a + (2/n)^a +.....(n/n)^a ] (1/n) > > Quando n-->oo , isso te lembra o que? > > []'s > Rogerio Ponce > > PS: acho que voce esqueceu de computar o primeiro > "a" no seu calculo. > > > > Em 14/12/07, Artur Costa > Steiner escreveu: > > Se a <= -1, podemos mostrar, sem maiores > dificuldades, que x_n --> oo > > > > Se a = 0, x_n --> 1 trivialmente > > > > Se a> 0, verificamos que x_n é uma sequencia de > somas de Riemman da função x --> x^a, computadas > sobre o intervalo [0,1], com relação a particoes > cuja norma (comprimento do maior intervalo, no caso > 1/n) tende a 0. Como x --> x^a é definida e > contínua, logo integrável, em [0,1] para a >0, temos > que x_n --> Integral (0 a 1) x^a dx = 1/(a + 1). > > > > Vemos, assim, que, para todo a >=0, x_n --> 1(a + > 1). > > > > Minha duvida eh quando a esta em (-1, 0). A função > x --> x^a continua tendo integral 1/(a +1) sobre > [0,1], mas é integral impropria, pois a funcao nao > eh definida e nao tem limite em x = 0 e nem mesmo eh > limitada em (0,1]. Assim, o argumento das somas de > Riemann nao eh mais valido. Mas acredito que o > limite de x_n continua sendo 1/(a +1), embora nao > tenha conseguido provar. Isto eh verdade? Se for, > como podemos provar? > > > > No caso de a >0 (e, talvez, no caso a> -1), > podemos ver x_n como uma sequencia de funcoes f_n de > a que converge para funcao f(a) = 1/(a +1). Tentei > analisar se a convergencia é uniforme, mas noa > conclui. Alguma sugestao? > > > > Obrigado > > Artur > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ____________________________________________________________________________________ Looking for last minute shopping deals? Find them fast with Yahoo! Search. http://tools.search.yahoo.com/newsearch/category.php?category=shopping ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 21:04:23 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBGMxa8l027575 for ; Sun, 16 Dec 2007 20:59:36 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBGMxaYq027573 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 20:59:36 -0200 Received: from bay0-omc2-s11.bay0.hotmail.com (bay0-omc2-s11.bay0.hotmail.com [65.54.246.147]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBGMxY8l027561 for ; Sun, 16 Dec 2007 20:59:35 -0200 Received: from BAY112-W29 ([64.4.26.129]) by bay0-omc2-s11.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sun, 16 Dec 2007 16:01:06 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_b31c10be-7663-4541-b94b-e0c900ce7d01_" X-Originating-IP: [201.37.214.138] From: Pedro Cardoso To: Subject: =?iso-8859-1?Q?[obm-l]_Combinat=F3ria?= Date: Mon, 17 Dec 2007 03:01:06 +0300 Importance: Normal In-Reply-To: References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> MIME-Version: 1.0 X-OriginalArrivalTime: 17 Dec 2007 00:01:06.0912 (UTC) FILETIME=[EC267600:01C8403F] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_b31c10be-7663-4541-b94b-e0c900ce7d01_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Bom, como minha quest=E3o n=E3o foi respondida, seguindo uma recomenda=E7= =E3o de decoro que algu=E9m da lista indicou, vou tentar de novo, e pela = =FAltima vez, expor minha d=FAvida. Se algu=E9m puder me indicar ao menos u= m livro ou t=F3pico que seja =FAtil =E0 quest=E3o, eu j=E1 estaria agradeci= do. =20 Quest=E3o: De quantas maneiras eu posso escrever um n=FAmero N como a soma = de parcelas, n=E3o importando a ordem delas? Como a pergunta pode ter sido = pouco clara, eu dou exemplos:[2] =3D 1+1 >> 1 maneira[3] =3D 1+1+1 =3D 1+2 = >> 2 maneiras[4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 2+2 >> 4 maneiras[5] =3D= 1+1+1+1+1 =3D 2+1+1+1 =3D 3+1+1 =3D 4+1 =3D 2+2+1 =3D 3+2 >> 6 maneiras ... [N] =3D ??? Obrigado, =20 Pedro Laz=E9ra Cardoso _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_b31c10be-7663-4541-b94b-e0c900ce7d01_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 
Bom, como minha quest=E3o n=E3o foi respondida, seguindo uma reco= menda=E7=E3o de decoro que algu=E9m da lista indicou, vou tentar de no= vo, e pela =FAltima vez, expor minha d=FAvida. Se algu=E9m puder me in= dicar ao menos um livro ou t=F3pico que seja =FAtil =E0 quest=E3o, eu&= nbsp;j=E1 estaria agradecido.
 
Quest=E3o:
 
De quantas maneiras eu posso escrever um n=FAmero N= como a soma de parcelas, n=E3o importando a ordem delas?
 
Como= a pergunta pode ter sido pouco clara, eu dou exemplos:

[2] =3D=  1+1 >> 1 maneira
[3] =3D 1+1+1 =3D 1+2 >> 2 = maneiras
[4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 2+2 >> 4 manei= ras
[5] =3D 1+1+1+1+1 =3D 2+1+1+1 =3D 3+1+1 =3D 4+1 =3D 2+2+1 =3D 3+2&nb= sp;>> 6 maneiras
...
[N] =3D ???

Obrigado,
 
Pedro Laz=E9ra Cardoso

Receba GR=C1TIS as mensa= gens do Messenger no seu celular quando voc=EA estiver offline. Conhe=E7a = o MSN Mobile! Crie j=E1 o seu! = --_b31c10be-7663-4541-b94b-e0c900ce7d01_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 22:47:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0hc8l002531 for ; Sun, 16 Dec 2007 22:43:39 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH0hc24002529 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 22:43:38 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.248]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0ha8l002525 for ; Sun, 16 Dec 2007 22:43:36 -0200 Received: by an-out-0708.google.com with SMTP id c31so485975ana.120 for ; Sun, 16 Dec 2007 17:45:08 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=uFHlDmNWIsb8YMkRjJ/l4stkeplNcmRsQfK02wiAeSQ=; b=tPcDSxyCMXZLrZep9gAjOPR7qXEw/Joh4KiqzXHdzhDYwqv4ADxL7C4P5Ubb0rdVoMYWCrtjhZ8uJ/MxIWq1RHRRbWmbj88m8bofD0yOnZH3bOwOi7sOGG77zaOYVv+XnOsrx2AOy4qjPlwBOk3MYNswv3CcGEVEHnXe8S9udzc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=PU9FIMBaeNSl23j5CZ/48GaSXoxkzACNmtIiH5j0he+mybyA0T9EpzVXAEL4Oh2Q1ebwhIyrbtkWq70QSIUiAY8FO9e2vAfS8HVY8x/esmaP2Opy0bxlyCDznx2ES9RIwxV9EYvdRGFnizOcwuvlVxPU9IjCuA52qBEP9pyRCEs= Received: by 10.100.207.5 with SMTP id e5mr13324079ang.103.1197855908643; Sun, 16 Dec 2007 17:45:08 -0800 (PST) Received: by 10.90.49.13 with HTTP; Sun, 16 Dec 2007 17:45:08 -0800 (PST) Message-ID: <2d483c770712161745o1590b502v6d84e02bef463f0e@mail.gmail.com> Date: Sun, 16 Dec 2007 23:45:08 -0200 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Combinat=F3ria?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_5612_16726574.1197855908637" References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=2.7 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_5612_16726574.1197855908637 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline A pergunta eh mais dificil do que parece, Pedro, talvez explicando o comportamento reticente do pessoal da lista. Mas achei algo informativo sobre esses "partition numbers": http://en.wikipedia.org/wiki/Partition_function_(number_theory) http://mathworld.wolfram.com/Partition.html http://www.research.att.com/~njas/sequences/A000041 Abraco, Ralph On Dec 16, 2007 10:01 PM, Pedro Cardoso wrote: > > Bom, como minha quest=E3o n=E3o foi respondida, seguindo uma recomenda=E7= =E3o de > decoro que algu=E9m da lista indicou, vou tentar de novo, e pela =FAltima= vez, > expor minha d=FAvida. Se algu=E9m puder me indicar ao menos um livro ou t= =F3pico > que seja =FAtil =E0 quest=E3o, eu j=E1 estaria agradecido. > > Quest=E3o: > > De quantas maneiras eu posso escrever um n=FAmero N como a soma de parcel= as, > n=E3o importando a ordem delas? > > Como a pergunta pode ter sido pouco clara, eu dou exemplos: > > [2] =3D 1+1 >> 1 maneira > [3] =3D 1+1+1 =3D 1+2 >> 2 maneiras > [4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 2+2 >> 4 maneiras > [5] =3D 1+1+1+1+1 =3D 2+1+1+1 =3D 3+1+1 =3D 4+1 =3D 2+2+1 =3D 3+2 >> 6 ma= neiras > ... > [N] =3D ??? > > Obrigado, > > Pedro Laz=E9ra Cardoso > > > ------------------------------ > Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA es= tiver > offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! > ------=_Part_5612_16726574.1197855908637 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
A pergunta eh mais dificil do que parece, Pedro, talvez explicando&nbs= p;o comportamento reticente do pessoal da lista. Mas achei algo inform= ativo sobre esses "partition numbers":
http://en.wikipedia.org/wiki/Partition_function_(number_theory)
 
Abraco,
          Ralph

On Dec 16, 2007 10:01 PM, Pedro Cardoso <pedrolazera@hotmail.com> wrot= e:
 
Bom, como minha quest=E3o n=E3o foi respondida, segui= ndo uma recomenda=E7=E3o de decoro que algu=E9m da lista indicou, vou = tentar de novo, e pela =FAltima vez, expor minha d=FAvida. Se algu=E9m= puder me indicar ao menos um livro ou t=F3pico que seja =FAtil =E0 qu= est=E3o, eu j=E1 estaria agradecido.
 
Quest=E3o:
 
De quantas maneiras eu posso escrever= um n=FAmero N como a soma de parcelas, n=E3o importando a ordem delas?
=  
Como a pergunta pode ter sido pouco clara, eu dou exemplos:<= br>
[2] =3D 1+1 >> 1 maneira
[3] =3D 1+1+1 =3D 1+2 >> 2 maneiras
[4] =3D 1+1+1+1 =3D 2= +1+1 =3D 3+1 =3D 2+2 >> 4 maneiras
[5] =3D 1+1+1+1+1 =3D 2+1+= 1+1 =3D 3+1+1 =3D 4+1 =3D 2+2+1 =3D 3+2 >> 6 maneiras
...
= [N] =3D ???

Obrigado,
 
Pedro Laz=E9ra Cardoso

Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu!

------=_Part_5612_16726574.1197855908637-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 22:51:09 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0lD8l002577 for ; Sun, 16 Dec 2007 22:47:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH0lCel002575 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 22:47:12 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.242]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0lA8l002572 for ; Sun, 16 Dec 2007 22:47:11 -0200 Received: by an-out-0708.google.com with SMTP id c31so486202ana.120 for ; Sun, 16 Dec 2007 17:48:43 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=rnr5qoq0SOf0EwyIsKBGIH0RLefg/Q/hJjYNwNbFDzc=; b=BnM2gEcALvTmiA8uyoDIN974s/jKmASw/96a4958Xw0sAE84pLtnA5E5UMo+1607YGOilojZPo8RsJIFBxVI4mdm5MA5uoTkmQ0kUShzsNx/dr6Lv0zNpNPDsNMna6TF94cEFNEqT+7BgbuAfDkcAdMxRNN0aYI0s9lcWNciWXM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=UB7Xd0ms/1A1eJ5OyaE11+cranBh0RfVaZ34+ghWWzRexlm0ZrzS0rq6TtMDnUjJ9MhikvnIXk1GsQMVJto2QObE//2tvhbEnv5lfB1eVCNmqmkzM4PpxouTU1nhiBvH5VK5Hf33dUOWNBVjNNUwpqJRm39Hm1um1kLGmmFChRQ= Received: by 10.100.8.10 with SMTP id 10mr13366719anh.59.1197856123304; Sun, 16 Dec 2007 17:48:43 -0800 (PST) Received: from svs ( [201.51.174.206]) by mx.google.com with ESMTPS id 67sm13804758wra.2007.12.16.17.48.40 (version=SSLv3 cipher=RC4-MD5); Sun, 16 Dec 2007 17:48:41 -0800 (PST) Message-ID: <000601c8404f$1dd7dfe0$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: "Lista OBM" Subject: [SPAM] [obm-l] =?Windows-1252?Q?C=F4nicas?= Date: Sun, 16 Dec 2007 23:49:45 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: Yes, hits=5.2 required=5.0 tests=QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Nicolau, Eu pensei nesta solução inicialmente mas não usei equacões parametrizadas. Obs: resposta demorada = trabalho + faculdade. Sérgio ========================================================= On Nov 24, 2007 4:36 PM, Sérgio Martins da Silva wrote: > Colegas, > > Como se demonstra que interseção de um plano com um cone é uma elipse, > parábola ou hipérbole? Tenho visto nos livros apenas a declaração disto mas > não o caminho. Suponho que você aceite usar geometria analítica e que você saiba que cônicas têm equações de grau 2 (e esta é uma das caracterizações mais importantes de cônicas). Uma forma então é observar que, tendo o cone a equação de 2o grau x^2+y^2=z^2, a interseção por um plano parametrizado por x=au+bv+c, y = du+ev+f, z = gu+hv+i é dada pela equação de 2o grau (au+bv+c)^2+(du+ev+f)^2=(gu+hv+i)^2, logo uma cônica. N. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 22:57:46 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0rl8l002789 for ; Sun, 16 Dec 2007 22:53:47 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH0rlgk002787 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 22:53:47 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.245]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH0rj8l002779 for ; Sun, 16 Dec 2007 22:53:46 -0200 Received: by an-out-0708.google.com with SMTP id c31so486721ana.120 for ; Sun, 16 Dec 2007 17:55:17 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:from:to:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=Ipr8viWb6U94SPEVoRmniI8mqzNbQ8KvWC9g2tTT6CU=; b=fYG2D+mi2OylMdWid7DoiZNzRDraXzL31MLcS3F78Ho9a2Cfsh6LYFBIHV7AY4q9o+lXA8zzhs1sAJYSnQTAg4gvwxCFNEtUaTNurEIAblhvy5EFpoBMhIBFzN6nPJ/zCkD7f64CPX4JbE4i5S2iRtw8bD2Jhpuc0FW9cH3KgTg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:from:to:subject:date:mime-version:content-type:content-transfer-encoding:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=cXBsVom9+Qe4h/QlMwk6R+yu/jeFnenseUoF83uvWw4HD7AKgZcuGYAV2QZI4zTUdm/QCj7YnA5lurieETkbSybm8dfxAFMsSa5/z5yDgb8wx9Bnkyu+ok9DwwS2ytqPH0i98bOfAJrtgOVaM9nyW5MLzi2tIWyj8CK9ippLqNA= Received: by 10.100.11.7 with SMTP id 7mr13374330ank.71.1197856517753; Sun, 16 Dec 2007 17:55:17 -0800 (PST) Received: from svs ( [201.51.174.206]) by mx.google.com with ESMTPS id 9sm16094114wrl.2007.12.16.17.55.14 (version=SSLv3 cipher=RC4-MD5); Sun, 16 Dec 2007 17:55:16 -0800 (PST) Message-ID: <000c01c84050$09433560$01fea8c0@svs> From: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= To: "Lista OBM" Subject: [SPAM] [obm-l] =?Windows-1252?Q?Demonstra=E7=F5es?= Date: Sun, 16 Dec 2007 23:56:23 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1914 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1914 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?Windows-1252?Q?S=E9rgio_Martins_da_Silva?= X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 245.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 245.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Doutores, Penso que a palavra mais comum nesta lista e, quiçá, da matemática é "demonstração". Por isto, gostaria de saber como se demonstra que uma demonstração está correta. E mais, que é completa. Quais são os requisitos, condições, etc ? Abraços, Sérgio ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 23:09:03 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH15E8l003146 for ; Sun, 16 Dec 2007 23:05:14 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH15DlN003144 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 23:05:13 -0200 Received: from smtp106.mail.mud.yahoo.com (smtp106.mail.mud.yahoo.com [209.191.85.216]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBH15A8l003141 for ; Sun, 16 Dec 2007 23:05:11 -0200 Received: (qmail 70963 invoked from network); 17 Dec 2007 02:06:43 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=1I0H7ts8SRjkN2N4Pamnou/JtF6hj0JKtsvZluK9brxRMFsjJSu5u4GSfos/6wlUJJJeS8YvpbMIB30ja53OZyfzVYn/WPgpdHDtVD5I6oB1VRnWPvHp0KWXbUE8RJUF6Dq7hdlPLjtRIjhWeqCeV0fg9dCAf4Xcz96k3azUeEk= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp106.mail.mud.yahoo.com with SMTP; 17 Dec 2007 02:06:39 -0000 X-YMail-OSG: _gba4u8VM1npiRfJiMlEL7IIRHQluyrVQEszrOyjOWZdWZVyKkNW05UYYaQf_aAQPvW8gaP_bzp6aAY8m812AGZV1Lr_eGE8yjx6HXWvOj3dJiTUOTA- Message-ID: <002a01c84059$f10f06e0$02270269@rodrigo7a25356> From: To: References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_Combinat=F3ria?= Date: Mon, 17 Dec 2007 00:07:18 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MAILTO_LINK,NO_REAL_NAME, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0027_01C84040.C98A5570" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (7.90 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 216.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 216.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0027_01C84040.C98A5570 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable N=E3o sei bem se =E9 isso, mas olhando superficialmente pode ter a ver = com o problema de parti=E7=F5es de ramanujan, a f=F3rmula =E9 bem = complexa... Se voc=EA levar em considera=E7=E3o o n=FAmero de parti=E7=F5es de um = conjunto de pedras, por exemplo, e colocar ainda como forma de arranjar = as parti=E7=F5es dessas pedras uma parti=E7=E3o com todas as pedras (em = outras palavras, se voc=EA considerar que no caso de 4 "uns", 4 + 0 seja = mais uma das maneiras; com 5 "uns", 5 + 0 seja mais uma das maneiras) = este ser=E1 exatamente o problema de ramanujan. Por exmeplo, num conjunto de 5 pedras, temos as seguintes parti=E7=F5es = distintas: 5 pedras separadas uma dupla mais 3 pedras separadas duas duplas mais uma pedra separada um trio mais duas pedras separadas um trio mais uma dupla um quarteto mais uma pedra separada 5 pedras juntas N=FAmero: 1 2 3 4 5 6 7 8 ... Parti=E7=F5es 1 2 3 5 7 11 15 22 ... Como o seu problema n=E3o conta N + 0 como uma "maneira" de somar as = parcelas, =E9 "s=F3" ( este =E9 um s=F3 bem pretencioso!) calcular o = n=FAmero de parti=E7=F5es e subtrair 1 do resultado.=20 Felizmente h=E1 a f=F3rmula de ramanujan-hardy para ajudar, mas a = f=F3rmula =E9 t=E3o grande e complexa que n=E3o tem como colocar em = texto aqui, ficaria quase incompreens=EDvel (procure na internet).=20 Sauda=E7=F5es ----- Original Message -----=20 From: Pedro Cardoso=20 To: obm-l@mat.puc-rio.br=20 Sent: Sunday, December 16, 2007 9:01 PM Subject: [obm-l] Combinat=F3ria Bom, como minha quest=E3o n=E3o foi respondida, seguindo uma = recomenda=E7=E3o de decoro que algu=E9m da lista indicou, vou tentar de = novo, e pela =FAltima vez, expor minha d=FAvida. Se algu=E9m puder me = indicar ao menos um livro ou t=F3pico que seja =FAtil =E0 quest=E3o, eu = j=E1 estaria agradecido. =20 Quest=E3o: =20 De quantas maneiras eu posso escrever um n=FAmero N como a soma de = parcelas, n=E3o importando a ordem delas? =20 Como a pergunta pode ter sido pouco clara, eu dou exemplos: [2] =3D 1+1 >> 1 maneira [3] =3D 1+1+1 =3D 1+2 >> 2 maneiras [4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 =3D 2+2 >> 4 maneiras [5] =3D 1+1+1+1+1 =3D 2+1+1+1 =3D 3+1+1 =3D 4+1 =3D 2+2+1 =3D 3+2 >> = 6 maneiras ... [N] =3D ??? Obrigado, =20 Pedro Laz=E9ra Cardoso -------------------------------------------------------------------------= ----- Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA = estiver offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! ------=_NextPart_000_0027_01C84040.C98A5570 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
N=E3o sei bem se =E9 isso, mas olhando = superficialmente pode=20 ter a ver com o problema de parti=E7=F5es de ramanujan, a f=F3rmula =E9 = bem=20 complexa...
 
Se voc=EA levar em considera=E7=E3o o n=FAmero = de parti=E7=F5es de um=20 conjunto de pedras, por exemplo, e colocar ainda como forma de arranjar = as=20 parti=E7=F5es dessas pedras uma parti=E7=E3o com todas as pedras (em = outras palavras, se=20 voc=EA considerar que no caso de 4 "uns", 4 + 0 seja mais uma das = maneiras; com 5=20 "uns", 5 + 0 seja mais uma das maneiras) este ser=E1 exatamente o = problema de=20 ramanujan.
 
Por exmeplo, num conjunto de 5 pedras, temos as = seguintes=20 parti=E7=F5es distintas:
 
5 pedras separadas
uma dupla mais 3 pedras separadas
duas duplas mais uma pedra separada
um trio mais duas pedras separadas
um trio mais uma dupla
um quarteto mais uma pedra separada
5 pedras juntas
 
N=FAmero:    1  2  = 3 =20 4   5   6  =  7    8 ...
Parti=E7=F5es  1  2  3 =  5  =20 7  11  15  22 ...
 
Como o seu problema n=E3o conta N + 0 como uma = "maneira" de=20 somar as parcelas, =E9 "s=F3" ( este =E9 um s=F3 bem pretencioso!) = calcular o n=FAmero de=20 parti=E7=F5es e subtrair 1 do resultado.
 
Felizmente h=E1 a f=F3rmula de ramanujan-hardy = para ajudar,=20 mas a f=F3rmula =E9 t=E3o grande e complexa que n=E3o tem como = colocar em texto=20 aqui, ficaria quase incompreens=EDvel (procure na internet). =
 
Sauda=E7=F5es
----- Original Message -----
From:=20 Pedro=20 Cardoso
Sent: Sunday, December 16, 2007 = 9:01=20 PM
Subject: [obm-l] = Combinat=F3ria


Bom, como minha quest=E3o n=E3o foi respondida, = seguindo uma=20 recomenda=E7=E3o de decoro que algu=E9m da lista indicou, vou = tentar de=20 novo, e pela =FAltima vez, expor minha d=FAvida. Se algu=E9m = puder me indicar=20 ao menos um livro ou t=F3pico que seja =FAtil =E0 quest=E3o, = eu j=E1 estaria=20 agradecido.
 
Quest=E3o:
 
De quantas maneiras = eu posso=20 escrever um n=FAmero N como a soma de parcelas, n=E3o importando a = ordem=20 delas?
 
Como a pergunta pode ter sido pouco clara, = eu dou=20 exemplos:

[2] =3D 1+1 >> 1 maneira
[3] =3D = 1+1+1 =3D=20 1+2 >> 2 maneiras
[4] =3D 1+1+1+1 =3D 2+1+1 =3D 3+1 = =3D=20 2+2 >> 4 maneiras
[5] =3D 1+1+1+1+1 =3D 2+1+1+1 =3D = 3+1+1 =3D 4+1 =3D=20 2+2+1 =3D 3+2 >> 6 maneiras
...
[N] =3D=20 ???

Obrigado,
 
Pedro Laz=E9ra = Cardoso

Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA = estiver=20 offline. Conhe=E7a o MSN Mobile! Crie j=E1=20 o seu! ------=_NextPart_000_0027_01C84040.C98A5570-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 16 23:22:03 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH1IG8l003695 for ; Sun, 16 Dec 2007 23:18:16 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH1IGMg003693 for obm-l-MllGbsmmN; Sun, 16 Dec 2007 23:18:16 -0200 Received: from smtp107.mail.mud.yahoo.com (smtp107.mail.mud.yahoo.com [209.191.85.217]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBH1IE8l003690 for ; Sun, 16 Dec 2007 23:18:14 -0200 Received: (qmail 31205 invoked from network); 17 Dec 2007 02:19:45 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=t1W7flg2F1Q/LykJXtugWNvaLYsaQTZH1kGTJ/3CKUHQT/8sk0lgT8uHQOpWJTISKjnlgZmgK900QT6PPiGLLQKVBEF/6z3GI/ma3BNAOrcoc6i/TS+1hPJfiDcrfRK1e8FrXrshWCszUoZ+D3VYhw89+5IoYG07J3NUOFKysDM= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp107.mail.mud.yahoo.com with SMTP; 17 Dec 2007 02:19:32 -0000 X-YMail-OSG: _cU89YkVM1nWCXApfD4ladROOWL4i3uwpJT2xrIqcRFvQzG5.0lhR5K6CzbJ2fbX1lwu16ZecWlxD8v7i04lKtg0p6XUFAN6ayXNsQNMhFI6xMf8cvw- Message-ID: <004f01c8405b$bda751c0$02270269@rodrigo7a25356> From: To: References: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_quest=E3o_da_OBM_7=AA_-_Terceira_Fase?= Date: Mon, 17 Dec 2007 00:20:09 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=8.0 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MAILTO_LINK,NO_REAL_NAME, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_004C_01C84042.953903A0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.00 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 217.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 217.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_004C_01C84042.953903A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable A pergunta =E9: de fato, algum(a) garoto(a) de 13 ou 14 anos resolveu = este problema durante a olimp=EDada? ----- Original Message -----=20 From: vitoriogauss=20 To: obm-l=20 Sent: Thursday, December 13, 2007 11:06 AM Subject: [obm-l] quest=E3o da OBM 7=AA - Terceira Fase Colegas.... A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM, mas = para um aluno de 7=AA e 8=AA parece-me complicada...=20 N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia, que = infelizmente n=E3o ensinei profundamente aos meus alunos. Vou ter que ensinar melhor em 2008, creio que at=E9 invari=E2ncia. Grato ------=_NextPart_000_004C_01C84042.953903A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
A pergunta =E9: de fato, algum(a) = garoto(a) de 13 ou=20 14 anos resolveu este problema durante a olimp=EDada?
----- Original Message -----
From:=20 vitoriogauss
To: obm-l
Sent: Thursday, December 13, = 2007 11:06=20 AM
Subject: [obm-l] quest=E3o da = OBM 7=AA -=20 Terceira Fase

Colegas....
 
A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM, = mas para um=20 aluno de 7=AA e 8=AA parece-me complicada...
 
N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia, = que infelizmente=20 n=E3o ensinei profundamente aos meus alunos.
 
Vou ter que ensinar melhor em 2008, creio que at=E9 = invari=E2ncia.
 
 
Grato
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Uma demonstração está correta se, em última instância, está de acordo com os axiomas mais básicos da matéria. Então, uma demonstração de demontração recorreria, também em última análise, exatamente aos mesmos axiomas, sendo assim redundante. Se você fala inglês, aqui está um fórum onde há diversos debates interessantes sobre esses assuntos, além de resolução técnica de questões de matemática, física química, engenharia em geral, etc... http://www.physicsforums.com/ abraços ----- Original Message ----- From: "Sérgio Martins da Silva" To: "Lista OBM" Sent: Sunday, December 16, 2007 10:56 PM Subject: [obm-l] Demonstrações > Doutores, > > Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > "demonstração". Por isto, gostaria de saber como se demonstra que uma > demonstração está correta. E mais, que é completa. Quais são os > requisitos, > condições, etc ? > > Abraços, > > Sérgio > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 02:19:42 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH4Ej8l015722 for ; Mon, 17 Dec 2007 02:14:45 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH4EjKs015720 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 02:14:45 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.251]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH4Eh8l015714 for ; Mon, 17 Dec 2007 02:14:44 -0200 Received: by an-out-0708.google.com with SMTP id c31so498611ana.120 for ; Sun, 16 Dec 2007 21:16:17 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=O8J71/H1bAw081PybxQpw36Xjd3Z3SAcOTPef2tkbEE=; b=AL67XhYxl9k7Mkq8TCmN8TsUhpkByS0Tvygj43txicdyq1YknO21KxhRowtfN1ONqj+XyuDw/diqXhk4xU/YXL+GiebCV4NqJqcHuIhPFPMQfqYX3RYEJhGsEtUTf5QzwZG2aE+rJPBnPFWSLwxk36XZbsNJtKAFcr2NpBBlSR4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=Lilt7oGIQxygSywK/ZWTuBGWgk/bX9wRwC7VSodQhKWAqaS4zMbiOv75qVWNns7Ug73sOCi2Y55RHZr5EiwOcIULJ6AuZQGE9H/ESmXH196hM5sQF8oBx2RkbJihYBYcjkb4Iv2o3UNzYDlVxFS5Tj94Rro/76UhPxKm2cvxxL8= Received: by 10.100.194.17 with SMTP id r17mr13706431anf.92.1197868576935; Sun, 16 Dec 2007 21:16:16 -0800 (PST) Received: from ?201.20.192.134? ( [201.20.192.134]) by mx.google.com with ESMTPS id c40sm5135107anc.2007.12.16.21.16.13 (version=SSLv3 cipher=RC4-MD5); Sun, 16 Dec 2007 21:16:14 -0800 (PST) Message-ID: <4766061A.4020102@gmail.com> Date: Mon, 17 Dec 2007 03:16:10 -0200 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: [obm-l] =?windows-1252?Q?Demonstra=E7=F5es?= References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> In-Reply-To: <006601c84063$53609e40$02270269@rodrigo7a25356> Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: 8bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: No, hits=3.2 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Acho que isso nos remete ao "terceiro problema do milênio" - o problema NP. rodrigocientista@yahoo.com.br escreveu: > Acredito que uma "demonstração de demonstração" seria algo como > "chover no molhado". Uma demonstração está correta se, em última > instância, está de acordo com os axiomas mais básicos da matéria. > Então, uma demonstração de demontração recorreria, também em última > análise, exatamente aos mesmos axiomas, sendo assim redundante. > > Se você fala inglês, aqui está um fórum onde há diversos debates > interessantes sobre esses assuntos, além de resolução técnica de > questões de matemática, física química, engenharia em geral, etc... > > http://www.physicsforums.com/ > > abraços > > ----- Original Message ----- From: "Sérgio Martins da Silva" > > To: "Lista OBM" > Sent: Sunday, December 16, 2007 10:56 PM > Subject: [obm-l] Demonstrações > > >> Doutores, >> >> Penso que a palavra mais comum nesta lista e, quiçá, da matemática é >> "demonstração". Por isto, gostaria de saber como se demonstra que uma >> demonstração está correta. E mais, que é completa. Quais são os >> requisitos, >> condições, etc ? >> >> Abraços, >> >> Sérgio >> >> ========================================================================= >> >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> ========================================================================= > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 07:41:35 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH9ci8l016730 for ; Mon, 17 Dec 2007 07:38:44 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBH9ci4Y016728 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 07:38:44 -0200 Received: from aacpdlotus.net.ms.gov.br (aacpdlotus.net.ms.gov.br [200.181.116.8]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBH9ch8l016725 for ; Mon, 17 Dec 2007 07:38:43 -0200 To: obm-l@mat.puc-rio.br MIME-Version: 1.0 From: JoaoCarlos_Junior@net.ms.gov.br Importance: X-Priority: Subject: [SPAM] Re: [obm-l] Re: [obm-l] [obm-l] =?ISO-8859-1?Q?quest=E3o_da_OBM?= Sensitivity: Date: Mon, 17 Dec 2007 07:40:21 -0400 Message-ID: X-Mailer: Lotus Domino Web Server Release 6.5.5 November 30, 2005 X-MIMETrack: Serialize by Router on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 17/12/2007 07:40:27 MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: JoaoCarlos_Junior@net.ms.gov.br X-Spam-Status: Yes, hits=7.3 required=5.0 tests=AWL,CTYPE_JUST_HTML,HTML_FONT_COLOR_BLUE,NO_REAL_NAME, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 X-Spam-Prev-Content-Transfer-Encoding: quoted-printable SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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Prezado Carlos Shine:

Por obs=E9quio, posta novamente a tua solu= =E7=E3o, pois n=E3o a tenho.

Fraternalmente, Jo=E3o.
Ah, no e-mail anterior eu esqueci de p= rovar que os primos de a^29 + 1 e a + 1 n=E3o se cortam todos. Mas =E9 s=F3= mais um trabalho de mdc (an=E1logo ao anterior) provar que mdc(a + 1; (a^2= 9 + 1)/(a + 1)) divide 29 e ver que a^29+1 =E9 muito maior do que a+1 para = mostrar que n=E3o se cortam todos.
Nesse =FAltimo mdc, eu a= dmito que usar congru=EAncia =E9 mais r=E1pido; todavia, n=E3o =E9 absoluta= mente necess=E1rio.
 =
[]'s
Shine

----- Original = Message ----
From: vitoriogauss &= lt;vitoriogauss@uol.com.br>
To= : obm-l <obm-l@mat.puc-rio.br>
Sent: Friday, December 14, 2007 1:34:07 PM
Subject: [obm-l] [obm-l] quest=E3o da OBM

> Colegas....
>
> A respeito= da quest=E3o (a^29 - 1)/a-1... para provar que h=E1 2007 fatores primos
 
s=F3 por congru=EAncia???
 
> Grato <= BR>>
Vit=F3rio Gauss



Be a better friend, newshound, a= nd know-it-all with Yahoo! Mobile. Try it now.

= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 13:17:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHFEm8l006639 for ; Mon, 17 Dec 2007 13:14:48 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHFEhnx006636 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 13:14:43 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.242]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHFEV8l006629 for ; Mon, 17 Dec 2007 13:14:31 -0200 Received: by an-out-0708.google.com with SMTP id c31so538302ana.120 for ; Mon, 17 Dec 2007 08:16:04 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:user-agent:mime-version:to:subject:content-type:content-transfer-encoding:from; bh=HSqGYCu5fSbolh5WRbtDZowrbvSnF14tI7qMYUV0oSA=; b=FB/qQMguoH6Z2Rfz1/hrP5+dx3sjrZBKEgyIEH2vv2gzD4lhe9dPajNnB5NjeWi3GPrKvDG7awAUMxRvetEuZ1b55sfmW3Ie+WlDUADAeJaD/wyIEP/i5kDQcc/VHKoy3K/0nNr3noLHSBORAkNFBap5kpTLff3y6BUGgI5faGk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:user-agent:mime-version:to:subject:content-type:content-transfer-encoding:from; b=qsNUjZE6XOUn7zLOkV5gST4ro1rZGLwt59Gi0kkPupTxq7utgAp5+d3mdGNBRCd7bQger7qNN9x8/z9zMB/b4IOUPjqoQ3ZPYbrxerAMQm9CSlsE7HKmGcsjVI0Z2WNkchgJ0wFqGrHVorLrSdbsF1YbgRlVmpVuwWH8zTM80aY= Received: by 10.100.239.11 with SMTP id m11mr15033892anh.15.1197908164027; Mon, 17 Dec 2007 08:16:04 -0800 (PST) Received: from ?201.20.192.134? ( [201.20.192.134]) by mx.google.com with ESMTPS id 6sm19426529agd.2007.12.17.08.15.54 (version=TLSv1/SSLv3 cipher=RC4-MD5); Mon, 17 Dec 2007 08:15:56 -0800 (PST) Message-ID: <4766A0B5.6070805@usp.br> Date: Mon, 17 Dec 2007 14:15:49 -0200 User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Patologia topologica Content-Type: text/plain; charset=ISO-8859-1; format=flowed From: albert Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBHFEY8l006631 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert X-Spam-Status: Yes, hits=5.3 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Na definição de topologia temos que dado um conjunto X, X e o conjunto nulo O pertencem ao conjunto das partes de X, o conjunto P={t_k} tal que t_k pertence a X. Alguém conhece algum conjunto X que não pertença a P ? Por quê tenho pra mim que se X não faz parte do conjunto de suas partes, então X não pertence a si mesmo, e se não existe tal conjunto, então este requisito da topologia é uma coisa redundante. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 13:43:46 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHFeM8l008951 for ; Mon, 17 Dec 2007 13:40:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHFeMNf008944 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 13:40:22 -0200 Received: from web56311.mail.re3.yahoo.com (web56311.mail.re3.yahoo.com [216.252.110.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBHFe38l008855 for ; Mon, 17 Dec 2007 13:40:19 -0200 Received: (qmail 74939 invoked by uid 60001); 17 Dec 2007 16:34:56 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=2U1ptVUVJ4Ts04JDAnOkKbcl/xnYXQaOvnVoXDbR/33UmER3CR5imVXf4cuwxngcQdy7if6tlafwaOGGabPIFPc58ebzPUBu1gfP5CYBGD378WJK8hSw5wFEH/isueYqhIaz9Y2RNVBitjOXe1GK1nubHAT7SSmKR9dTiHqzzJs=; X-YMail-OSG: XtndP.4VM1k15TKUzQ_ahA0dLacQloNEdxFz2SHM8aSlfVj3Tb5tRb1vislsSLasq1duP3QgejyzxnB1WmeLTzzWM9uXEWhq8YlPwrm_UhhOlWYZTv8N764wfC0dSw-- Received: from [201.69.153.11] by web56311.mail.re3.yahoo.com via HTTP; Mon, 17 Dec 2007 13:34:56 ART Date: Mon, 17 Dec 2007 13:34:56 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] [obm-l] =?iso-8859-1?q?Biologia=20ou=20matem=E1tica=3F?= To: =?iso-8859-1?q?Lista=20discuss=E3o=20obm?= MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <490579.74903.qm@web56311.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=7.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 235.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 235.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Um problema de uma linha nos foi apresentado com o seguinte enunciado: Se uma mãe tem dois filhos( não gemeos), qual a probabilidade de que eles sejam totalmente semelhantes? Devemos entender que tudo é igual, ou seja , mesmo nariz, mesma cor de cabelos, como se fossem clones. É um problema de biologia ou de matemática ? Dissera-me que se os aspectos biológicos para que os filhos sejam semelhantes fossem apresentados no texto , seria de matemática, caso contrario de biologia. Acho que é de biomatemática(hahahah). O que vocês acham? Respondido isso, considerando alguém que entende de biologia, qual a porbabildade de ocorrer o que foi exposto acima?? Um abraço Ruy Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 14:02:47 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHG0g8l012237 for ; Mon, 17 Dec 2007 14:00:42 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHG0fGd012234 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 14:00:41 -0200 Received: from relay2.bol.com.br (relay2.bol.com.br [200.221.4.106]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHG0d8l012199 for ; Mon, 17 Dec 2007 14:00:39 -0200 Received: from localhost (localhost [127.0.0.1]) by salsa2.bol.com.br (Postfix) with ESMTP id 737A0E006489 for ; Mon, 17 Dec 2007 15:02:13 -0200 (BRST) Received: from bol.com.br (whisper2.mail.sys.intranet [172.26.5.137]) by salsa2.bol.com.br (Postfix) with ESMTP id 43E15E006461 for ; Mon, 17 Dec 2007 15:02:13 -0200 (BRST) Date: Mon, 17 Dec 2007 15:02:13 -0200 Message-Id: Subject: [obm-l] MARCO E MAURO MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197910933.2A.240874.42.31597.52.42.007.574382472" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 6dccaff45f87cd86ecd8216193d81960 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,LINES_OF_YELLING,LINES_OF_YELLING_2, LINES_OF_YELLING_3,SPAM_PHRASE_00_01,SUPERLONG_LINE, TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1197910933.2A.240874.42.31597.52.42.007.574382472 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA: Marco e Mauro costumam treinar nata=E7=E3o na mesma piscina e no mesmo ho= r=E1rio. Eles iniciam os treinos simultaneamente, a partir de lados opost= os da piscina, nadando um em dire=E7=E3o ao outro. Marco vai de um lado a= outro da piscina em 45 segundos, enquanto Mauro vai de um lado ao outro = em 30 segundos. Durante 12 minutos, eles nadam de um lado para outro, sem= perder qualquer tempo nas viradas. Durante esses 12 minutos, eles podem = encontrar-se quer quando est=E3o nadando no mesmo sentido, quer quando es= t=E3o nadando em sentidos opostos, assim como podem encontrar-se quando a= mbos est=E3o fazendo a virada no mesmo extremo da piscina. Dessa forma, o= n=FAmero de vezes que Marco e Mauro se encontram durante esses 12 minuto= s =E9: a) 10. b) 12. c) 15. d) 18. e) 20. GABARITO LETRA E DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1197910933.2A.240874.42.31597.52.42.007.574382472 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:<= /FONT>

 

Marco e Mauro costumam treinar= nata=E7=E3o na mesma piscina e no mesmo hor=E1rio. Eles iniciam os trein= os simultaneamente, a partir de lados opostos da piscina, nadando um em d= ire=E7=E3o ao outro. Marco vai de um lado a outro da piscina em 45 segund= os, enquanto Mauro vai de um lado ao outro em 30 segundos. Durante 12 min= utos, eles nadam de um lado para outro, sem perder qualquer tempo nas vir= adas. Durante esses 12 minutos, eles podem encontrar-se quer quando est=E3= o nadando no mesmo sentido, quer quando est=E3o nadando em sentidos opost= os, assim como podem encontrar-se quando ambos est=E3o fazendo a virada n= o mesmo extremo da piscina. Dessa forma, o n=FAmero de vezes que Marco e = Mauro se encontram durante esses 12 minutos =E9:=

 

a) 10.  = ;    b) 12. =      c) 15.&= nbsp;     d) 18.    e) 20.

 

GA= BARITO LETRA E

 

DESDE J=C1 MUITO OBRIGADO

--_=__=_XaM3_.1197910933.2A.240874.42.31597.52.42.007.574382472-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 14:59:21 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHGv38l021219 for ; Mon, 17 Dec 2007 14:57:03 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHGv2Rc021217 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 14:57:02 -0200 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.251]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHGux8l021204 for ; Mon, 17 Dec 2007 14:57:00 -0200 Received: by an-out-0708.google.com with SMTP id c31so546259ana.120 for ; Mon, 17 Dec 2007 09:58:33 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Zy/lfaJ0cOtvz4PcDI6Zb9I1RfC8C13cXf4Nv9lzg0o=; b=TjBbCrAhmxcr3UjM2FVIqdOqbQdnv4MgIqu9bWpxOHTGtHFp9w5JkdnA0N/xyZ44v5+mnVfXuyUiFyiFbv6TKxtljHDzdiKP00jei75CyndIOdsApWDpYyaCLVr1/akWpNylwl6VbCnjYOtTounrwyoVgxAvJS4Pue9bmw3A3Ss= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=lk4xSmk03Q4EBhkJyXFeZBYlVdtYQzDFJSpYp5nfo/dC4FISreaF3TxZCx74pmhn86Xtguoggx3ZQARKn0VdyGsM0G1mw16vkPurBq3K7Pl4d3cEYab+r4B2WKi+PhtJwqexuRVM0clryqlaPs7oG/QyGXLafWMbyWQlb1kkRZQ= Received: by 10.100.229.10 with SMTP id b10mr15248597anh.33.1197914313068; Mon, 17 Dec 2007 09:58:33 -0800 (PST) Received: by 10.90.49.13 with HTTP; Mon, 17 Dec 2007 09:58:32 -0800 (PST) Message-ID: <2d483c770712170958l347fe4fdn9f9053c9caf27ad1@mail.gmail.com> Date: Mon, 17 Dec 2007 15:58:32 -0200 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Patologia topologica In-Reply-To: <4766A0B5.6070805@usp.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7758_4770347.1197914312989" References: <4766A0B5.6070805@usp.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=3.4 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_7758_4770347.1197914312989 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Vou usar "E" para "pertence a" e "C" para "=E9 subconjunto de". >> Na defini=E7=E3o de topologia temos que dado um conjunto X, X e o conjun= to >> nulo O pertencem ao conjunto das partes de X, o conjunto P=3D{t_k} tal q= ue >> t_k pertence a X. >> >> Algu=E9m conhece algum conjunto X que n=E3o perten=E7a a P ? Uma pequena corre=E7=E3o no que voc=EA escreveu: o conjunto das partes de = X =E9 P(X)=3D{t | tCX}, que =E9 diferente de {t | tEX} (este =E9 o pr=F3prio conjunto X). Basicamente, para todo conjunto X, tem-se XCX, portanto XEP(X). Ent=E3o, literalmente, a resposta =E0 primeira pergunta =E9 N=C3O: "n=E3o existe X q= ue n=E3o perten=E7a a P(X)". >> Por qu=EA tenho pra mim que se X n=E3o faz parte do conjunto de suas par= tes, >> ent=E3o X n=E3o pertence a si mesmo, e se n=E3o existe tal conjunto, ent= =E3o >> este requisito da topologia =E9 uma coisa redundante. Parece-me aqui que a pergunta =E9 outra -- ser=E1 que XEX (note o s=EDmbolo= !)? Exemplo: se X=3D{a,b}, temos P(X)=3D{vazio,{a},{b},{a,b}}. Ent=E3o XEP(X) e= XCX; temos aEX, temos bEX, mas n=E3o temos XEX. =C9 dif=EDcil arrumar um exemplo em que XEX... Se pud=E9ssemos definir "o c= onjunto de todos os conjuntos", ele n=E3o s=F3 estaria contido em si mesmo (que n= =E3o =E9 novidade, como voc=EA mesmo disse, vale para todo X), mas ele PERTENCERIA a= si mesmo (ah! isso =E9 BEM estranho!). (Por outro lado, esse neg=F3cio de "conjunto de todos os conjuntos" n=E3o = =E9 uma constru=E7=E3o muito bem aceita n=E3o, e rapidamente leva a outras contradi= =E7=F5es.) Abra=E7o, Ralph ------=_Part_7758_4770347.1197914312989 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Vou usar "E" para "pertence a" e "C" par= a "=E9 subconjunto de".
 
>> Na defini=E7=E3o de topologia temos que dado um conjunto X, X= e o conjunto
>> nulo O pertencem ao conjunto das partes de X, o c= onjunto P=3D{t_k} tal que
>> t_k pertence a X.
>>
>= > Algu=E9m conhece algum conjunto X que n=E3o perten=E7a a P ?
Uma pequena corre=E7=E3o no que voc=EA escreveu: o conjunto das partes= de X =E9 P(X)=3D{t | tCX},
que =E9 diferente de {t | tEX} (este =E9 o pr=F3prio conjunto X).
 
Basicamente, para todo conjunto X, tem-se XCX, portanto XEP(X). Ent=E3= o, literalmente, a resposta =E0 primeira pergunta =E9 N=C3O: "n=E3o ex= iste X que n=E3o perten=E7a a P(X)".
 
>> Por qu=EA tenho pra mim que se X n=E3o faz parte do conjunto = de suas partes,
>> ent=E3o X n=E3o pertence a si mesmo, e se n=E3o= existe tal conjunto, ent=E3o
>> este requisito da topologia =E9 u= ma coisa redundante.
Parece-me aqui que a pergunta =E9 outra -- ser=E1 que XEX (n= ote o s=EDmbolo!)?
 
Exemplo: se X=3D{a,b}, temos P(X)=3D{vazio,{a},{b},{a,b}}. Ent=E3o XEP= (X) e XCX; temos aEX, temos bEX, mas n=E3o temos XEX.
 
=C9 dif=EDcil arrumar um exemplo em que XEX... Se pud=E9ssemos de= finir "o conjunto de todos os conjuntos", ele n=E3o s=F3 estaria = contido em si mesmo (que n=E3o =E9 novidade, como voc=EA mesmo disse, vale = para todo X), mas ele PERTENCERIA a si mesmo (ah! isso =E9 BEM estranho!).
(Por outro lado, esse neg=F3cio de "conjunto de todos os conjunto= s" n=E3o =E9 uma constru=E7=E3o muito bem aceita n=E3o, e rapidamente = leva a outras contradi=E7=F5es.)
 
Abra=E7o,
         Ralph
------=_Part_7758_4770347.1197914312989-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 16:02:51 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHI028l025769 for ; Mon, 17 Dec 2007 16:00:02 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHI01sC025767 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 16:00:01 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHI008l025759 for ; Mon, 17 Dec 2007 16:00:01 -0200 Received: from SRV015.mme.gov.br ([172.16.1.16]) by srv017.mme.gov.br ([172.16.1.46]) with mapi; Mon, 17 Dec 2007 17:02:03 -0200 From: Artur Costa Steiner To: "obm-l@mat.puc-rio.br" Date: Mon, 17 Dec 2007 17:01:59 -0200 Subject: RES: [obm-l] Patologia topologica Thread-Topic: [obm-l] Patologia topologica Thread-Index: AchAzicHQENFlkPUQBS70Vp9BbBS2gADa2kA Message-ID: In-Reply-To: <4766A0B5.6070805@usp.br> Accept-Language: pt-BR, en-US Content-Language: pt-BR X-MS-Has-Attach: X-MS-TNEF-Correlator: acceptlanguage: pt-BR, en-US x-tm-as-product-ver: SMEX-8.0.0.1181-5.000.1023-15584.003 x-tm-as-result: No--30.116300-4.000000-31 x-tm-as-user-approved-sender: No x-tm-as-user-blocked-sender: No Content-Type: text/plain; charset="iso-8859-1" MIME-Version: 1.0 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBHI018l025764 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: No, hits=2.3 required=5.0 tests=AWL,IN_REP_TO,SPAM_PHRASE_00_01,SUPERLONG_LINE, TO_ADDRESS_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: ** Nao entendi sua duvida. Vamos por partes. Se X eh um conjunto qualquer, definimos como uma topologia T em X a uma colecao de subconjuntos de X tal que: 1) X e o conjunto vazio estao em T 2) A uniao de qualquer subcolecao de T esta em T 3) I interseccao de qualquer subcolecao finita de T esta em T O par (X,T) eh denominado de espaco topologico (com relacao aa topologia T). O membros de T sao denominados de subconjuntos abertos de X. T nao tem que ser - e, de modo geral nao eh - o conjunto das partes de X. O conjunto das partes e a maior topologia que se pode definir em X, e eh denominada de topologia indiscreta. Pela definicao, TODO conjunto pertence ao conjunto de suas partes. Mas isto em nada conflita com a definicao de topologia. Uma das topologias mais comuns são as induzidas por métricas, dando origem aos espacos metricos, notadamente a métrica Euclidiana que caracteriza os R^n. Neste caso, T é definida declarando-se como abertos subconjuntos de R^n cujos elementos sejam centros de bolas abertas contidas no conjunto. Os membros de T sao justamente estes conjuntos e T, conforme vc sabe, nao eh o conjunto das partes de R^n. Tente colocar sua duvida de forma mais clara, nao entendi bem. Artur PS. O termo conjunto nulo, pelo menos no uso comum, nao significa conjunto vazio, mas sim um comjunto com medida nula. Conjuntos nulos nao tem que ser vazios. Por exemplo, todo subconjunto enumeravel de R^n é nulo. Assim, os racionais, que ate densos em R sao, tem medida nula. -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome de albert Enviada em: segunda-feira, 17 de dezembro de 2007 14:16 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Patologia topologica Na definição de topologia temos que dado um conjunto X, X e o conjunto nulo O pertencem ao conjunto das partes de X, o conjunto P={t_k} tal que t_k pertence a X. Alguém conhece algum conjunto X que não pertença a P ? Por quê tenho pra mim que se X não faz parte do conjunto de suas partes, então X não pertence a si mesmo, e se não existe tal conjunto, então este requisito da topologia é uma coisa redundante. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 17:19:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHJGE8l030957 for ; Mon, 17 Dec 2007 17:16:14 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHJG05X030947 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 17:16:00 -0200 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.236]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHJFt8l030937 for ; Mon, 17 Dec 2007 17:15:56 -0200 Received: by wr-out-0506.google.com with SMTP id c8so1667881wra.18 for ; Mon, 17 Dec 2007 12:17:24 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=HTkgZA1Yy1H1AtIlBj9lLm/8Sz2T+msZ5npuztlMC4o=; b=HrmInXRqVM7Vq1EbEaMIxAAF2LstAGflbHencda/j6PwmCXGWwoSk+iJLVFLRKTslfsnkSR+b9A2V7x6M15DN6Uca+FP5/nNLn4MXa2Ou/or8ndvYmwvNJ0yCl3Z3MWwQ0Ro7JX/nDgh4SwARDfUFrWCVo4bYng1jOhrYf2KG2s= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=TUDop+iS59cAUkVGTAWZ2mtjZycr8imGqzj9XogSv9B2EYWJCGEU33xQH0lpUdR9F6iWljljnzJQyECPFJurnXn0VA9LHKeLcBvlHs+UGF4u00fZmR2AON6/Eyd/ze/QJFPKnyxs0vkCNjV5ocGbQUP963jifcZeF07es/Vxv0I= Received: by 10.142.102.5 with SMTP id z5mr1017646wfb.15.1197922642908; Mon, 17 Dec 2007 12:17:22 -0800 (PST) Received: from ?201.20.192.134? ( [201.20.192.134]) by mx.google.com with ESMTPS id i40sm11257165wxd.2007.12.17.12.17.19 (version=SSLv3 cipher=RC4-MD5); Mon, 17 Dec 2007 12:17:20 -0800 (PST) Message-ID: <4766D94C.4080105@gmail.com> Date: Mon, 17 Dec 2007 18:17:16 -0200 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: RES: [obm-l] Patologia topologica References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: No, hits=3.2 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Eu só queria saber mesmo se existe um conjunto X que não pertenca a T, não estou contestando as definições de topologia. É que para colocar a condição 1) na definição, suponho que deva existir ao menos um conjunto que não pertença a T, senão seria ingenuidade colocar esta primeira condição. Mas obrigado pela resposta Artur. Artur Costa Steiner escreveu: > Nao entendi sua duvida. Vamos por partes. > > Se X eh um conjunto qualquer, definimos como uma topologia T em X a uma colecao de subconjuntos de X tal que: > > 1) X e o conjunto vazio estao em T > 2) A uniao de qualquer subcolecao de T esta em T > 3) I interseccao de qualquer subcolecao finita de T esta em T > > O par (X,T) eh denominado de espaco topologico (com relacao aa topologia T). O membros de T sao denominados de subconjuntos abertos de X. > > T nao tem que ser - e, de modo geral nao eh - o conjunto das partes de X. O conjunto das partes e a maior topologia que se pode definir em X, e eh denominada de topologia indiscreta. > > Pela definicao, TODO conjunto pertence ao conjunto de suas partes. Mas isto em nada conflita com a definicao de topologia. > > Uma das topologias mais comuns são as induzidas por métricas, dando origem aos espacos metricos, notadamente a métrica Euclidiana que caracteriza os R^n. Neste caso, T é definida declarando-se como abertos subconjuntos de R^n cujos elementos sejam centros de bolas abertas contidas no conjunto. Os membros de T sao justamente estes conjuntos e T, conforme vc sabe, nao eh o conjunto das partes de R^n. > > Tente colocar sua duvida de forma mais clara, nao entendi bem. > > Artur > > PS. O termo conjunto nulo, pelo menos no uso comum, nao significa conjunto vazio, mas sim um comjunto com medida nula. Conjuntos nulos nao tem que ser vazios. Por exemplo, todo subconjunto enumeravel de R^n é nulo. Assim, os racionais, que ate densos em R sao, tem medida nula. > > > > -----Mensagem original----- > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em > nome de albert > Enviada em: segunda-feira, 17 de dezembro de 2007 14:16 > Para: obm-l@mat.puc-rio.br > Assunto: [obm-l] Patologia topologica > > > Na definição de topologia temos que dado um conjunto X, X e o conjunto > nulo O pertencem ao conjunto das partes de X, o conjunto P={t_k} tal que > t_k pertence a X. > > Alguém conhece algum conjunto X que não pertença a P ? > > Por quê tenho pra mim que se X não faz parte do conjunto de suas partes, > então X não pertence a si mesmo, e se não existe tal conjunto, então > este requisito da topologia é uma coisa redundante. > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 17:51:08 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHJmt8l002047 for ; Mon, 17 Dec 2007 17:48:55 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHJmsCd002044 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 17:48:54 -0200 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHJmr8l002040 for ; Mon, 17 Dec 2007 17:48:53 -0200 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 6980B711DF8 for ; Mon, 17 Dec 2007 18:50:27 -0200 (EDT) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 2D375705960 for ; Mon, 17 Dec 2007 18:50:27 -0200 (EDT) Message-ID: <4766E0E5.1030407@infolink.com.br> Date: Mon, 17 Dec 2007 18:49:41 -0200 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: RES: [obm-l] Patologia topologica References: <4766D94C.4080105@gmail.com> In-Reply-To: <4766D94C.4080105@gmail.com> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 071217-0, 17/12/2007), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.6 required=5.0 tests=CTYPE_JUST_HTML,IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Oi,

Você está supondo que uma topologia T tem que POSSUIR TODOS OS SUBCONJUNTOS de X.  Este é seu equívoco.  Por isto você não entendeu a explicação do Arthur.    T é apenas um conjunto de subconjuntos de X...  Inclusive Arthur sacou que este devia ser seu equivoco e mencionou este fato na detalhada explicação enviada.

Abraços,
Nehab

arcguede@gmail.com escreveu: 
Eu só queria saber mesmo se existe um conjunto X que não pertenca a T,
não estou contestando as definições de topologia.
É que para colocar a condição 1) na definição, suponho que deva existir
ao menos um conjunto que não pertença a T, senão seria ingenuidade
colocar esta primeira condição.
Mas obrigado pela resposta Artur.

Artur Costa Steiner escreveu:
  
Nao entendi sua duvida. Vamos por partes.

Se X eh um conjunto qualquer, definimos como uma topologia T em X a uma colecao de subconjuntos de X tal que:

1) X e o conjunto vazio estao em T
2) A uniao de qualquer subcolecao de T esta em T
3) I interseccao de qualquer subcolecao finita de T esta em T

O par (X,T) eh denominado de espaco topologico (com relacao aa topologia T). O membros de T sao denominados de subconjuntos abertos de X.

T nao tem que ser - e, de modo geral nao eh - o conjunto das partes de X. O conjunto das partes e a maior topologia que se pode definir em X, e eh denominada de topologia indiscreta.

Pela definicao, TODO conjunto pertence ao conjunto de suas partes. Mas isto em nada conflita com a definicao de topologia.

Uma das topologias mais comuns são as induzidas por métricas, dando origem aos espacos metricos, notadamente a métrica Euclidiana que caracteriza os R^n. Neste caso, T é definida declarando-se como abertos subconjuntos de R^n cujos elementos sejam centros de bolas abertas contidas no conjunto. Os membros de T sao justamente estes conjuntos e T, conforme vc sabe,  nao eh o conjunto das partes de R^n.

Tente colocar sua duvida de forma mais clara, nao entendi bem.

Artur

PS. O termo conjunto nulo, pelo menos no uso comum, nao significa conjunto vazio, mas sim um comjunto com medida nula. Conjuntos nulos nao tem que ser vazios. Por exemplo, todo subconjunto enumeravel de R^n é nulo. Assim, os racionais, que ate densos em R sao, tem medida nula.



-----Mensagem original-----
De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em
nome de albert
Enviada em: segunda-feira, 17 de dezembro de 2007 14:16
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] Patologia topologica


Na definição de topologia temos que dado um conjunto X, X e o conjunto
nulo O pertencem ao conjunto das partes de X, o conjunto P={t_k} tal que
t_k pertence a X.

Alguém conhece algum conjunto X que não pertença a P ?

Por quê tenho pra mim que se X não faz parte do conjunto de suas partes,
então X não pertence a si mesmo, e se não existe tal conjunto, então
este requisito da topologia é uma coisa redundante.



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========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 20:14:44 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHMBl8l012569 for ; Mon, 17 Dec 2007 20:11:47 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBHMBlbX012567 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 20:11:47 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBHMBh8l012546 for ; Mon, 17 Dec 2007 20:11:45 -0200 Received: by rv-out-0910.google.com with SMTP id c27so1890812rvf.9 for ; Mon, 17 Dec 2007 15:13:16 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=s5ryscAx5GFL5Czy+jyK7erN5QyVHdKJZkJj8+JxOoQ=; b=kZeG1cti1ErqyA52jWxi4xICjH6ltEzpKx8MQoJLgddI0mNb7XDNAWRdhsxWD8GkLRdleTWMISDV5Oi5w04tAMx3+3GBmrfLoNOBP5BbQIFX73iDgX2Za+ogziGDgg6JPtnw+ivUefRMWZlIaMNK1poYOdNbzD0I+tOgaZRwSoc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=xB4Wp9LDiVBhxFSvJM8x/vqxTqFgCoVP/SRO4ZEhZGXumTBAl6H3P+ai2TOPqPI508Pi7qi/Bj3GJxL17IHxIO8PPpu8xsdMFV+H5v6mlIxn1hkNK6kQPekUkI9ozuJS08PtM9K23LYlSv5YPehM0gBacW1r4YO5boydgiXpJ7U= Received: by 10.140.187.10 with SMTP id k10mr1715685rvf.86.1197933196236; Mon, 17 Dec 2007 15:13:16 -0800 (PST) Received: by 10.141.152.1 with HTTP; Mon, 17 Dec 2007 15:13:16 -0800 (PST) Message-ID: <4de96b200712171513h14161c79m61afe01c994f81b7@mail.gmail.com> Date: Mon, 17 Dec 2007 21:13:16 -0200 From: "Antonio Manuel Castro del Rio" To: obm-l@mat.puc-rio.br Subject: [obm-l] 2 Problemas MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_9398_18591401.1197933196286" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Antonio Manuel Castro del Rio" X-Spam-Status: No, hits=3.2 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_9398_18591401.1197933196286 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Algu=E9m poderia me ajudar nesses problemas. Desde j=E1 agrade=E7o. 1) (x,y) s=E3o n=BAs reais n=E3o negativos, tal que x + y =3D 2. Qual a probabilidade de termos um par ordenado em que a dist=E2ncia para a ori= gem =E9 menor ou igual a 5/3. 2) Entre 100.000 a 999.999 coma mesma quantidade algarismos, e com a classe n=E3o importando. Quantas classes existem? Entende-se por mesma classe o n=BA em que os algarismos aparecem na mes= ma quantidade de vezes em qualuqer ordem. Ex.: 125588 e 852158 s=E3o da mesma classe. ------=_Part_9398_18591401.1197933196286 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Algu=E9m poderia me ajudar nesses problemas. Desde j=E1 agrade=E7o.
 
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    Entende-se por mesma classe o n=BA em que os algari= smos aparecem na mesma quantidade de vezes em qualuqer ordem.
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------=_Part_9398_18591401.1197933196286-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 22:47:55 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBI0iA8l025059 for ; Mon, 17 Dec 2007 22:44:10 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBI0iAno025057 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 22:44:10 -0200 Received: from smtp108.mail.mud.yahoo.com (smtp108.mail.mud.yahoo.com [209.191.85.218]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBI0i78l025052 for ; Mon, 17 Dec 2007 22:44:07 -0200 Received: (qmail 78790 invoked from network); 18 Dec 2007 01:45:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-YMail-OSG:Message-ID:From:To:References:Subject:Date:MIME-Version:Content-Type:Content-Transfer-Encoding:X-Priority:X-MSMail-Priority:X-Mailer:X-MimeOLE; b=u7iHwTNXeL02nDSiZykI5DyzQ8YqccnGgBJ+htJrzIlS93SX6kpVS97CgMVF8oVFBZ55JcCmlMG0OpW/23IbueXVi5lN32RN6Yoaj/22Zz+CIt0yQ8bidyfDUQd1jOJTAwLXyZGiWw3tgEHKvkXfiH/QBNyXsvudKShZUPDArEw= ; Received: from unknown (HELO rodrigo7a25356) (rodrigocientista@200.181.23.157 with login) by smtp108.mail.mud.yahoo.com with SMTP; 18 Dec 2007 01:45:33 -0000 X-YMail-OSG: 45Rz4M0VM1kMvOEGmdxcX701kqn6i4rPnALJ6NNcoOmiPVPYDKWg5kTSzJQCrjjBHmkbztGjGzZD4TvmDKRkRAaJJEuxUxWgC2kiKxb221ORSvcVuJQ- Message-ID: <00ca01c84120$28301da0$02270269@rodrigo7a25356> From: To: References: <000c01c84050$09433560$01fea8c0@svs> <006601c84063$53609e40$02270269@rodrigo7a25356> <4766061A.4020102@gmail.com> Subject: [SPAM] [obm-l] =?Windows-1252?Q?Re:_=5Bobm-l=5D_Re:_=5Bobm-l=5D_Demonstra=E7=F5es?= Date: Mon, 17 Dec 2007 23:46:07 -0300 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="Windows-1252"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=7.5 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,NO_REAL_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.50 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 218.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 218.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Acredito que o problema NP seja provar que existe ou não uma forma matemática, objetiva, de transformar problemas NP (com tempo de processamento não polinomial) em problemas P (tempo de processamento polinomial). Correto? qual seria a remissão a que você se referiu? ----- Original Message ----- From: To: Sent: Monday, December 17, 2007 2:16 AM Subject: Re: [obm-l] Re: [obm-l] Demonstrações > Acho que isso nos remete ao "terceiro problema do milênio" - o problema > NP. > > rodrigocientista@yahoo.com.br escreveu: >> Acredito que uma "demonstração de demonstração" seria algo como >> "chover no molhado". Uma demonstração está correta se, em última >> instância, está de acordo com os axiomas mais básicos da matéria. >> Então, uma demonstração de demontração recorreria, também em última >> análise, exatamente aos mesmos axiomas, sendo assim redundante. >> >> Se você fala inglês, aqui está um fórum onde há diversos debates >> interessantes sobre esses assuntos, além de resolução técnica de >> questões de matemática, física química, engenharia em geral, etc... >> >> http://www.physicsforums.com/ >> >> abraços >> >> ----- Original Message ----- From: "Sérgio Martins da Silva" >> >> To: "Lista OBM" >> Sent: Sunday, December 16, 2007 10:56 PM >> Subject: [obm-l] Demonstrações >> >> >>> Doutores, >>> >>> Penso que a palavra mais comum nesta lista e, quiçá, da matemática é >>> "demonstração". Por isto, gostaria de saber como se demonstra que uma >>> demonstração está correta. E mais, que é completa. Quais são os >>> requisitos, >>> condições, etc ? >>> >>> Abraços, >>> >>> Sérgio >>> >>> ========================================================================= >>> >>> Instruções para entrar na lista, sair da lista e usar a lista em >>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >>> ========================================================================= >> >> >> ========================================================================= >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> ========================================================================= >> > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 17 23:40:04 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBI1b68l000727 for ; Mon, 17 Dec 2007 23:37:07 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBI1b5sQ000722 for obm-l-MllGbsmmN; Mon, 17 Dec 2007 23:37:05 -0200 Received: from bay0-omc2-s37.bay0.hotmail.com (bay0-omc2-s37.bay0.hotmail.com [65.54.246.173]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBI1as8l000660 for ; Mon, 17 Dec 2007 23:36:55 -0200 Received: from BAY112-W37 ([64.4.26.137]) by bay0-omc2-s37.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Mon, 17 Dec 2007 18:38:28 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_c62e6ed7-a842-4074-8700-57e071d0c317_" X-Originating-IP: [201.37.214.138] From: Pedro Cardoso To: Subject: =?iso-8859-1?Q?RE:_[obm-l]_Re:_[obm-l]_Combinat=F3ria?= Date: Tue, 18 Dec 2007 05:38:28 +0300 Importance: Normal In-Reply-To: <002a01c84059$f10f06e0$02270269@rodrigo7a25356> References: <1388.200.232.239.58.1196782373.squirrel@mail.claretianas.com.br> <002a01c84059$f10f06e0$02270269@rodrigo7a25356> MIME-Version: 1.0 X-OriginalArrivalTime: 18 Dec 2007 02:38:28.0337 (UTC) FILETIME=[12175610:01C8411F] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_c62e6ed7-a842-4074-8700-57e071d0c317_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 =20 S=F3 pra agradecer ao Ralph e ao Rogiro cientista pelos explica=E7=F5es e p= elos links (sobre o problema das parti=E7=F5es de n=FAmeros naturais). Vou = tentar entender um pouco mais o assunto dentro do que a matem=E1tica que do= mino permite.=20 =20 Obrigado aos dois. _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_c62e6ed7-a842-4074-8700-57e071d0c317_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable  
 
S=F3 pra agradecer ao Ralph e ao Rogiro cientista pelos explica=E7=F5es e p= elos links (sobre o problema das parti=E7=F5es de n=FAmeros naturais). Vou = tentar entender um pouco mais o assunto dentro do que a matem=E1tica que do= mino permite.
 
Obrigado aos dois.

Receba GR=C1TIS as mensagens do Messenger= no seu celular quando voc=EA estiver offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! = --_c62e6ed7-a842-4074-8700-57e071d0c317_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 18 09:21:28 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBIBHH8l008714 for ; Tue, 18 Dec 2007 09:17:17 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBIBHBRK008709 for obm-l-MllGbsmmN; Tue, 18 Dec 2007 09:17:11 -0200 Received: from relay3.uol.com.br (relay3.uol.com.br [200.221.4.110]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBIBGt8l008678 for ; Tue, 18 Dec 2007 09:16:56 -0200 Received: from localhost (localhost [127.0.0.1]) by sniper3.uol.com.br (Postfix) with ESMTP id 0B04AB0019C2 for ; Tue, 18 Dec 2007 10:18:29 -0200 (BRST) Received: from uol.com.br (whisky8.mail.sys.intranet [172.26.5.19]) by sniper3.uol.com.br (Postfix) with ESMTP id A5938B0019CA for ; Tue, 18 Dec 2007 10:18:28 -0200 (BRST) Date: Tue, 18 Dec 2007 10:18:28 -0200 Message-Id: Subject: [obm-l] =?iso-8859-1?b?UmU6cXVlc3TjbyBkYSBPQk0gN6ogLSBUZXJjZWk=?= =?iso-8859-1?b?cmEgRmFzZQ==?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1197980308.2A.338877.42.14630.52.42.007.515238576" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.1.10.93 X-SIG5: 845c6cf36c4e4487664f32a780c03396 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=-0.2 required=5.0 tests=AWL,QUOTED_EMAIL_TEXT,SPAM_PHRASE_00_01, TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1197980308.2A.338877.42.14630.52.42.007.515238576 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Realmente. Eu mesmo, comentei com alguns alunos como iniciaram a solu=E7=E3= o do problema, nenhum deles pensou em congru=EAncia. Creio que a sua pergunta =E9 bem pertinente. As quest=F5es da OBM N1 e N2 est=E3o se tornando bem complicadas, e aqui = em Recife, o que percebo =E9 que isso est=E1 gerando uma certa desanima=E7= =E3o de alguns alunos da rede particular. A pergunta =E9: de fato, algum(a) garoto(a) de 13 ou 14 anos resolveu est= e problema durante a olimp=EDada? > ----- Original Message ----- > From: vitoriogauss > To: obm-l > Sent: Thursday, December 13, 2007 11:06 AM > Subject: [obm-l] quest=E3o da OBM 7=AA - Terceira Fase > > > Colegas.... > > A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM, mas par= a um aluno de 7=AA e 8=AA parece-me complicada... > > N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia, que inf= elizmente n=E3o ensinei profundamente aos meus alunos. > > Vou ter que ensinar melhor em 2008, creio que at=E9 invari=E2ncia. > > > Grato Vit=F3rio Gauss --_=__=_XaM3_.1197980308.2A.338877.42.14630.52.42.007.515238576 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Realmente. Eu mesmo, comentei com alguns alunos como iniciaram = a solu=E7=E3o do problema, nenhum deles pensou em congru=EAncia.
 
Creio que a sua pergunta =E9 bem pertinente.
 
As quest=F5es da OBM N1 e N2 est=E3o se tornando bem complicadas, e = aqui em Recife, o que percebo =E9 que isso est=E1 gerando uma certa desan= ima=E7=E3o de alguns alunos da rede particular.
 
 
 
 
 
A pergunta =E9: de fato, algum(a) garoto(a) de 13 ou 14 anos resolve= u este problema durante a olimp=EDada?
> ----- Original Message -----
> From: vitoriogauss
> To: obm-l
> Sent: Thursday, December 13, 2007 11:06 AM
> Subject: [obm-l] quest=E3o da OBM 7=AA - Terceira Fase
>
>
> Colegas....
>
> A respeito da quest=E3o (a^29 - 1)/a-1... tudo bem que =E9 OBM,= mas para um aluno de 7=AA e 8=AA parece-me complicada...
>
> N=E3o consigo ver outra solu=E7=E3o, sen=E3o por congru=EAncia,= que infelizmente n=E3o ensinei profundamente aos meus alunos.
>
> Vou ter que ensinar melhor em 2008, creio que at=E9 invari=E2nc= ia.
>
>
> Grato
Vit=F3rio Gauss
--_=__=_XaM3_.1197980308.2A.338877.42.14630.52.42.007.515238576-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 18 18:50:28 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBIKlK8l023308 for ; Tue, 18 Dec 2007 18:47:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBIKlK4s023299 for obm-l-MllGbsmmN; Tue, 18 Dec 2007 18:47:20 -0200 Received: from web56312.mail.re3.yahoo.com (web56312.mail.re3.yahoo.com [216.252.110.236]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBIKlH8l023293 for ; Tue, 18 Dec 2007 18:47:18 -0200 Received: (qmail 4332 invoked by uid 60001); 18 Dec 2007 21:48:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=uuelgqvnsdeMmYyVloa6PXMCgzPt1VqtJvk8nKCdbAseiu83tW9781duXYrkRTvZdlCE9l0XXBTUYSCnR6YXIe5YmmxuoSVZpSkLL5hVNuetTdty/az+bsJcVzgTvwfQD38bZUCPcYbgQxC+yodJlw5+FFaVsVajnrhMORa4xpw=; X-YMail-OSG: mcCIF8AVM1nKC_HkyJh5RMz1XDKujZ2oeNYgxneLND78x4q1UszStxJcWaUYKILKxpOW44vVwgunHFNMeLWQ1QtqGCh59ZHxIlLNqLWgf8TgLnwWN_fkhctJIURicak6uTb5yaRG6G7vc0qlJcz.gzA- Received: from [201.69.154.94] by web56312.mail.re3.yahoo.com via HTTP; Tue, 18 Dec 2007 18:48:48 ART Date: Tue, 18 Dec 2007 18:48:48 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] [obm-l] Filhos semelhantes... To: =?iso-8859-1?q?Lista=20discuss=E3o=20obm?= MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <536036.3359.qm@web56312.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=7.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 236.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 236.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Dois amigos biólogos calcularam a probabilidade de uma familia ter dois filhos ( não gemêos ) , totalmente semelhantes. Eles , óbviamente consideraram os aspectos biológicos para a ocorrencia de tal evento. chegaram a resposta (1/2)^45... Alguém me ajudaria a sacanear esses caras?? Abraço Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 10:12:09 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJC9O8l016159 for ; Wed, 19 Dec 2007 10:09:24 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJC9OlB016157 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 10:09:24 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJC9L8l016119 for ; Wed, 19 Dec 2007 10:09:21 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4833412wag.13 for ; Wed, 19 Dec 2007 05:10:56 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=IMyJVk6Dc4AFQv50Sqbv+wN02X6RclEFaz+jgqzErrU=; b=nW4N15wo2bmse1KpV685hiWKw69DgLKQ7mqCocTHFN8xrHdCuSrmw4Y1vJSOwP69VmxbPia136ftdyI6/U8N/+JKbg/gY1OoXK2Yg3quB7wcUdjr1Z6Xd2GAOWkuD89V1UHVC/Oqj9X43OlyE84EbmOgPCqNjgmUtpSg2oUNkSM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=MNPIGcnkx09LhOZ8aRn+bKN7EIgiV350eNmsSS3BTDYJqS+86Cq/BLa+jgrYqrH6b3LYev87diQVxNNND+VWVXHPVi3ve0O17whWUmtBqZmMFFRQZNrBFziG79V3rZQ3Nf6+YfJthcNHOHZAdKxPTrxTfxSyIEArwl60afeyCW4= Received: by 10.114.146.1 with SMTP id t1mr1749475wad.20.1198069855991; Wed, 19 Dec 2007 05:10:55 -0800 (PST) Received: by 10.114.136.9 with HTTP; Wed, 19 Dec 2007 05:10:55 -0800 (PST) Message-ID: <3bd00efc0712190510v7ec2ea83h9d047057ca4d4b5c@mail.gmail.com> Date: Wed, 19 Dec 2007 11:10:55 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] 2 Problemas In-Reply-To: <4de96b200712171513h14161c79m61afe01c994f81b7@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_17819_11242778.1198069855985" References: <4de96b200712171513h14161c79m61afe01c994f81b7@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=2.5 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_17819_11242778.1198069855985 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Antonio, 1) queremos que x^2 + y^2 <=3D 25/9 temos que x+y=3D2... elevando ao quadrado, temos: x^2 + y^2 + 2xy =3D 4, e, portanto: x^2 + y^2 =3D 4 - 2xy ... substituindo na desigualdade, ficamos com: 2xy >= =3D 4 - 25/9 .. xy >=3D 11/18 mass.. x+y=3D2... logo: y =3D 2-x ... substituindo em xy >=3D 11/18, temos: x(2-x) >=3D 11/18 ... x^2 - 2x + 11/18 <=3D 0 neste caso, a probabilidade =E9 obtida dividindo-se a soma dos comprimentos dos intervalos que satisfazem x^2 + y^2 <=3D 25/9 pelo comprimento do intervalo inteiro (no caso, 2). como temos uma par=E1bola, basta pegarmos a dist=E2ncia entre as ra=EDzes e dividir por 2.. sejam x1 e x2 as raizes, x2 >=3D x1, ent=E3o: P =3D (x2 - x1)/2 calculando as ra=EDzes, obtemos: x2 =3D 1 + sqrt(14)/6, e, x1 =3D 1 - sqrt(= 14)/6 portanto: P =3D sqrt(14)/6 abra=E7os, Salhab On Dec 17, 2007 9:13 PM, Antonio Manuel Castro del Rio < antoniomcdelrio@gmail.com> wrote: > Algu=E9m poderia me ajudar nesses problemas. Desde j=E1 agrade=E7o. > > 1) (x,y) s=E3o n=BAs reais n=E3o negativos, tal que x + y =3D 2. Qual a > probabilidade de termos um par ordenado em que a dist=E2ncia para a o= rigem > =E9 menor ou igual a 5/3. > > 2) Entre 100.000 a 999.999 coma mesma quantidade algarismos, e com a > classe n=E3o importando. Quantas classes existem? > Entende-se por mesma classe o n=BA em que os algarismos aparecem na > mesma quantidade de vezes em qualuqer ordem. > Ex.: 125588 e 852158 s=E3o da mesma classe. > ------=_Part_17819_11242778.1198069855985 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Antonio,

1) queremos que x^2 + y^2 <=3D 25/9
temos que x= +y=3D2... elevando ao quadrado, temos: x^2 + y^2 + 2xy =3D 4, e, portanto:<= br>x^2 + y^2 =3D 4 - 2xy ... substituindo na desigualdade, ficamos com: 2xy= >=3D 4 - 25/9 ..
xy >=3D 11/18

mass.. x+y=3D2... logo: y =3D 2-x ... substitui= ndo em xy >=3D 11/18, temos:
x(2-x) >=3D 11/18 ... x^2 - 2x + 11/1= 8 <=3D 0

neste caso, a probabilidade =E9 obtida dividindo-se a so= ma dos comprimentos dos intervalos que satisfazem x^2 + y^2 <=3D 25/9 pe= lo comprimento do intervalo inteiro (no caso, 2).
como temos uma par=E1bola, basta pegarmos a dist=E2ncia entre as ra=EDz= es e dividir por 2..
sejam x1 e x2 as raizes, x2 >=3D x1, ent=E3o: P = =3D (x2 - x1)/2

calculando as ra=EDzes, obtemos: x2 =3D 1 + sqrt(14)= /6, e, x1 =3D 1 - sqrt(14)/6
portanto: P =3D sqrt(14)/6

abra=E7os,
Salhab



<= div class=3D"gmail_quote">On Dec 17, 2007 9:13 PM, Antonio Manuel Castro de= l Rio <antoniomcdelrio@gmai= l.com > wrote:
To: obm-l@mat.puc-rio.br Subject: [obm-l] Trigonometria... MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBJDRa8l010211 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Olá pessoal, Estou precisando de uma ajuda para resolver este problema: No intervalo [0º,360º], a soma dos valores que satisfazem a eqaução sen(2x+30º)=cosx. Agradeço desde já a ajuda. Abraços, Joao Victor ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 12:28:41 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJEJXHL013916 for ; Wed, 19 Dec 2007 12:26:59 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJCMIv9019647 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 10:22:18 -0200 Received: from web30115.mail.mud.yahoo.com (web30115.mail.mud.yahoo.com [209.191.69.47]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBJCM78l019560 for ; Wed, 19 Dec 2007 10:22:08 -0200 Received: (qmail 46757 invoked by uid 60001); 19 Dec 2007 13:23:41 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=qGVS89tEc9xMsUaWgc3uApJ4/YvTuJag7XMd9dkPO02ryskxEXxrLffdIuu3lZMI3gsOdSo84xg99DPonZrF4SBo/AgakbeeMsAVZyNkH9fYvZ8IF0q1FMsFiIYgkUjiU+/jrbu+m2X8E7mZ0u6N70m+rTbfmm2gWTqj2FZU63U=; X-YMail-OSG: kw.3sksVM1lkM4W1AsJlH2evyrUWEvX23Q2RI8_Ryxv5WWks4G2Gd6aQKxMeQUswyqr0AT_boyqytpBmvj6LHnR4zcWSpodrLExF Received: from [201.63.131.82] by web30115.mail.mud.yahoo.com via HTTP; Wed, 19 Dec 2007 10:23:41 ART Date: Wed, 19 Dec 2007 10:23:41 -0300 (ART) From: Angelo Schranko Subject: [SPAM] [obm-l] =?iso-8859-1?q?Poss=EDveis=20interpreta=E7=F5es=20de=20um=20par=E2metro?= To: obm-l@mat.puc-rio.br In-Reply-To: <99886d920712140901m20a6e117m277b50524554ddcd@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <688908.46628.qm@web30115.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Angelo Schranko X-Spam-Status: Yes, hits=8.0 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,MIME_BOUND_DIGITS_5, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-364662715-1198070621=:46628" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.00 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 47.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 47.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-364662715-1198070621=:46628 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Meus caros, gostaria de interpretações dos Srs. a respeito da medida abaixo. Sejam: 4 caixas 12 gatos (distintos) Todos os gatos devem pertencer a alguma caixa. Um gato não pode pertencer a mais de uma caixa ao mesmo tempo. Todos o gatos podem estar contidos na mesma caixa. Um exemplo de distribuição seria: 1 caixa contém 3 gatos 2 caixas contém 2 gatos 1 caixa contém 5 gatos É claro que 1*3 + 2*2 + 1*5 = 12 gatos. Há então (1*3 + 2*2 + 1*5) / (1 + 2 + 1) = 12 / 4 = 3 gatos por caixa em média. Agora considere o seguinte cálculo: (1*3 + 2*2 + 1*5) / (3 + 2 + 5) = 12 / 10 = 1.2 E nas situações limite: 4 caixas contém 3 gatos, ou seja: 4*3 / 3 = 4 E também: 3 caixas contém 0 gatos e 1 caixa contém 12 gatos (3*0 + 1*12) / 12 = 1 Existe algum parâmetro estatístico equivalente a isso ? O que isso está medindo ? Obrigado a todos, Saudações, Angelo --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-364662715-1198070621=:46628 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Meus caros, gostaria de interpretações dos Srs. a respeito da medida abaixo.
 
Sejam:
 
4 caixas
12 gatos (distintos)
 
Todos os gatos devem pertencer a alguma caixa.
Um gato não pode pertencer a mais de uma caixa ao mesmo tempo.
Todos o gatos podem estar contidos na mesma caixa.
 
Um exemplo de distribuição seria:
 
1 caixa contém 3 gatos
2 caixas contém 2 gatos
1 caixa contém 5 gatos
 
É claro que 1*3 + 2*2 + 1*5 = 12 gatos. Há então (1*3 + 2*2 + 1*5) / (1 + 2 + 1) = 12 / 4 = 3 gatos por caixa em média.
 
Agora considere o seguinte cálculo:
 
(1*3 + 2*2 + 1*5) / (3 + 2 + 5) = 12 / 10 = 1.2
 
E nas situações limite:
 
4 caixas contém 3 gatos, ou seja: 4*3 / 3 = 4
 
E também: 3 caixas contém 0 gatos e 1 caixa contém 12 gatos
(3*0 + 1*12) / 12 = 1
 
Existe algum parâmetro estatístico equivalente a isso ? O que isso está medindo ?
 
Obrigado a todos,
Saudações,
Angelo

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-364662715-1198070621=:46628-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 12:29:57 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJESk8l016271 for ; Wed, 19 Dec 2007 12:28:46 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJESk8x016269 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 12:28:46 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJESi8l016255 for ; Wed, 19 Dec 2007 12:28:44 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4900901wag.13 for ; Wed, 19 Dec 2007 07:30:19 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=VOXZxmvGIDUdkqsTItsb7ME9UuYA9g0jJHSPjMk2YPw=; b=kC5MXlQxWdw0/WP5aH6IAmhDt/9he13786CX5ilO8TY+9K7DfTGsyHB7aGbX8DCXrWkDUdohRnhf5pRC87KMXcOGsDr+cdgAULK6HmQ7LDP1uZgxvlwm/YtBDBjtoD5EAHjEHaUJb4M6bCFr+Tsdz17AN3AjZ0Ji4gJB9Knt1KE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=HG0PwpPBNlYS4yS4waicid3oF0WrlnOPtCgx0Ll7Eht/NUBf1twrYW+uXmzl913ignL15D1sclUlc7dFkzbYf7ohdujvzstcMPF+Bto+dR3zxcXT7SnRkZN8RvGPpX+PZ8i/bZNa4KX5dUi7qTAHMIZhH02SyZYyyIeiDopkh/E= Received: by 10.141.178.5 with SMTP id f5mr5988252rvp.112.1198077825377; Wed, 19 Dec 2007 07:23:45 -0800 (PST) Received: by 10.141.99.13 with HTTP; Wed, 19 Dec 2007 07:23:45 -0800 (PST) Message-ID: <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> Date: Wed, 19 Dec 2007 16:23:45 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Filhos semelhantes... In-Reply-To: <536036.3359.qm@web56312.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_17038_15073952.1198077825373" References: <536036.3359.qm@web56312.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.6 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_17038_15073952.1198077825373 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Isso =E9 uma quest=E3o de matem=E1tica? O que vc quer dizer com "sacanear" esses caras? A primeira imagem que me ve= m na cabe=E7a =E9 vc furar os pneus dos carros deles, o que n=E3o =E9 nada ma= tem=E1tico (tampouco correto). 2007/12/18, Ruy Oliveira : > > Dois amigos bi=F3logos calcularam a probabilidade de uma > familia ter dois filhos ( n=E3o gem=EAos ) , totalmente > semelhantes. Eles , =F3bviamente consideraram os > aspectos biol=F3gicos para a ocorrencia de tal evento. > chegaram a resposta (1/2)^45... > Algu=E9m me ajudaria a sacanear esses caras?? > Abra=E7o > > > > > Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o par= a > armazenamento! > http://br.mail.yahoo.com/ > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_17038_15073952.1198077825373 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Isso =E9 uma quest=E3o de matem=E1tica?
O que vc quer dizer com "sa= canear" esses caras? A primeira imagem que me vem na cabe=E7a =E9 vc f= urar os pneus dos carros deles, o que n=E3o =E9 nada matem=E1tico (tampouco= correto).

2007/12/18, Ruy Oliveira <ruyhigh@yahoo.com.br>: Dois amigos bi=F3logos calcularam a probabilidade de uma
familia ter doi= s filhos ( n=E3o gem=EAos ) , totalmente
semelhantes. Eles , =F3bviament= e consideraram os
aspectos biol=F3gicos para a ocorrencia de tal evento.=
chegaram a resposta (1/2)^45...
    Algu=E9m me ajudaria a sacanear esses caras??        Abra=E7o



<= br>      Abra sua conta no Yahoo! Mail, o =FA= nico sem limite de espa=E7o para armazenamento!
http://br.mail.yahoo.com/
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em=
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=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D



--
Bruno FRAN=C7A D= OS REIS

msn: brunoreis66= 6@hotmail.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16

e^(pi*i)+1= =3D0 ------=_Part_17038_15073952.1198077825373-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 12:36:44 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJEZJ8l016685 for ; Wed, 19 Dec 2007 12:35:19 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJEZJpV016683 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 12:35:19 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJEZI8l016679 for ; Wed, 19 Dec 2007 12:35:18 -0200 Received: from SRV015.mme.gov.br ([172.16.1.16]) by srv016.mme.gov.br ([172.16.1.45]) with mapi; Wed, 19 Dec 2007 13:37:21 -0200 From: Artur Costa Steiner To: "obm-l@mat.puc-rio.br" Date: Wed, 19 Dec 2007 13:37:18 -0200 Subject: [obm-l] Mostrar que sequenciais subaditivas convergem Thread-Topic: Mostrar que sequenciais subaditivas convergem Thread-Index: AchCUSzmHM130NnsQeiFp8ZT+X3LKgAA2hZg Message-ID: In-Reply-To: <5bb472220712190629u74ee42acld034384c749a3f76@mail.gmail.com> Accept-Language: pt-BR, en-US Content-Language: pt-BR X-MS-Has-Attach: X-MS-TNEF-Correlator: acceptlanguage: pt-BR, en-US x-tm-as-product-ver: SMEX-8.0.0.1181-5.000.1023-15616.000 x-tm-as-result: No--29.136500-4.000000-31 x-tm-as-user-approved-sender: No x-tm-as-user-blocked-sender: No Content-Type: text/plain; charset="iso-8859-1" MIME-Version: 1.0 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBJEZI8l016681 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: No, hits=2.2 required=5.0 tests=AWL,IN_REP_TO,SPAM_PHRASE_00_01,TO_ADDRESS_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: ** Acho este interessante: Seja x_n uma sequencias de números positivos tais que, para todos m e n, tenhamos x_(m + n) <= x_m + x_n. Tais sequencia sao denominadas de subaditivas. Mostre que lim (x_n)/n = infimo x_n Artur ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 13:14:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJFCZ8l018636 for ; Wed, 19 Dec 2007 13:12:35 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJFCZhH018634 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 13:12:35 -0200 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJFCX8l018625 for ; Wed, 19 Dec 2007 13:12:34 -0200 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id AB9D9712BE8 for ; Wed, 19 Dec 2007 14:14:08 -0200 (EDT) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 3A5A670179B for ; Wed, 19 Dec 2007 14:14:08 -0200 (EDT) Message-ID: <4769431E.4060004@infolink.com.br> Date: Wed, 19 Dec 2007 14:13:18 -0200 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Filhos semelhantes... e naturalmente offtopics.... References: <536036.3359.qm@web56312.mail.re3.yahoo.com> <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> In-Reply-To: <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 071218-0, 18/12/2007), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Bem, Ruy, um relax ...

Se os biólogos consideram que há 45 genes "binários" que determinam a semelhança entre os filhos, quero crer que a resposta deles estaria absolutamente correta... e o pneu de seu carro seria furado ... (hahaha).

Feliz Natal a todos, independente do credo, e um ótimo Ano Novo a todos,

Abraços biológicos,
Nehab

Bruno França dos Reis escreveu:
Isso é uma questão de matemática?
O que vc quer dizer com "sacanear" esses caras? A primeira imagem que me vem na cabeça é vc furar os pneus dos carros deles, o que não é nada matemático (tampouco correto).

2007/12/18, Ruy Oliveira <ruyhigh@yahoo.com.br>:
Dois amigos biólogos calcularam a probabilidade de uma
familia ter dois filhos ( não gemêos ) , totalmente
semelhantes. Eles , óbviamente consideraram os
aspectos biológicos para a ocorrencia de tal evento.
chegaram a resposta (1/2)^45...
    Alguém me ajudaria a sacanear esses caras??
        Abraço




      Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!
http://br.mail.yahoo.com/
=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================



--
Bruno FRANÇA DOS REIS

msn: brunoreis666@hotmail.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16

e^(pi*i)+1=0
========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 14:31:04 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJGSm8l026711 for ; Wed, 19 Dec 2007 14:28:48 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJGSmNH026709 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 14:28:48 -0200 Received: from nz-out-0506.google.com (nz-out-0506.google.com [64.233.162.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJGSj8l026702 for ; Wed, 19 Dec 2007 14:28:46 -0200 Received: by nz-out-0506.google.com with SMTP id z6so1462154nzd.9 for ; Wed, 19 Dec 2007 09:30:21 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=ypsC0K6ILRtGnLxdJf/KRZeFu4+o8z8Qpb/TZ3gC7yk=; b=omGM7EH9b5+Z5ImbLntTmyCL0k8nVOwqHCnYE9Rt3RqmYTs8/Q8x+95etj2fjwcGVJwJ+iIh42gLf1dnhgjOgzSzxoDD/lNnPTqGx7b9ePZn2tQ9s2R1DiIuz09hsLvptZuxGaJKx3YI9LbZOy+eh2zlNXmtYpTUcu2bGFFpWvw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=tRf6nqxoJ0wTXQxltMgd6TK85EGpzlzCUrOH/kzGPZisUmWDpKpObTDzLfsPwH1+MyXiR+Jk92PmDppEH1L7pI+zsYXoGP8RSLeVkKlL2gL3hO/PEOT2QDQGCamLbh4KgZCj6VUtDIr41SQpAH1XyCGXlX/Lv3qMkph4uaR//MY= Received: by 10.142.148.7 with SMTP id v7mr1530602wfd.153.1198085420146; Wed, 19 Dec 2007 09:30:20 -0800 (PST) Received: by 10.142.101.2 with HTTP; Wed, 19 Dec 2007 09:30:20 -0800 (PST) Message-ID: Date: Wed, 19 Dec 2007 15:30:20 -0200 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Trigonometria... In-Reply-To: <5bb472220712190629u74ee42acld034384c749a3f76@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_25913_19298347.1198085420133" References: <5bb472220712190629u74ee42acld034384c749a3f76@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_25913_19298347.1198085420133 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 3x+30=3D90 x=3D20=BA 3x+30=3D270 x=3D80 On 12/19/07, Joao Victor Brasil wrote: > > Ol=E1 pessoal, > > Estou precisando de uma ajuda para resolver este problema: > > No intervalo [0=BA,360=BA], a soma dos valores que satisfazem a eqau=E7= =E3o > sen(2x+30=BA)=3Dcosx. > > Agrade=E7o desde j=E1 a ajuda. > > Abra=E7os, > > Joao Victor > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_25913_19298347.1198085420133 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
3x+30=3D90
x=3D20=BA
3x+30=3D270
x=3D80


 
On 12/19/07, Joao Victor Brasil <jvbrasil@= gmail.com> wrote:
Ol=E1 pessoal,

Estou prec= isando de uma ajuda para resolver este problema:

No intervalo [0=BA,= 360=BA], a soma dos valores que satisfazem a eqau=E7=E3o
sen(2x+30=BA)=3Dcosx.

Agrade=E7o desde j=E1 a ajuda.

Abra= =E7os,

Joao Victor

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da= lista e usar a lista em
http://www.= mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_25913_19298347.1198085420133-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 14:55:14 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJGrX8l027817 for ; Wed, 19 Dec 2007 14:53:33 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJGrXMm027815 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 14:53:33 -0200 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJGrU8l027809 for ; Wed, 19 Dec 2007 14:53:31 -0200 Received: by el-out-1112.google.com with SMTP id s27so726995ele.13 for ; Wed, 19 Dec 2007 09:55:05 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=ClVBM4mEZz+L8jnPXyXt/4Svca2ezkdh0l8Q7VCH8mI=; b=FPAQn4ENp/1R2ym4Le3WVyvlrfHPZWTMw5zQYmk2K6ZdpjjyY6FT/WL7UdJsK2gT8NSO+ERKAvhGOayMZDF1znWeUS2ttrluEfM1xk6jOIoSmWPMGwRZ4FY7IxehDZPT01PFqTWjN+MsX3Klacbkyikm3ewr9W9neeQAX+R3k0s= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=jS4WvHSpkqs8gSh0IWGgceJwPKcjtgBBoP/dnMi6+1DnDOiDG0EyLXwa/bCp7jKtsJs41/4SV6hzHnY5QNFZQs1hT9TqkzRyY8NG6phm7E55y/hpa/zNg8YTrAOSzXqtprzDMESQ1bF9hOiH24TXg/bpBV53zU+8v+p0yJ+Cehc= Received: by 10.142.132.2 with SMTP id f2mr2303217wfd.221.1198086904877; Wed, 19 Dec 2007 09:55:04 -0800 (PST) Received: by 10.142.101.2 with HTTP; Wed, 19 Dec 2007 09:55:04 -0800 (PST) Message-ID: Date: Wed, 19 Dec 2007 15:55:04 -0200 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] MARCO E MAURO In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_26146_6202024.1198086904853" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,BIG_FONT,IN_REP_TO,LINES_OF_YELLING,LINES_OF_YELLING_2, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_26146_6202024.1198086904853 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline os dois andam em MHS, x1=3DA*cos(2pit/90) x2=3DA*cos(2pit/60+180) pit/45+pit/30+pi=3Dn*2pi t/45+t/30=3D2n-1 t=3D(2n-1)*45*30/75=3D(2n-1)(18) 36n-18<720 36n<738 n<369/18~20,5 n=3D20 On 12/17/07, arkon wrote: > > *ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:* > > * * > > *Marco e Mauro costumam treinar nata=E7=E3o na mesma piscina e no mesmo > hor=E1rio. Eles iniciam os treinos simultaneamente, a partir de lados opo= stos > da piscina, nadando um em dire=E7=E3o ao outro. Marco vai de um lado a ou= tro da > piscina em 45 segundos, enquanto Mauro vai de um lado ao outro em 30 > segundos. Durante 12 minutos, eles nadam de um lado para outro, sem perde= r > qualquer tempo nas viradas. Durante esses 12 minutos, eles podem > encontrar-se quer quando est=E3o nadando no mesmo sentido, quer quando es= t=E3o > nadando em sentidos opostos, assim como podem encontrar-se quando ambos > est=E3o fazendo a virada no mesmo extremo da piscina. Dessa forma, o n=FA= mero de > vezes que Marco e Mauro se encontram durante esses 12 minutos =E9:* > > * * > > *a) 10. b) 12. c) 15. d) 18. e) 20.* > > * * > > *GABARITO LETRA E* > > * * > > *DESDE J=C1 MUITO OBRIGADO* > ------=_Part_26146_6202024.1198086904853 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
os dois andam em MHS,
x1=3DA*cos(2pit/90)
x2=3DA*cos(2pit/60+180)
pit/45+pit/30+pi=3Dn*2pi
t/45+t/30=3D2n-1
t=3D(2n-1)*45*30/75=3D(2n-1)(18)
36n-18<720
36n<738
n<369/18~20,5
n=3D20

 
On 12/17/07, arkon <arkon@bol.com.br>= wrote:

<= font face=3D"Times New Roman">ALGU=C9M PODE, POR FAVOR, RESOLVER ESTA:

 

<= font face=3D"Times New Roman">Marco e Mauro costumam treinar nata=E7=E3o na= mesma piscina e no mesmo hor=E1rio. Eles iniciam os treinos simultaneament= e, a partir de lados opostos da piscina, nadando um em dire=E7=E3o ao outro= . Marco vai de um lado a outro da piscina em 45 segundos, enquanto Mauro va= i de um lado ao outro em 30 segundos. Durante 12 minutos, eles nadam de um = lado para outro, sem perder qualquer tempo nas viradas. Durante esses 12 mi= nutos, eles podem encontrar-se quer quando est=E3o nadando no mesmo sentido= , quer quando est=E3o nadando em sentidos opostos, assim como podem encontr= ar-se quando ambos est=E3o fazendo a virada no mesmo extremo da piscina. De= ssa forma, o n=FAmero de vezes que Marco e Mauro se encontram durante esses= 12 minutos =E9:

 

a) 10.      b) 12.&nbs= p;     c) 15.     = ; d) 18.    = e) 20.

 

GABARITO LETRA E<= /font>

 

DESDE J=C1 MUITO OBRIGADO


------=_Part_26146_6202024.1198086904853-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 16:20:35 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJIHS8l002067 for ; Wed, 19 Dec 2007 16:17:28 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJIHS40002065 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 16:17:28 -0200 Received: from web56306.mail.re3.yahoo.com (web56306.mail.re3.yahoo.com [216.252.110.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBJIHD8l002054 for ; Wed, 19 Dec 2007 16:17:15 -0200 Received: (qmail 96439 invoked by uid 60001); 19 Dec 2007 19:18:45 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=gonHdyDp2x1OMnlFiUCMiGK+hQDsksikueLHBhjszuTDmcRKuSOMmR2VqyYAT/GCygd6xWU4851zcFq0oAvJourre3MkrjECbNU3L8wKg+99F6/kLQ2nE041FhnR0Se0P9voUtDLVCMqLU5IIoWGNkfFNw9wIjn44C0OHZtJ868=; X-YMail-OSG: qbaBFHAVM1kuTAxzTir3VrO495H7DOqtvxfC0b3ClzT8iNrZVmo_GnKo5bW.EYYoQAJ_OemP7YrIMqNO1yz6zajQagjUfim10SrtY34a775VUp_CTEQ- Received: from [200.100.164.202] by web56306.mail.re3.yahoo.com via HTTP; Wed, 19 Dec 2007 16:18:44 ART Date: Wed, 19 Dec 2007 16:18:44 -0300 (ART) From: Ruy Oliveira Subject: [SPAM] Re: [obm-l] Filhos semelhantes... e naturalmente offtopics.... To: obm-l@mat.puc-rio.br In-Reply-To: <4769431E.4060004@infolink.com.br> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <31432.96019.qm@web56306.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Ruy Oliveira X-Spam-Status: Yes, hits=7.1 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 230.110.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 230.110.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Não acho que seja tão simples assim. Considerando crossing-over e outros aspectos da biologia , acho que a probabilidade é menor que a apresentada por eles..... Apostei que eles tinham errado e sacanear é dizer, considerando que são meus amigos, que eles não conseguiram fazer um exercicio " elementar ". Também tive duvidas se era um problema off-topic, mas para alguém que conheça as circunstâncias em que se pode ter um filho semelhante a outro , passa a ser de probabilidade. Mesmo assim, obrigado..... Ruy --- Carlos Nehab escreveu: --------------------------------- Bem, Ruy, um relax ... Se os biólogos consideram que há 45 genes "binários" que determinam asemelhança entre os filhos, quero crer que a resposta deles estariaabsolutamente correta... e o pneu de seu carro seria furado ...(hahaha). Feliz Natal a todos, independente do credo, e um ótimo Ano Novo atodos, Abraços biológicos, Nehab Bruno França dos Reis escreveu:Isso é uma questão de matemática? O que vc quer dizer com "sacanear" esses caras? A primeira imagem queme vem na cabeça é vc furar os pneus dos carros deles, o que não é nadamatemático (tampouco correto). 2007/12/18, Ruy Oliveira : Doisamigos biólogos calcularam a probabilidade de uma familia ter dois filhos ( não gemêos ) , totalmente semelhantes. Eles , óbviamente consideraram os aspectos biológicos para a ocorrencia de tal evento. chegaram a resposta (1/2)^45... Alguém me ajudaria a sacanear esses caras?? Abraço Abra sua conta no Yahoo! Mail, o único sem limite de espaço paraarmazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= -- Bruno FRANÇA DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=0=========================================================================Instruções para entrar na lista, sair da lista e usar a lista emhttp://www.mat.puc-rio.br/~obmlistas/obm-l.html========================================================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 19 19:29:11 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJLR48l010541 for ; Wed, 19 Dec 2007 19:27:04 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBJLR4Ck010539 for obm-l-MllGbsmmN; Wed, 19 Dec 2007 19:27:04 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBJLR28l010489 for ; Wed, 19 Dec 2007 19:27:02 -0200 Received: from localhost (localhost [127.0.0.1]) by socom8.uol.com.br (Postfix) with ESMTP id D11DA1C000070 for ; Wed, 19 Dec 2007 20:28:37 -0200 (BRST) Received: from PAVILION (unknown [189.12.0.1]) by socom8.uol.com.br (Postfix) with ESMTP id 3B5011C0001DC for ; Wed, 19 Dec 2007 20:28:35 -0200 (BRST) Message-ID: From: "Ojesed Mirror" To: References: <536036.3359.qm@web56312.mail.re3.yahoo.com> <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> In-Reply-To: <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> Subject: [SPAM] Re: [obm-l] Filhos semelhantes... Date: Wed, 19 Dec 2007 19:28:32 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Windows Mail 6.0.6000.16480 X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6000.16545 X-SIG5: 5f381f78fddfce3c087932331e8b6c03 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ojesed Mirror" X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, MIME_EXCESSIVE_QP,MISSING_OUTLOOK_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0047_01C84275.57841560" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 1.0.12.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 1.0.12.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (-1.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0047_01C84275.57841560 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ruy, est=E1 errado, o correto seria (1/2)^46, pois s=E3o 23 cromossomos = do =F3vulo e 23 do espermatozoide. O 1/2 vem do fato da mitose resultar sempre duas c=E9lulas a partir de = uma. Ojesed. ----- Original Message -----=20 From: Bruno Fran=E7a dos Reis=20 To: obm-l@mat.puc-rio.br=20 Sent: Wednesday, December 19, 2007 12:23 PM Subject: Re: [obm-l] Filhos semelhantes... Isso =E9 uma quest=E3o de matem=E1tica? O que vc quer dizer com "sacanear" esses caras? A primeira imagem que = me vem na cabe=E7a =E9 vc furar os pneus dos carros deles, o que n=E3o = =E9 nada matem=E1tico (tampouco correto). 2007/12/18, Ruy Oliveira : Dois amigos bi=F3logos calcularam a probabilidade de uma familia ter dois filhos ( n=E3o gem=EAos ) , totalmente semelhantes. Eles , =F3bviamente consideraram os aspectos biol=F3gicos para a ocorrencia de tal evento. chegaram a resposta (1/2)^45...=20 Algu=E9m me ajudaria a sacanear esses caras?? Abra=E7o Abra sua conta no Yahoo! Mail, o =FAnico sem limite de = espa=E7o para armazenamento! http://br.mail.yahoo.com/=20 = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html=20 = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com=20 skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_NextPart_000_0047_01C84275.57841560 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ruy, est=E1 errado, o correto seria = (1/2)^46, pois=20 s=E3o 23 cromossomos do =F3vulo e 23 do espermatozoide.
O 1/2 vem do fato da = mitose resultar sempre=20 duas c=E9lulas a partir de uma.
 
Ojesed.
----- Original Message -----
From:=20 Bruno = Fran=E7a dos=20 Reis
Sent: Wednesday, December 19, = 2007 12:23=20 PM
Subject: Re: [obm-l] Filhos=20 semelhantes...

Isso =E9 uma quest=E3o de matem=E1tica?
O que vc = quer dizer com=20 "sacanear" esses caras? A primeira imagem que me vem na cabe=E7a =E9 = vc furar os=20 pneus dos carros deles, o que n=E3o =E9 nada matem=E1tico (tampouco=20 correto).

2007/12/18, Ruy Oliveira <ruyhigh@yahoo.com.br>:=
Dois=20 amigos bi=F3logos calcularam a probabilidade de uma
familia ter = dois filhos=20 ( n=E3o gem=EAos ) , totalmente
semelhantes. Eles , =F3bviamente = consideraram=20 os
aspectos biol=F3gicos para a ocorrencia de tal = evento.
chegaram a=20 resposta (1/2)^45...
    Algu=E9m me = ajudaria a=20 sacanear esses=20 = caras??
        Abra=E7o



      Abra=20 sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para=20 armazenamento!
http://br.mail.yahoo.com/=20 =
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D
Instru=E7=F5es=20 para entrar na lista, sair da lista e usar a lista em
http://www.mat.p= uc-rio.br/~obmlistas/obm-l.html=20 =
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D


--
Bruno FRAN=C7A DOS REIS

msn: brunoreis666@hotmail.com =
skype:=20 brunoreis666
tel: +33 (0)6 28 43 42 16

e^(pi*i)+1=3D0=20 ------=_NextPart_000_0047_01C84275.57841560-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 01:11:54 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBK39x8l031154 for ; Thu, 20 Dec 2007 01:09:59 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBK39xk2031152 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 01:09:59 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.247]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBK39t8l031105 for ; Thu, 20 Dec 2007 01:09:56 -0200 Received: by hs-out-2122.google.com with SMTP id 4so3382006hsl.13 for ; Wed, 19 Dec 2007 20:11:30 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=qcPoGxy0qLTmIQHQz3+kuZNSUzU2GVvpXDnWMPXw2YE=; b=Yv0ahqWuigebVtTI5EH1aB+BseDVrq9WUDRYY4AQywBrmcL/9LzY6siKNr2nphvppE1oC3g4k7H/q213ETdyecHY3DZZSCaJvwXEe4ibLJ0FAtffYA0b1uuralq2hiyyytQfeGgyqrWS81QYiEFpdJJS8v5o5jFzSLd+dlQXW44= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=wXS3GoDsvc/BwEKvj2QT0pog/s35CknG2kAi5Qc8Qgr4viHwu4eJvnCixvtIoDn0ykI2YjFb3ssu8vE8fsoaqpODHl5N5pFi4TBryhCvsgOLpMeMOKfY71eQZ2xUMk8+ZzRSgggGl9MU1oDgcPRc6FF1DXFf1MN/P5yFrahHQpo= Received: by 10.150.201.13 with SMTP id y13mr3978574ybf.53.1198123890464; Wed, 19 Dec 2007 20:11:30 -0800 (PST) Received: by 10.150.158.20 with HTTP; Wed, 19 Dec 2007 20:11:30 -0800 (PST) Message-ID: <5bb472220712192011u4401e8c8p49d124da23637572@mail.gmail.com> Date: Thu, 20 Dec 2007 02:11:30 -0200 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Trigonometria... In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <5bb472220712190629u74ee42acld034384c749a3f76@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBK39v8l031146 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caro Saulo, Tente numa calculadora cos80-sin190(2*80+30)=0???? Não bate!!! mas valeu assim mesmo. JVB On 12/19/07, saulo nilson wrote: > 3x+30=90 > x=20º > 3x+30=270 > x=80 > > > > On 12/19/07, Joao Victor Brasil wrote: > > > > Olá pessoal, > > > > Estou precisando de uma ajuda para resolver este problema: > > > > No intervalo [0º,360º], a soma dos valores que satisfazem a eqaução > > sen(2x+30º)=cosx. > > > > Agradeço desde já a ajuda. > > > > Abraços, > > > > Joao Victor > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 08:39:05 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKAaa8l020167 for ; Thu, 20 Dec 2007 08:36:36 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKAaaoH020165 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 08:36:36 -0200 Received: from web33807.mail.mud.yahoo.com (web33807.mail.mud.yahoo.com [209.191.69.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBKAaY8l020161 for ; Thu, 20 Dec 2007 08:36:34 -0200 Received: (qmail 56138 invoked by uid 60001); 20 Dec 2007 11:38:09 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=prD2bznBE9n3mbgVy0C1mWTwZ4lbYUZJh1wze/bc31gFHttAN/GvSXWQa8g1Kk47vjuWdSLpsexp8wgGH94N6xGnpdEalHiQyLaqxH3E4IxvwcoXGFCWS/NfD+NSFHm8K7uttFH6jEipZClhzU+st8gUXZtAWjh/ePSBzz0v7i8=; X-YMail-OSG: QJeE0ioVM1m4jtaCCiDlYac1kCtKNmuelJ12g5x44TfAbrxoPSoPtGOeDF_hEqcI93txhScjD91wttAtL.MY9rS_y5xV5EOmaQr8BDi9r.fBkq4XSc5jBqNgyDkBIg-- Received: from [201.51.43.19] by web33807.mail.mud.yahoo.com via HTTP; Thu, 20 Dec 2007 03:38:09 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Thu, 20 Dec 2007 03:38:09 -0800 (PST) From: Klaus Ferraz Subject: [SPAM] [obm-l] equacao funcional To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <369302.55965.qm@web33807.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Klaus Ferraz X-Spam-Status: Yes, hits=8.2 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-105069605-1198150689=:55965" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 170.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 170.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-105069605-1198150689=:55965 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy) = para todo x e y positivos. Mostre que f =C3=A9 uma funcao constante.=0A=0A= =0A Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3= =A7o para armazenamento!=0Ahttp://br.mail.yahoo.com/ --0-105069605-1198150689=:55965 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Seja f uma funcao real definida= por todo x positivo tal que f(x+y)=3Df(xy) para todo x e y positivos. Most= re que f =C3=A9 uma  funcao constante.
=0A

<= /div>
=0A=0A=0A
Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento! =0A --0-105069605-1198150689=:55965-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 09:57:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKBsx8l026377 for ; Thu, 20 Dec 2007 09:54:59 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKBsxbh026373 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 09:54:59 -0200 Received: from bay0-omc2-s6.bay0.hotmail.com (bay0-omc2-s6.bay0.hotmail.com [65.54.246.142]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKBsu8l026364 for ; Thu, 20 Dec 2007 09:54:57 -0200 Received: from BAY135-W45 ([65.55.140.80]) by bay0-omc2-s6.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Thu, 20 Dec 2007 04:56:26 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_30ddbfed-489d-43f6-abaa-2fab31281ef3_" X-Originating-IP: [161.148.51.149] From: Anselmo Alves de Sousa To: Subject: RE: [obm-l] equacao funcional Date: Thu, 20 Dec 2007 15:56:26 +0300 Importance: Normal In-Reply-To: <369302.55965.qm@web33807.mail.mud.yahoo.com> References: <369302.55965.qm@web33807.mail.mud.yahoo.com> MIME-Version: 1.0 X-OriginalArrivalTime: 20 Dec 2007 12:56:26.0015 (UTC) FILETIME=[BAEF82F0:01C84307] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Anselmo Alves de Sousa X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,HTML_FONT_COLOR_RED,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_30ddbfed-489d-43f6-abaa-2fab31281ef3_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy) = para todo x e y positivos. Mostre que f =E9 uma funcao constante. Suponhamos que f =E9 n=E3o constante; Assim existe algum x nos reais, digam= os x_1, tal que f(x_1) =E9 diferente de f(x_2), x_2 tamb=E9m nos reais e x_= 1 diferente de x_2. =20 Assim f(x_1+x_2) =3D f(x_1*x_2); =20 f(x_1+0) =3D f(0*0) , isto =E9 f(x_1) =3D f(0). f(x_2+0) =3D f(x_2*0), que nos d=E1 f(x_2) =3D f(0) =20 O que nos mostra que f(x_1) =3D f(x_2). O que =E9 absurdo pois supomos que = f =E9 n=E3o constante. =20 Logo, conclu=EDmos que f =E9 fun=E7=E3o constante. =20 =20 Anselmo :-) _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_30ddbfed-489d-43f6-abaa-2fab31281ef3_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Seja f uma funcao real definida por todo x p= ositivo tal que f(x+y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 = uma  funcao constante.

Suponhamos que f =E9 n=E3o constante; Assim exis= te algum x nos reais, digamos x_1, tal que f(x_1) =E9 diferente de f(x_2), = x_2 tamb=E9m nos reais e x_1 diferente de x_2.
 
Assim f(x_1+x_2) =3D f(x_1*x_2);
 
f(x_1+0) =3D f(0*0) , isto =E9 f(x_1) =3D f(0).
f(x_2+0) =3D f(x_2*0), que nos d=E1 f(x_2) =3D f(0)
 
O que nos mostra que f(x_1) =3D f(x_2). O que =E9 abs= urdo pois supomos que f =E9 n=E3o constante.
 
Logo, conclu=EDmos que f =E9 fun=E7=E3o constante.
 
 
Anselmo :-)

Receba= GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA estiver of= fline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! = --_30ddbfed-489d-43f6-abaa-2fab31281ef3_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 09:57:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKBtm8l026410 for ; Thu, 20 Dec 2007 09:55:48 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKBtl4C026408 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 09:55:47 -0200 Received: from bay0-omc2-s13.bay0.hotmail.com (bay0-omc2-s13.bay0.hotmail.com [65.54.246.149]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKBtj8l026405 for ; Thu, 20 Dec 2007 09:55:46 -0200 Received: from BAY135-W36 ([65.55.140.71]) by bay0-omc2-s13.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Thu, 20 Dec 2007 04:57:21 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_35e17b2f-1158-42c9-9ab3-1d33cc49424f_" X-Originating-IP: [161.148.51.149] From: Anselmo Alves de Sousa To: Subject: RE: [obm-l] equacao funcional Date: Thu, 20 Dec 2007 15:57:21 +0300 Importance: Normal In-Reply-To: <369302.55965.qm@web33807.mail.mud.yahoo.com> References: <369302.55965.qm@web33807.mail.mud.yahoo.com> MIME-Version: 1.0 X-OriginalArrivalTime: 20 Dec 2007 12:57:21.0380 (UTC) FILETIME=[DBEF8A40:01C84307] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Anselmo Alves de Sousa X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_35e17b2f-1158-42c9-9ab3-1d33cc49424f_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 =20 DESCULPEM n=C2O Vi A RESTRI=C7=C2O Date: Thu, 20 Dec 2007 03:38:09 -0800From: klausferraz@yahoo.com.brSubject:= [obm-l] equacao funcionalTo: obm-l@mat.puc-rio.br Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy) = para todo x e y positivos. Mostre que f =E9 uma funcao constante. Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armaze= namento!=20 _________________________________________________________________ Conhe=E7a o Windows Live Spaces, a rede de relacionamentos do Messenger! http://www.amigosdomessenger.com.br/= --_35e17b2f-1158-42c9-9ab3-1d33cc49424f_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable  
 


DESCULPEM n=C2O Vi A RESTRI=C7=C2O


Date: Thu, 20 Dec 2007 03:38:09 -0800
From: klausferraz@yahoo.com.br
= Subject: [obm-l] equacao funcional
To: obm-l@mat.puc-rio.br

Seja f uma funcao real definida por todo x p= ositivo tal que f(x+y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 = uma  funcao constante.


Abra sua conta no Yahoo! Mail, o =FAnico sem limi= te de espa=E7o para armazenamento!

Conhe=E7a j=E1 = o Windows Live Spaces, o site de relacionamentos do Messenger! Crie j=E1 o seu! = --_35e17b2f-1158-42c9-9ab3-1d33cc49424f_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 12:29:29 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKEJaHN021178 for ; Thu, 20 Dec 2007 12:26:24 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKDKOMi016604 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 11:20:24 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKDK88l016494 for ; Thu, 20 Dec 2007 11:20:10 -0200 Received: by rv-out-0910.google.com with SMTP id c27so2772178rvf.9 for ; Thu, 20 Dec 2007 06:21:44 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=jeCITmP1hKbo813WM5Jt6Vu8BO8SALCWaQxggZPppDM=; b=To/cuPKKgm9FhoP4THbU5plScb/JbQylV0+SvQfP9xegMnGhcgq/pv0smes/Mt2vd8UulG5tmehViHJJNuSodjzGk65AuII617ecJqtuQ3rpKMycIGE4dwghAzKMfZYGKzlXanAVQHFP9uzF6R2e5Ff5PBWhITyF8DZrKUVYv7g= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=cW/sTSmlsDTnhW99qhKP+tFed936LT/IESNIl10RjTO1V1axrsurvCoKzG98Sx8uJmltartx3Br+VhT3cSpO2NBhBw37/kQ0VtTgdKcOY07UUH1+HEqhafba/+C1Iux7x60JSPbeSdxf5k3sUaNeP11qSHjXz2pscSvGcQis/Eg= Received: by 10.140.125.4 with SMTP id x4mr6840432rvc.229.1198160504251; Thu, 20 Dec 2007 06:21:44 -0800 (PST) Received: by 10.141.99.13 with HTTP; Thu, 20 Dec 2007 06:21:44 -0800 (PST) Message-ID: <99886d920712200621mca7e56dg108984494a3754a7@mail.gmail.com> Date: Thu, 20 Dec 2007 15:21:44 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] equacao funcional In-Reply-To: <369302.55965.qm@web33807.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_21269_1484694.1198160504242" References: <369302.55965.qm@web33807.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_21269_1484694.1198160504242 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Note que para todo t >=3D 2, podemos encontrar um s real positivo tal que t= =3D s + 1/s =3D (s^2+1)/s. Com efeito, s^2 - ts + 1 =3D 0, onde o discriminante= =E9 t^2 - 4. Da=ED tiramos que f(t) =3D f(s + 1/s) =3D f(1) para t >=3D 2. Para todo t, 1 < t < 2, encontramos s, 1 < s (2) ) =3D f(1). Finalmente, para 0 < t < 1= , f(t) =3D f(1*t) =3D f(1 + t) =3D f(1). Bruno 2007/12/20, Klaus Ferraz : > > Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy= ) > para todo x e y positivos. Mostre que f =E9 uma funcao constante. > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_21269_1484694.1198160504242 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Note que para todo t >=3D 2, podemos encontrar um s real positivo tal qu= e t =3D s + 1/s =3D (s^2+1)/s. Com efeito, s^2 - ts + 1 =3D 0, onde o discr= iminante =E9 t^2 - 4. Da=ED tiramos que f(t) =3D f(s + 1/s) =3D f(1) para t= >=3D 2.
Para todo t, 1 < t < 2, encontramos s, 1 < s (<t) < 2, tal q= ue s^2 =3D t. Assim f(t) =3D f(s*s) =3D f(s+s (>2) ) =3D f(1). Finalment= e, para 0 < t < 1, f(t) =3D f(1*t) =3D f(1 + t) =3D f(1).

Brun= o

2007/12/20, Klaus Ferraz <klausferraz@yahoo.com.br>:
Seja f uma funcao real definida por todo x positivo= tal que f(x+y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 uma&nbs= p; funcao constante.


Abra sua conta no Yahoo! Mail, o =FAnico sem= limite de espa=E7o para armazenamento!=20



--
Bruno FRAN= =C7A DOS REIS

msn: bruno= reis666@hotmail.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16=

e^(pi*i)+1=3D0 ------=_Part_21269_1484694.1198160504242-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 12:29:29 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKEJaHP021178 for ; Thu, 20 Dec 2007 12:26:25 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKDLD2c016866 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 11:21:14 -0200 Received: from mu-out-0910.google.com (mu-out-0910.google.com [209.85.134.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKDL28l016763 for ; Thu, 20 Dec 2007 11:21:04 -0200 Received: by mu-out-0910.google.com with SMTP id i10so4989573mue.5 for ; Thu, 20 Dec 2007 06:22:38 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=jeCITmP1hKbo813WM5Jt6Vu8BO8SALCWaQxggZPppDM=; b=To/cuPKKgm9FhoP4THbU5plScb/JbQylV0+SvQfP9xegMnGhcgq/pv0smes/Mt2vd8UulG5tmehViHJJNuSodjzGk65AuII617ecJqtuQ3rpKMycIGE4dwghAzKMfZYGKzlXanAVQHFP9uzF6R2e5Ff5PBWhITyF8DZrKUVYv7g= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=cW/sTSmlsDTnhW99qhKP+tFed936LT/IESNIl10RjTO1V1axrsurvCoKzG98Sx8uJmltartx3Br+VhT3cSpO2NBhBw37/kQ0VtTgdKcOY07UUH1+HEqhafba/+C1Iux7x60JSPbeSdxf5k3sUaNeP11qSHjXz2pscSvGcQis/Eg= Received: by 10.140.125.4 with SMTP id x4mr6840432rvc.229.1198160504251; Thu, 20 Dec 2007 06:21:44 -0800 (PST) Received: by 10.141.99.13 with HTTP; Thu, 20 Dec 2007 06:21:44 -0800 (PST) Message-ID: <99886d920712200621mca7e56dg108984494a3754a7@mail.gmail.com> Date: Thu, 20 Dec 2007 15:21:44 +0100 From: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] equacao funcional In-Reply-To: <369302.55965.qm@web33807.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_21269_1484694.1198160504242" References: <369302.55965.qm@web33807.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Bruno_Fran=E7a_dos_Reis?=" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_21269_1484694.1198160504242 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Note que para todo t >=3D 2, podemos encontrar um s real positivo tal que t= =3D s + 1/s =3D (s^2+1)/s. Com efeito, s^2 - ts + 1 =3D 0, onde o discriminante= =E9 t^2 - 4. Da=ED tiramos que f(t) =3D f(s + 1/s) =3D f(1) para t >=3D 2. Para todo t, 1 < t < 2, encontramos s, 1 < s (2) ) =3D f(1). Finalmente, para 0 < t < 1= , f(t) =3D f(1*t) =3D f(1 + t) =3D f(1). Bruno 2007/12/20, Klaus Ferraz : > > Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy= ) > para todo x e y positivos. Mostre que f =E9 uma funcao constante. > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > --=20 Bruno FRAN=C7A DOS REIS msn: brunoreis666@hotmail.com skype: brunoreis666 tel: +33 (0)6 28 43 42 16 e^(pi*i)+1=3D0 ------=_Part_21269_1484694.1198160504242 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Note que para todo t >=3D 2, podemos encontrar um s real positivo tal qu= e t =3D s + 1/s =3D (s^2+1)/s. Com efeito, s^2 - ts + 1 =3D 0, onde o discr= iminante =E9 t^2 - 4. Da=ED tiramos que f(t) =3D f(s + 1/s) =3D f(1) para t= >=3D 2.
Para todo t, 1 < t < 2, encontramos s, 1 < s (<t) < 2, tal q= ue s^2 =3D t. Assim f(t) =3D f(s*s) =3D f(s+s (>2) ) =3D f(1). Finalment= e, para 0 < t < 1, f(t) =3D f(1*t) =3D f(1 + t) =3D f(1).

Brun= o

2007/12/20, Klaus Ferraz <klausferraz@yahoo.com.br>:
Seja f uma funcao real definida por todo x positivo= tal que f(x+y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 uma&nbs= p; funcao constante.


Abra sua conta no Yahoo! Mail, o =FAnico sem= limite de espa=E7o para armazenamento!=20



--
Bruno FRAN= =C7A DOS REIS

msn: bruno= reis666@hotmail.com
skype: brunoreis666
tel: +33 (0)6 28 43 42 16=

e^(pi*i)+1=3D0 ------=_Part_21269_1484694.1198160504242-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 13:28:25 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKFJZHT026807 for ; Thu, 20 Dec 2007 13:26:37 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKEMcbY022159 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 12:22:38 -0200 Received: from mu-out-0910.google.com (mu-out-0910.google.com [209.85.134.191]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKEMP8l022065 for ; Thu, 20 Dec 2007 12:22:26 -0200 Received: by mu-out-0910.google.com with SMTP id i10so5026275mue.5 for ; Thu, 20 Dec 2007 07:24:01 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=3rk+TMw3YmatRhUQSDArUfUE8XqHd8PcTMsagEHowZs=; b=ap48H2PIVOPwferqkM/bnCN3qpJ3XC5x5INBcDerP/K85VBYHrzLbNJV8eJZ832iNPe5jEzntOxp3R1HUE4lEWzn+/XXgCkEp1my8nwEidQUIdxffWve49bQIQAzv2upSJmvLO8EzB1IWftrM1aHRRzW+GbPFXoLOyczXsPXsd8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=cKbRSzrt/XEJbE7zevKUhemjMgmXwH5AfoHBwqwvyHrspeFFjBCadG+RY1nxVBS8G3k2lrXHdvO5+LSGw22CSD1mExp50AriHLS8a4wATixDETrqnvfGEvkDsHum55rhI4vST2i/UOprX4LAB8PAzt1dPNY3PxdbsOYlcAdU0T8= Received: by 10.78.200.20 with SMTP id x20mr184686huf.16.1198164240751; Thu, 20 Dec 2007 07:24:00 -0800 (PST) Received: by 10.78.97.9 with HTTP; Thu, 20 Dec 2007 07:24:00 -0800 (PST) Message-ID: <29e1bfbd0712200724p5b81995dj5703c0e244557352@mail.gmail.com> Date: Thu, 20 Dec 2007 13:24:00 -0200 From: "Felipe Diniz" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] equacao funcional In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_19634_23274819.1198164240743" References: <369302.55965.qm@web33807.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Felipe Diniz" X-Spam-Status: No, hits=2.4 required=5.0 tests=EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_19634_23274819.1198164240743 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline como f(x+y)=3Df(xy), fazendo x=3D1 f(y+1)=3Df(y) assim se provarmos que f(t) =E9 constante para t pertencente a (0,1] acaba. da propriedade acima tambem temos tambem que f(nx)=3Df(x) e f(n+x)=3Df(x) p= ara x real positivo e n natural. seja r um irracional e b natural, temos que f(br)=3Df(r) e tambem temos que f( br )=3D f( [br] + {br} )=3Df( [br]{br} )=3Df( {br} ) pois [br] =E9 natu= ral.. onde [br] =E9 o menor inteiro maior ou igual a br e {br} =E9 a parte fracionaria. assim f( {br} ) =3D f(r) Pelo teorema de Kronecker temos que {br} =E9 denso em (0,1) logo, como f( {= br} ) =3D f(r) para b natural, temos que f(x) =E9 constante para x pertencente = a (0,1). Como f(1)=3Df(1/2+ 1/2)=3Df(1/4) acabou. espero que esteja correto. Abra=E7os, Felipe Diniz On Dec 20, 2007 10:57 AM, Anselmo Alves de Sousa wrote: > > > > > DESCULPEM n=C2O Vi A RESTRI=C7=C2O > > > ------------------------------ > Date: Thu, 20 Dec 2007 03:38:09 -0800 > From: klausferraz@yahoo.com.br > Subject: [obm-l] equacao funcional > To: obm-l@mat.puc-rio.br > > Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(x= y) > para todo x e y positivos. Mostre que f =E9 uma funcao constante. > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > > ------------------------------ > Conhe=E7a j=E1 o Windows Live Spaces, o site de relacionamentos do Messen= ger! Crie > j=E1 o seu! > ------=_Part_19634_23274819.1198164240743 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline como f(x+y)=3Df(xy), fazendo x=3D1
f(y+1)=3Df(y)
assim se provarmos q= ue f(t) =E9 constante para t pertencente a (0,1] acaba.

da proprieda= de acima tambem temos tambem que f(nx)=3Df(x) e f(n+x)=3Df(x) para x real p= ositivo e n natural.


seja r um irracional e b natural, temos que
f(br)=3Df(r)
= e tambem temos que
f( br )=3D  f( [br] + {br} )=3Df( [br]{br} )=3Df= ( {br} ) pois [br] =E9 natural.. onde [br] =E9 o menor inteiro maior ou igu= al a br e {br} =E9 a parte fracionaria.
assim f( {br} ) =3D f(r)
Pelo teorema de Kronecker temos que {br} = =E9 denso em (0,1) logo, como f( {br} ) =3D f(r) para b natural, temos que = f(x) =E9 constante para x pertencente a (0,1).

Como f(1)=3Df(1/2+ 1/= 2)=3Df(1/4) acabou.


espero que esteja correto.

Abra=E7os,
Felipe Diniz



On Dec 20, 2007 10:57 AM, Ansel= mo Alves de Sousa < anselmo_rj@hotmail.com > wrote:
klausferraz@yahoo.com.br
Subject: = [obm-l] equacao funcional
To: obm-l@mat.puc-rio.br


Seja f uma funcao real definida por todo x positivo tal que f(x+= y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 uma  funcao con= stante.


Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!

Conhe=E7a j= =E1 o Windows Live Spaces, o site de relacionamentos do Messenger!=20 Crie j=E1= o seu!

------=_Part_19634_23274819.1198164240743-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 13:31:10 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKFTp8l029926 for ; Thu, 20 Dec 2007 13:29:51 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKFToJm029923 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 13:29:50 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKFTn8l029892 for ; Thu, 20 Dec 2007 13:29:49 -0200 Received: from localhost (localhost [127.0.0.1]) by socom4.uol.com.br (Postfix) with ESMTP id BB099E00DB90 for ; Thu, 20 Dec 2007 14:31:25 -0200 (BRST) Received: from PAVILION (unknown [189.12.2.119]) by socom4.uol.com.br (Postfix) with ESMTP id 8CAE6E0009D8 for ; Thu, 20 Dec 2007 14:31:20 -0200 (BRST) Message-ID: <66F665E9F7124DD7AB1E1DB20965926D@PAVILION> From: "Ojesed Mirror" To: References: <369302.55965.qm@web33807.mail.mud.yahoo.com> In-Reply-To: <369302.55965.qm@web33807.mail.mud.yahoo.com> Subject: [SPAM] [obm-l] cossenos sucessivos Date: Thu, 20 Dec 2007 13:31:11 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Windows Mail 6.0.6000.16480 X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6000.16545 X-SIG5: 7c05bb1d0efe81aa8c45e3d17fe70448 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ojesed Mirror" X-Spam-Status: Yes, hits=5.2 required=5.0 tests=AWL,IN_REP_TO,MISSING_OUTLOOK_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0037_01C8430C.96147210" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 119.2.12.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 119.2.12.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0037_01C8430C.96147210 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Numa calculadora operando em radianos, submete-se qualquer n=C3=BAmero a = opera=C3=A7=C3=B5es sucessivas de cosseno e observa-se que o n=C3=BAmero = converge para um mesmo valor, independente do valor inicial adotado. O valor pode ser obtido numericamente de cos(x)=3Dx. Mostrar que esta opera=C3=A7=C3=A3o transforma qualquer real neste = n=C3=BAmero. Ojesed ------=_NextPart_000_0037_01C8430C.96147210 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable =EF=BB=BF
Numa calculadora operando em=20 radianos, submete-se qualquer n=C3=BAmero a = opera=C3=A7=C3=B5es sucessivas de cosseno=20 e observa-se que o n=C3=BAmero converge para um mesmo valor, = independente=20 do valor inicial adotado.
O valor pode ser obtido numericamente = de=20 cos(x)=3Dx.
 
Mostrar que esta = opera=C3=A7=C3=A3o transforma=20 qualquer real neste n=C3=BAmero.
 
Ojesed
------=_NextPart_000_0037_01C8430C.96147210-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 14:06:28 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKG5D8l006855 for ; Thu, 20 Dec 2007 14:05:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKG5CGD006847 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 14:05:12 -0200 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKG5A8l006818 for ; Thu, 20 Dec 2007 14:05:10 -0200 Received: from SRV015.mme.gov.br ([172.16.1.16]) by srv016.mme.gov.br ([172.16.1.45]) with mapi; Thu, 20 Dec 2007 15:07:11 -0200 From: Artur Costa Steiner To: "obm-l@mat.puc-rio.br" Date: Thu, 20 Dec 2007 15:07:09 -0200 Subject: RES: [obm-l] equacao funcional Thread-Topic: [obm-l] equacao funcional Thread-Index: AchDKPRwaGf1iTvOQcCAoNHSlteH5AAAb0zQ Message-ID: In-Reply-To: <29e1bfbd0712200724p5b81995dj5703c0e244557352@mail.gmail.com> Accept-Language: pt-BR, en-US Content-Language: pt-BR X-MS-Has-Attach: X-MS-TNEF-Correlator: acceptlanguage: pt-BR, en-US x-tm-as-product-ver: SMEX-8.0.0.1181-5.000.1023-15618.000 x-tm-as-result: No--29.379200-4.000000-31 x-tm-as-user-approved-sender: No x-tm-as-user-blocked-sender: No Content-Type: multipart/alternative; boundary="_000_AE9C7C4248A5904297801DE13EF8DD131A2362E953SRV015mmegovb_" MIME-Version: 1.0 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: No, hits=1.8 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,HTML_FONT_COLOR_BLUE,IN_REP_TO, MAILTO_LINK,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, TO_ADDRESS_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_000_AE9C7C4248A5904297801DE13EF8DD131A2362E953SRV015mmegovb_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Nesta prova, n=E3o foi implicitamente admitida a continuidae de f? Artur -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome d= e Felipe Diniz Enviada em: quinta-feira, 20 de dezembro de 2007 13:24 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] equacao funcional como f(x+y)=3Df(xy), fazendo x=3D1 f(y+1)=3Df(y) assim se provarmos que f(t) =E9 constante para t pertencente a (0,1] acaba. da propriedade acima tambem temos tambem que f(nx)=3Df(x) e f(n+x)=3Df(x) p= ara x real positivo e n natural. seja r um irracional e b natural, temos que f(br)=3Df(r) e tambem temos que f( br )=3D f( [br] + {br} )=3Df( [br]{br} )=3Df( {br} ) pois [br] =E9 natu= ral.. onde [br] =E9 o menor inteiro maior ou igual a br e {br} =E9 a parte = fracionaria. assim f( {br} ) =3D f(r) Pelo teorema de Kronecker temos que {br} =E9 denso em (0,1) logo, como f( {= br} ) =3D f(r) para b natural, temos que f(x) =E9 constante para x pertence= nte a (0,1). Como f(1)=3Df(1/2+ 1/2)=3Df(1/4) acabou. espero que esteja correto. Abra=E7os, Felipe Diniz On Dec 20, 2007 10:57 AM, Anselmo Alves de Sousa < anselmo_rj@hotmail.com <= mailto:anselmo_rj@hotmail.com> > wrote: DESCULPEM n=C2O Vi A RESTRI=C7=C2O _____ Date: Thu, 20 Dec 2007 03:38:09 -0800 From: klausferraz@yahoo.com.br Subject: [obm-l] equacao funcional To: obm-l@mat.puc-rio.br Seja f uma funcao real definida por todo x positivo tal que f(x+y)=3Df(xy) = para todo x e y positivos. Mostre que f =E9 uma funcao constante. _____ Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamen= to! _____ Conhe=E7a j=E1 o Windows Live Spaces, o site de relacionamentos do Messenge= r! Crie j=E1 o seu! --_000_AE9C7C4248A5904297801DE13EF8DD131A2362E953SRV015mmegovb_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Nesta prova, n=E3o foi implicitamente admitida a continuidae= de f?
Artur
 --_000_AE9C7C4248A5904297801DE13EF8DD131A2362E953SRV015mmegovb_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 17:01:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKIxH8l023925 for ; Thu, 20 Dec 2007 16:59:17 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKIxHkC023923 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 16:59:17 -0200 Received: from web63714.mail.re1.yahoo.com (web63714.mail.re1.yahoo.com [69.147.97.99]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBKIxF8l023916 for ; Thu, 20 Dec 2007 16:59:16 -0200 Received: (qmail 95085 invoked by uid 60001); 20 Dec 2007 20:00:51 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=CiD9BTy6lCJkxvwlTy9Amaek/glgkqQ82gAItT0quL13XAilHHXnJpK/700FbJICGQvHUPOYqEEdUgQKJzXU4O1cd7K9WLhqb0FtvVQYJ6ZnHKSBXhXJR81KQ+rghNby9CW4ANAlsvIMC1ZQy3cs7iWL+YiKg+pZfND0eoNUUXk=; X-YMail-OSG: Xem7GMkVM1mkL30wsm2uiA55uUeQUfjdAkE8mWI5TicEehyyV.rVQrB7uHe07k8fQTnozbJgoHPLvev.P4Zp.ASpWw-- Received: from [189.24.133.180] by web63714.mail.re1.yahoo.com via HTTP; Thu, 20 Dec 2007 17:00:50 ART Date: Thu, 20 Dec 2007 17:00:50 -0300 (ART) From: fagner almeida Subject: [SPAM] Re: [obm-l] Trigonometria... To: obm-l@mat.puc-rio.br In-Reply-To: <5bb472220712192011u4401e8c8p49d124da23637572@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <36492.93572.qm@web63714.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=8.4 required=5.0 tests=FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,HTML_FONT_COLOR_CYAN, HTML_FONT_COLOR_UNSAFE,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1072343034-1198180850=:93572" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 99.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 99.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1072343034-1198180850=:93572 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit http://imagetoker.com/viewer.php?id=890318geometria.JPG http://imagetoker.com/viewer.php?id=541398geometria2.JPG quem puder ajuda valeu --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1072343034-1198180850=:93572 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
http://imagetoker.com/viewer.php?id=890318geometria.JPG

http://imagetoker.com/viewer.php?id=541398geometria2.JPG
 
 
quem puder  ajuda  valeu

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1072343034-1198180850=:93572-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 17:40:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKJdB8l027592 for ; Thu, 20 Dec 2007 17:39:11 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKJdB3t027590 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 17:39:11 -0200 Received: from web63715.mail.re1.yahoo.com (web63715.mail.re1.yahoo.com [69.147.97.100]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBKJd88l027586 for ; Thu, 20 Dec 2007 17:39:08 -0200 Received: (qmail 28265 invoked by uid 60001); 20 Dec 2007 20:40:44 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=CtWjKiPZxDFfwqJwRZigwdAC2HWiS7ckSgPc7AU60/fUIpaQwxjLbxIjom/0ma27jnwzQxs6oCubfNzpBK9EEU3kXt/Z87lmbQv7pRnfGEipZgbEuTolRRiGZ+ZxrY1gWOm5f+ZIFJyySvAU8/2eivmAySN/imU9fIBo3T94Uxg=; X-YMail-OSG: woqS63gVM1mStvU.fIqlNN9F9ftjy1bJIIoOkzxi4DkneFpQy1WtL2AIs8ll4epZZMKBAbX8bdiSP69VBMoYdpg_eg-- Received: from [189.24.133.180] by web63715.mail.re1.yahoo.com via HTTP; Thu, 20 Dec 2007 17:40:44 ART Date: Thu, 20 Dec 2007 17:40:44 -0300 (ART) From: fagner almeida Subject: [SPAM] Re: [obm-l] Trigonometria... To: obm-l@mat.puc-rio.br In-Reply-To: <5bb472220712192011u4401e8c8p49d124da23637572@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <321300.27178.qm@web63715.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=8.5 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,IN_REP_TO, MIME_BOUND_DIGITS_5,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-139216107-1198183244=:27178" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 100.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 100.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-139216107-1198183244=:27178 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit vamos lá sabendo que cosx =sen( 90 - x) temos sen(2x + 30) - sen(90 - x) = 0 aplicando a relação para transforma soma em produto sen x - seny = 2sen[(x - y)/2].cos[(x + y)/2] então 2sen[( 2x +30 -90 +x )/2].cos](2x + 30 + 90 - x)/2] =0 2sen[(3x -60)/2].cos[(x + 120)/2] =0 sen[(3x -60)/2]=0 ou cos[(x + 120)/2] =0 (3x - 60)/2 = k180 ou (x+ 120)/2= 90 + k180 x = 120k + 20 ou x = 60 + k360 k=0 x = 20 k=0 x=60 k=1 x = 140 k=1 x=420 não pertence (0,360) k=2 x = 260 k=3 x não pertence (0,360) a soma é 20 + 140 + 260 + 60 =480 espero ter ajudado Joao Victor Brasil escreveu: Caro Saulo, Tente numa calculadora cos80-sin190(2*80+30)=0???? Não bate!!! mas valeu assim mesmo. JVB On 12/19/07, saulo nilson wrote: > 3x+30=90 > x=20º > 3x+30=270 > x=80 > > > > On 12/19/07, Joao Victor Brasil wrote: > > > > Olá pessoal, > > > > Estou precisando de uma ajuda para resolver este problema: > > > > No intervalo [0º,360º], a soma dos valores que satisfazem a eqaução > > sen(2x+30º)=cosx. > > > > Agradeço desde já a ajuda. > > > > Abraços, > > > > Joao Victor > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-139216107-1198183244=:27178 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
vamos lá
 
sabendo que   cosx =sen( 90 - x)
temos
 
sen(2x + 30)  -   sen(90 - x) = 0
 
aplicando a  relação  para  transforma  soma  em produto
sen x  -  seny = 2sen[(x - y)/2].cos[(x + y)/2]
então
 
2sen[( 2x +30 -90  +x )/2].cos](2x + 30 + 90 - x)/2] =0
 
2sen[(3x -60)/2].cos[(x + 120)/2] =0
 
sen[(3x -60)/2]=0   ou   cos[(x + 120)/2] =0
 
(3x - 60)/2 =  k180    ou   (x+  120)/2= 90  + k180
 
x = 120k + 20            ou   x = 60 + k360
 
k=0   x = 20                    k=0     x=60
k=1   x = 140                  k=1      x=420  não  pertence (0,360)
k=2   x  = 260
k=3   x  não pertence  (0,360)
 
a  soma  é   20 + 140 + 260 + 60  =480
espero  ter  ajudado
 
 
 
 
 
 
 
 
 
 


Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Caro Saulo,

Tente numa calculadora cos80-sin190(2*80+30)=0????

Não bate!!!

mas valeu assim mesmo.
JVB

On 12/19/07, saulo nilson wrote:
> 3x+30=90
> x=20º
> 3x+30=270
> x=80
>
>
>
> On 12/19/07, Joao Victor Brasil wrote:
> >
> > Olá pessoal,
> >
> > Estou precisando de uma ajuda para resolver este problema:
> >
> > No intervalo [0º,360º], a soma dos valores que satisfazem a eqaução
> > sen(2x+30º)=cosx.
> >
> > Agradeço desde já a ajuda.
> >
> > Abraços,
> >
> > Joao Victor
> >
> > =========================================================================
> > Instruções para entrar na lista, sair da lista e usar a lista em
> > http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> > =========================================================================
> >
>

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Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-139216107-1198183244=:27178-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 20 18:11:31 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKK9C8l028974 for ; Thu, 20 Dec 2007 18:09:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBKK9CjK028972 for obm-l-MllGbsmmN; Thu, 20 Dec 2007 18:09:12 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBKK9A8l028969 for ; Thu, 20 Dec 2007 18:09:10 -0200 Received: from 172.26.20.83 (unknown [172.26.20.42]) by socom7.uol.com.br (Postfix) with SMTP id 3558D180648E1 for ; Thu, 20 Dec 2007 19:11:54 -0200 (BRST) Received: from jo5a6ef363071f (unknown [201.80.191.99]) by socom7.uol.com.br (Postfix) with ESMTP id 03F721806409A for ; Thu, 20 Dec 2007 19:11:53 -0200 (BRST) Message-ID: <00cc01c84355$257adff0$63bf50c9@jo5a6ef363071f> From: =?iso-8859-1?Q?Jo=E3o_Lu=EDs_Gomes_Guimar=E3es?= To: References: <36492.93572.qm@web63714.mail.re1.yahoo.com> Subject: [SPAM] Re: [obm-l] Trigonometria... Date: Thu, 20 Dec 2007 19:10:33 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-UOL-AVCHECK-SMTP: OK Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Jo=E3o_Lu=EDs_Gomes_Guimar=E3es?= X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,HTML_FONT_COLOR_CYAN,HTML_FONT_COLOR_UNSAFE, MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_00C9_01C8433B.FEF7C000" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 99.191.80.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 99.191.80.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_00C9_01C8433B.FEF7C000 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable No primeiro, =E9 s=F3 observar que, na figura, os dois tri=E2ngulos ROP = e QOP possuem as caracter=EDsitcas do enunciado (porque RO =3D QO (pela = informa=E7=E3o que est=E1 no desenho), OP =3D OP (lado comum aos dois = tri=E2ngulos) e P =3D P (=E2ngulo comum aos dois tri=E2ngulos)), mas = obviamente os dois tri=E2ngulos n=E3o s=E3o congruentes; O segundo link =E9 um pouco extenso para a minha falta de tempo no = momento. quando puder, volto a ele, ou ent=E3o algum outro colega da = lista responde pra voc=EA. Um abra=E7o, Jo=E3o Lu=EDs. ----- Original Message -----=20 From: fagner almeida=20 To: obm-l@mat.puc-rio.br=20 Sent: Thursday, December 20, 2007 5:00 PM Subject: Re: [obm-l] Trigonometria... http://imagetoker.com/viewer.php?id=3D890318geometria.JPG http://imagetoker.com/viewer.php?id=3D541398geometria2.JPG=20 quem puder ajuda valeu -------------------------------------------------------------------------= ----- Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento! ------=_NextPart_000_00C9_01C8433B.FEF7C000 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
No primeiro, =E9 s=F3 observar que, na figura, = os dois=20 tri=E2ngulos ROP e QOP possuem as caracter=EDsitcas do enunciado (porque = RO =3D QO=20 (pela informa=E7=E3o que est=E1 no desenho), OP =3D OP (lado comum aos = dois tri=E2ngulos)=20 e P =3D P (=E2ngulo comum aos dois tri=E2ngulos)), mas obviamente os = dois tri=E2ngulos=20 n=E3o s=E3o congruentes;
 
O segundo link =E9 um pouco extenso para a minha = falta de tempo=20 no momento. quando puder, volto a ele, ou ent=E3o algum outro colega da = lista=20 responde pra voc=EA.
 
Um abra=E7o,
 
Jo=E3o Lu=EDs.
----- Original Message -----
From:=20 fagner almeida
-----Mensagem original-----
De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome de Felipe Diniz
Enviada em: quinta-feira, 20 de dezembro de 2007 13:24
Para: obm-l@mat.puc-rio.br
Assunto: Re: [obm-l] equacao funcional

como f(x+y)=3Df(xy), fazendo x=3D1
f(y+1)=3Df(y)
assim se provarmos que f(t) =E9 constante para t pertencente a (0,1] acaba.=

da propriedade acima tambem temos tambem que f(nx)=3Df(x) e f(n+x)=3Df(= x) para x real positivo e n natural.


seja r um irracional e b natural, temos que
f(br)=3Df(r)
e tambem temos que
f( br )=3D  f( [br] + {br} )=3Df( [br]{br} )=3Df( {br} ) pois [br]= =E9 natural.. onde [br] =E9 o menor inteiro maior ou igual a br e {br} =E9= a parte fracionaria.
assim f( {br} ) =3D f(r)
Pelo teorema de Kronecker temos que {br} =E9 denso em (0,1) logo, como f( {= br} ) =3D f(r) para b natural, temos que f(x) =E9 constante para x pertence= nte a (0,1).

Como f(1)=3Df(1/2+ 1/2)=3Df(1/4) acabou.


espero que esteja correto.

Abra=E7os,
Felipe Diniz




On Dec 20, 2007 10:57 AM, Anselmo Alves de Sousa= < anselmo_r= j@hotmail.com > wrote:

 


DESCULPEM n=C2O Vi A RESTRI=C7=C2O


Date: Thu, 20 Dec 2007 03:38:09 -0800
From: klausfe= rraz@yahoo.com.br
Subject: [obm-l] equacao funcional
To: obm-l@mat.puc= -rio.br


Seja f uma funcao real definida por todo x positivo tal que f(x&= #43;y)=3Df(xy) para todo x e y positivos. Mostre que f =E9 uma  funcao= constante.


Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamento!

Conhe=E7a j=E1 o Windows Live Spaces, o site de relacionamentos do Messenge= r! Crie j=E1 o seu!

Sent: Sunday, December 23, 2007 = 8:00=20 PM
Subject: [obm-l] Re: [obm-l] = Re: [obm-l]=20 Re: [obm-l] Re: [obm-l] Demonstra=E7=F5es

Realmente eu deixei pouco claro o modo como escrevi = sobre o=20 problema.
Eu quis dizer que a correla=E7=E3o com o problema P = versus NP =E9 a=20 "demonstra=E7=E3o de uma demonstra=E7=E3o" =E9 que
=E9 preciso = provar se existe uma=20 "demonstra=E7=E3o" para demonstra=E7=E3o antes de tentar achar = uma.
Isso est=E1 no=20 ambito de pesquisa do problema NP.

Quanto aos problemas do = mil=EAnio=20 S=E9rgio, s=E3o 7 problemas matem=E1ticos apresentados pelo Instituto = de matem=E1tica=20 Clay, e eles est=E3o oferecerendo $ 1.000.000,00 por problema para = quem os=20 resolver.

O link oficial dos problemas:

http://www.claymath.org/mill= ennium/

Para=20 uma vers=E3o em portugues

http://w= ww.dm.ufscar.br/hp/hp853/hp853001/hp853001.html

Um=20 noticia legal =E9 que foi apresenteada este ano a solu=E7=E3o de um = dos problemas do=20 mil=EAnio - a conjectura de Poincar=E9 - ele foi resolvido pelo =
matem=E1tico=20 russo Grigory Perelman.
O cara faturou um milh=E3o de verdinhas = alem de=20 ganhar a medalha Fields - o nobel da matem=E1tica.
Aqui tem a = noticia:
http://www.e-= escola.pt/site/destaque.asp?dest=3D87

Ainda=20 t=EAm os problemas de Hilbert, caso voc=EA n=E3o conhe=E7a:

http://pt.wiki= pedia.org/wiki/Problemas_de_Hilbert

Espero=20 ter te inspirado ainda mais a pratica da matem=E1tica. Pra mim estes = problemas=20 s=E3o extremamente estimulantes, alem claro do meu gosto natural pela=20 matematica.
Abra=E7os.

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( [201.20.228.254]) by mx.google.com with ESMTPS id 7sm5539429agd.33.2007.12.23.16.03.58 (version=TLSv1/SSLv3 cipher=RC4-MD5); Sun, 23 Dec 2007 16:03:59 -0800 (PST) Message-ID: <476EF76B.9020606@gmail.com> Date: Sun, 23 Dec 2007 22:03:55 -0200 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.6 (X11/20070728) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Simbolos para emails References: <476EE950.6000304@gmail.com> <99886d920712231546y239af375jf573e2977faf012c@mail.gmail.com> In-Reply-To: <99886d920712231546y239af375jf573e2977faf012c@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBNN2P8l026776 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=3.9 required=5.0 tests=IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Foi só uma sugestão. Me passou batido as codificações. Bruno França dos Reis escreveu: > Esses caracteres são bonitos, desde que quem os leia tenha seu > navegador/leitor de emails a codificação de caracteres configurada > como Unicode (aka UTF-8). Em outras codificações (como ISO-8859-1, a > codificação predominante em computadores de brasileiros), a maioria > desses símbolos não pode ser exibida, e eles aparecem normalmente > como um quadradinho branco de borda preta. > > Fora que para digitar esses simbolos, ou vc tem que ter um editor de > emails que eles sejam muito faceis de serem colocados, ou vc tem que > conhecer de cabeça um codigo para inserir cada um desses símbolos ou > tem que ficar procurando com o mouse em uma longa lista de simbolos, > que também terá todas as letras gregas e muitas e muitas outras > coisas, ou, agora que vc nos enviou a tabela, teremos que abrir seu > email, selecionar o que quisermos, CTRL+C e CTRL+V. > > Nenhuma dessas opções me parece muito prática. Assim como não acho > pratico o estabelecimento de normas para a escrita de emails para a > lista, conforme foi sugerido há algumas semanas. Nem tampouco o uso de > notação LaTeX, que, embora muito clara para quem saiba do que estou > falando, não é lá muito prática para escrever em diversos casos, e é > desnecessária para uma lista que não discute a publicação e editoração > profissional de artigos em revistas. > > Acho melhor continuarmos como sempre foi: usando o bom senso aliado à > vontade de ser compreendido na hora de enviar um email, que certamente > fará com que o autor seja compreendido por pelo menos um membro da lista. > > Abraços, > Bruno > > 2007/12/24, albert richerd carnier guedes >: > > Tabelinha de símbolos em ASCII para quem quiser incrementar suas > mensagens.Os caracteres a e b sao apenas para comparação. > [...] > > > > -- > Bruno FRANÇA DOS REIS > > msn: brunoreis666@hotmail.com > skype: brunoreis666 > tel: +33 (0)6 28 43 42 16 > > e^(pi*i)+1=0 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 21:38:41 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNNbS8l002251 for ; Sun, 23 Dec 2007 21:37:28 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBNNbQFH002249 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 21:37:26 -0200 Received: from smtp.bol.com.br (smtpout1.bol.com.br [200.221.4.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBNNbF8l002235 for ; Sun, 23 Dec 2007 21:37:15 -0200 Received: from localhost (localhost [127.0.0.1]) by smart3.bol.com.br (Postfix) with ESMTP id 084194800081A for ; Sun, 23 Dec 2007 22:38:55 -0200 (BRST) Received: from pai (unknown [201.88.134.242]) by smart3.bol.com.br (Postfix) with ESMTP id 2911348000815 for ; Sun, 23 Dec 2007 22:38:54 -0200 (BRST) Message-ID: <000e01c845c5$cb90d6c0$6601a8c0@pai> From: "Tio Cabri st" To: Subject: [SPAM] [obm-l] outra tangente a curva Date: Sun, 23 Dec 2007 22:42:00 -0200 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 9a18f30e3f6546b7e56bfab22ebda0f1 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Boa noite, será que alguém entre uma ceia e outra poderia me auxiliar nesta: Determine uma reta paralela a x+y=1 (daqui extraio que esta reta tem coeficiente angular -1) e tangente à curva y^3 +xy+ x^3=0 em um ponto (x0,y0), com x0<0 e y0<0. Reposta: x + y = -1 Obrigado Cabri ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 23:05:01 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBO13L8l007226 for ; Sun, 23 Dec 2007 23:03:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBO13Lw2007223 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 23:03:21 -0200 Received: from web50612.mail.re2.yahoo.com (web50612.mail.re2.yahoo.com [206.190.38.158]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBO13J8l007218 for ; Sun, 23 Dec 2007 23:03:19 -0200 Received: (qmail 12567 invoked by uid 60001); 24 Dec 2007 02:04:57 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=c88iUfucrUs4mszbV1Y26Fq6r3yebr6edvFaU6r3g1YUBvxX+HqkladVq7zei0maHzBv5gBaeXU+/khMuOncEuVv9mcS1Y+uJXMKXJI+LN5hga/okXFK+3XSdAWZ6i0H1AQhVZpiemODLq4vGXwRV8YuCskBsEKi4cbGn56kkvQ=; Received: from [201.51.222.249] by web50612.mail.re2.yahoo.com via HTTP; Sun, 23 Dec 2007 18:04:57 PST X-Mailer: YahooMailRC/818.31 YahooMailWebService/0.7.158.1 Date: Sun, 23 Dec 2007 18:04:57 -0800 (PST) From: Rodrigo Cientista Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Res=3A_=5Bobm-l=5D_Re=3A_=5Bobm-l=5D_Re=3A_=5Bobm-l=5D_Re?= =?iso-8859-1?Q?=3A_=5Bobm-l=5D_Demonstra=E7=F5es?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <680082.12206.qm@web50612.mail.re2.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBO13K8l007221 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Rodrigo Cientista X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 158.38.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 158.38.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Acredito que o que o albert quer dizer é o seguinte: o problema do milênio relacionado aos problemas NP é demonstrar que um problema NP pode ser expresso em termos de um problema P (mas não necessariamente dar um exemplo disso). Imagine uma empresa de entregas que deseja minimizar seus custos de frete, devendo-se para tal determinar qual a menor rota entre um município brasileiro e outro, passando por todos, nos seguinte termos: Tempo para ir do município A ao B: x horas Tempo para ir do município A ao C: y horas Tempo para ir do município A ao D: z horas . . . Tempo para ir do município Y ao Z: n horas supondo 27 municípios que permitam um caminho entre cada um deles, isto é, cada um se combina com todos os demais, todos formam duplas com todos, pra efeitos de simplificação. neste sentido, todas rotas possíveis são em número = 27! claramente a cada incremento de um município teremos um incremento muito maior de rotas a serem examinadas por um programa computacional qualquer, sendo este um problema com tempo de processamento não polinomial (NP) agora imagine um problema em que pede-se pra calcular o tempo médio de cada rota que parte de A e termina em A, tal que cada rota seguinte seja escolhida dentre as com menor tempo, passando por todos os municípios pelo menos uma vez. Se formos aumentando o número de municípios o tempo de processamento crescrerá aritmeticamente. Este é um problema com tempo de processamento polinomial (P). existe alguma forma de contruir-se uma máquina capaz de resolver problemas não-polinomiais como esses em tempos polinomiais? o problema do milênio pede que se demonstre apenas a possibilidade, não que se dê um exemplo concreto, acho q era isso que o albert estava querendo dizer com "demonstração de demonstração", o que em última análise poderia ser melhor expresso como "demonstração de possibilidade" ----- Mensagem original ---- De: Sérgio Martins da Silva Para: obm-l@mat.puc-rio.br Enviadas: Domingo, 23 de Dezembro de 2007 18:21:50 Assunto: [obm-l] Re: [obm-l] Re: [obm-l] Re: [obm-l] Demonstrações Caros Rodrigo e arcguede, Poderiam me esclarecer o que demonstração de uma demonstração tem a ver com problemas NP? Qual bibliografia recomendam sobre isso? Abraços, Sérgio ----- Original Message ----- From: To: Sent: Tuesday, December 18, 2007 12:46 AM Subject: [obm-l] Re: [obm-l] Re: [obm-l] Demonstrações > Acredito que o problema NP seja provar que existe ou não uma forma > matemática, objetiva, de transformar problemas NP (com tempo de > processamento não polinomial) em problemas P (tempo de processamento > polinomial). Correto? > > qual seria a remissão a que você se referiu? > > ----- Original Message ----- > From: > To: > Sent: Monday, December 17, 2007 2:16 AM > Subject: Re: [obm-l] Re: [obm-l] Demonstrações > > > > Acho que isso nos remete ao "terceiro problema do milênio" - o problema > > NP. > > > > rodrigocientista@yahoo.com.br escreveu: > >> Acredito que uma "demonstração de demonstração" seria algo como > >> "chover no molhado". Uma demonstração está correta se, em última > >> instância, está de acordo com os axiomas mais básicos da matéria. > >> Então, uma demonstração de demontração recorreria, também em última > >> análise, exatamente aos mesmos axiomas, sendo assim redundante. > >> > >> Se você fala inglês, aqui está um fórum onde há diversos debates > >> interessantes sobre esses assuntos, além de resolução técnica de > >> questões de matemática, física química, engenharia em geral, etc... > >> > >> http://www.physicsforums.com/ > >> > >> abraços > >> > >> ----- Original Message ----- From: "Sérgio Martins da Silva" > >> > >> To: "Lista OBM" > >> Sent: Sunday, December 16, 2007 10:56 PM > >> Subject: [obm-l] Demonstrações > >> > >> > >>> Doutores, > >>> > >>> Penso que a palavra mais comum nesta lista e, quiçá, da matemática é > >>> "demonstração". Por isto, gostaria de saber como se demonstra que uma > >>> demonstração está correta. E mais, que é completa. Quais são os > >>> requisitos, > >>> condições, etc ? > >>> > >>> Abraços, > >>> > >>> Sérgio > >>> > >>> ========================================================================= > >>> > >>> Instruções para entrar na lista, sair da lista e usar a lista em > >>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >>> ========================================================================= > >> > >> > >> ========================================================================= > >> Instruções para entrar na lista, sair da lista e usar a lista em > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >> ========================================================================= > >> > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 23 23:47:22 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBO1kK8l011495 for ; Sun, 23 Dec 2007 23:46:20 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBO1kKMc011493 for obm-l-MllGbsmmN; Sun, 23 Dec 2007 23:46:20 -0200 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBO1kI8l011489 for ; Sun, 23 Dec 2007 23:46:18 -0200 Received: by fk-out-0910.google.com with SMTP id 22so1702165fkq.13 for ; Sun, 23 Dec 2007 18:47:56 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=yqUQ5PQw5prhyO9cSAzh93kQW8EGrtyDYOvayMocLEc=; b=IKMhb9DdukZBE8a4Suj+y1SIqztsaL0DzNb/vs+lRuEAKsn/l6WEOmXunQ1KOkI1C0YeW+6KfMLYao01mmkinkn/0lhDvNoybVeuob4ObU+bk6VDycgcFzGzI6F5U1V72M8FdGu9KminoymusCHgMrh/94YuCDfZ/xyU6W/ByVo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=IqhNWZXTOEx2sdIcZlWI4QxIiI8N7HOpcUu1l/O6Bj21/DKqBbTIQO39aAtXewcaJKTSG3m7dh7vPpqzpJMbKvjaAVWvu65KHwi+hBp0SNIzLOaURzVOKk1KcE5hzE0b7rWmDhM9fqaDN+aAHxCjtWXCrjRdTr58q2G5uKrMZ0M= Received: by 10.78.167.12 with SMTP id p12mr5059170hue.20.1198464475533; Sun, 23 Dec 2007 18:47:55 -0800 (PST) Received: by 10.78.42.5 with HTTP; Sun, 23 Dec 2007 18:47:55 -0800 (PST) Message-ID: <8994b830712231847n1285c426va9da6dec5608bd0b@mail.gmail.com> Date: Sun, 23 Dec 2007 23:47:55 -0300 From: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Res:_[obm-l]_Re:_[obm-l]_?= =?ISO-8859-1?Q?Re:_[obm-l]_Re:_[obm-l]_Demonstra=E7=F5es?= In-Reply-To: <680082.12206.qm@web50612.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <680082.12206.qm@web50612.mail.re2.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBO1kJ8l011491 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** On Dec 23, 2007 11:04 PM, Rodrigo Cientista wrote: > claramente a cada incremento de um município teremos um incremento muito maior de rotas a serem > examinadas por um programa computacional qualquer, sendo este um problema com tempo de > processamento não polinomial (NP) Só uma observação pedante: NP não significa não-polinomial. NP é a classe de todos os problemas que podem ser resolvidos em tempo polinomial numa máquina de Turing não-determinística. Uma formulação alternativa é a seguinte: um problema está na classe de complexidade NP se, dada uma possível resposta, uma máquina de Turing determinística consegue *verificar* a veracidade da mesma em tempo polinomial. Em particular, a classe de complexidade NP contém a classe de complexidade P, que é a classe dos problemas que podem ser resolvidos em tempo polinomial por uma máquina de Turing determinística. Existe também a classe dos problemas NP-difíceis, que pode ser descrita assim: Se um computador pudesse resolver um problema NP-difícil (basta saber resolver um tipo de problema), ele poderia resolver qualquer problema da classe NP em tempo polinomial. Além disso, a classe NP-completo é a interseção da classe NP com a classe NP-difícil. Quanto a pergunta original, não consegui entender a relação da classe de complexidade NP com a dúvida do Sérgio (se alguém pudesse me mandar alguma referência sobre isso, ficaria agradecido), mas existem coisas interessantes quanto a verificação computadorizada de provas de teoremas; o programa mais famoso para fazer isso é o Coq. Além disso, existe um site bastante interessante chamado Metamath () com um monte de proposições matemáticas escritas de um modo bastante cru, propício para verificação automática. Dá pra perder horas clicando nas várias proposições até chegar aos axiomas ZFC. -- Abraços, Maurício ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 24 01:06:33 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBO35G8l016546 for ; Mon, 24 Dec 2007 01:05:16 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBO35Frm016544 for obm-l-MllGbsmmN; Mon, 24 Dec 2007 01:05:16 -0200 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBO35E8l016541 for ; Mon, 24 Dec 2007 01:05:14 -0200 Received: (qmail 26074 invoked from network); 24 Dec 2007 04:06:54 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from 201-13-105-238.dsl.telesp.net.br (HELO apple.local) (fabricio82@[201.13.105.238]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 24 Dec 2007 04:06:54 -0000 Message-ID: <476F2F62.6070503@usp.br> Date: Mon, 24 Dec 2007 02:02:42 -0200 From: "fabricio82@usp.br" User-Agent: Thunderbird 2.0.0.9 (Macintosh/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] Re: [obm-l] outra tangente a curva References: <000e01c845c5$cb90d6c0$6601a8c0@pai> In-Reply-To: <000e01c845c5$cb90d6c0$6601a8c0@pai> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "fabricio82@usp.br" X-Spam-Status: Yes, hits=7.3 required=5.0 tests=FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_DSBL, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 238.105.13.201.list.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 72.254.107.143.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 72.254.107.143.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Tio Cabri st wrote: > Boa noite, será que alguém entre uma ceia e outra poderia me auxiliar nesta: > > Determine uma reta paralela a x+y=1 (daqui extraio que esta reta tem > coeficiente angular -1) e tangente à curva y^3 +xy+ x^3=0 em um ponto > (x0,y0), com x0<0 e y0<0. > > Reposta: x + y = -1 > > Obrigado Cabri > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > Derivando implicitamente a equação, você obtém: 3y^2.y' + y + x.y' + 3x^2 = 0 y'.(3y^2 + x) = -(3x^2 + y) y' = - (3x^2 + y)/(3y^2 + x) Buscamos o ponto onde a inclinação (derivada) tem valor -1. y' = -1 ou seja, - (3x^2 + y)/(3y^2 + x) = -1 3x^2 + y = 3y^2 + x 3x^2 - 3y^2 + y - x = 0 3(x^2 - y^2) - 1(x - y) = 0 3(x + y)(x - y) - 1(x - y) = 0 (x - y).(3x + 3y -1) = 0 Logo (A) x - y = 0 E a intersecção de x - y = 0 com y^3 + xy + x^3 = 0 é o ponto (-1/2; -1/2) ou (B) 3x + 3y - 1 = 0 impossível, pois como x + y = 1/3, não podemos ter ambas coordenadas negativas. A reta tangente, com inclinação -1 que passa pelo ponto (-1/2; -1/2) é: x + y = -1 Pio. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 24 16:49:41 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBOIlt8l002434 for ; Mon, 24 Dec 2007 16:47:55 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBOIltuZ002432 for obm-l-MllGbsmmN; Mon, 24 Dec 2007 16:47:55 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.245]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBOIlr8l002426 for ; Mon, 24 Dec 2007 16:47:53 -0200 Received: by hs-out-2122.google.com with SMTP id m63so1143354hsc.13 for ; Mon, 24 Dec 2007 11:49:32 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=ic4KqCe1hatbETBbvjOhax9qqplhL620Td1Gmw/udCI=; b=uJfTGNDbzsTQn9YFmhRMi2R18x+WrSDcMsELTp36AvXth++oI+Fq1MjFwzk+927QpTanH7LJUdfClx21fqGIr+IAN/ZZJZq5PA7qQGvp/Cu+T3o7pRb5Pir6ZhdP5Byx4n9L47IjUlcv+sN1eVlxiHdyEedT03PZTAuEclBWfrw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=IBS52DMCftPt2aXHHguSGbYrP2gWhIuSslBrICztZwpcTGtfebrndn5JsIhkyXn6Uska7fJgK9EbZ0Zzz17g34b6DdJNAJxZ4g7GqHNFrOOZVKl9N7JziDNjjl8d6ELNlQD3zbG17S6ioW3vCIEN7dRnghQRLVfFWvAS5zf68Sk= Received: by 10.150.197.8 with SMTP id u8mr1347072ybf.62.1198525770691; Mon, 24 Dec 2007 11:49:30 -0800 (PST) Received: by 10.150.96.3 with HTTP; Mon, 24 Dec 2007 11:49:30 -0800 (PST) Message-ID: <9f4be2240712241149h419c4477lb311474000be7b94@mail.gmail.com> Date: Mon, 24 Dec 2007 17:49:30 -0200 From: "Lucas Prado Melo" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Res:_[obm-l]_Re:_[obm-l]_?= =?ISO-8859-1?Q?Re:_[obm-l]_Re:_[obm-l]_Demonstra=E7=F5es?= In-Reply-To: <8994b830712231847n1285c426va9da6dec5608bd0b@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <680082.12206.qm@web50612.mail.re2.yahoo.com> <8994b830712231847n1285c426va9da6dec5608bd0b@mail.gmail.com> X-Google-Sender-Auth: ed05e2edc8e23d5e Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBOIls8l002430 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Lucas Prado Melo" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Não achei pedante, achei as informações muito legais! Você sabe se existe alguma lista parecida com esta da obm mas para discussões de computação? abraços On Dec 24, 2007 12:47 AM, Maurício Collares wrote: > > Só uma observação pedante: NP não significa não-polinomial. NP é a > classe de todos os problemas que podem ser resolvidos em tempo > polinomial numa máquina de Turing não-determinística. Uma formulação > alternativa é a seguinte: um problema está na classe de complexidade > NP se, dada uma possível resposta, uma máquina de Turing > determinística consegue *verificar* a veracidade da mesma em tempo > polinomial. Em particular, a classe de complexidade NP contém a classe > de complexidade P, que é a classe dos problemas que podem ser > resolvidos em tempo polinomial por uma máquina de Turing > determinística. > > Existe também a classe dos problemas NP-difíceis, que pode ser > descrita assim: Se um computador pudesse resolver um problema > NP-difícil (basta saber resolver um tipo de problema), ele poderia > resolver qualquer problema da classe NP em tempo polinomial. Além > disso, a classe NP-completo é a interseção da classe NP com a classe > NP-difícil. > > Quanto a pergunta original, não consegui entender a relação da classe > de complexidade NP com a dúvida do Sérgio (se alguém pudesse me mandar > alguma referência sobre isso, ficaria agradecido), mas existem coisas > interessantes quanto a verificação computadorizada de provas de > teoremas; o programa mais famoso para fazer isso é o Coq. Além disso, > existe um site bastante interessante chamado Metamath > () com um monte de proposições matemáticas > escritas de um modo bastante cru, propício para verificação > automática. Dá pra perder horas clicando nas várias proposições até > chegar aos axiomas ZFC. > > -- > Abraços, > Maurício > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 01:36:06 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBP3YT8l022697 for ; Tue, 25 Dec 2007 01:34:29 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBP3YTJR022695 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 01:34:29 -0200 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBP3YS8l022692 for ; Tue, 25 Dec 2007 01:34:28 -0200 Received: from localhost (localhost [127.0.0.1]) by socom10.uol.com.br (Postfix) with ESMTP id 4720D2B0 for ; Tue, 25 Dec 2007 02:36:08 -0200 (BRST) Received: from microcf7b75528 (unknown [201.9.186.62]) by socom10.uol.com.br (Postfix) with SMTP id 890A521A for ; Tue, 25 Dec 2007 02:36:07 -0200 (BRST) Message-ID: <000e01c846af$a8cd5830$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] =?Windows-1252?B?Q29tcG9zaefjbyBkZSBGdW7n9WVz?= Date: Tue, 25 Dec 2007 01:36:03 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: 7e53c5e0f0b3ab740b4ea7559d7cdc63 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_000B_01C84696.8301C870" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 62.186.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 62.186.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_000B_01C84696.8301C870 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Ol=E1, Dada a fun=E7=E3o f(x) =3D (2x + 1)/(x - 2), o valor se = fof(2), =E9:=20 a) 1/4 b) 1/2 c) 2 d) 4 e) -4 O problema acima foi aplicado num exame de vestibular e o gabarito = oficial apontava a alternativa C como correta. =C9 f=E1cil ver que f(2) n=E3o existe, pois D(f) =3D R - {2}. Desse = modo, ser=EDamos levados a concluir que o problema n=E3o apresenta = alternativa correta, pois f(f(2)) n=E3o existe. Por outro lado, f(f(x)) =3D x, donde f(f(2)) =3D 2. O que parece ter = sido levado em considera=E7=E3o pelo examinador. Pergunta: Onde est=E1 o erro? Abra=E7os. =20 ------=_NextPart_000_000B_01C84696.8301C870 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable
Ol=E1,
 
 
          &nbs= p; Dada a fun=E7=E3o = f(x) =3D (2x + 1)/(x=20 - 2), o valor se fof(2), =E9:
          &nbs= p; a)=20 1/4     b) 1/2    c)=20 2    d)=20 4      e) -4
 
 
O problema acima foi aplicado num = exame de=20 vestibular e o gabarito oficial apontava a alternativa C como=20 correta.
 
=C9 f=E1cil ver que f(2) n=E3o existe, pois D(f) =3D = R - {2}. Desse=20 modo, ser=EDamos levados a concluir que o problema n=E3o apresenta = alternativa=20 correta, pois f(f(2)) n=E3o existe.
 
Por outro lado, f(f(x)) =3D x, donde f(f(2)) =3D 2. = O que parece=20 ter sido levado em considera=E7=E3o pelo examinador.
 
Pergunta: Onde est=E1 o erro?
 
Abra=E7os.   
 
 
------=_NextPart_000_000B_01C84696.8301C870-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 08:57:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPAt28l020692 for ; Tue, 25 Dec 2007 08:55:02 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPAt1Nw020689 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 08:55:01 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.241]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPAsw8l020665 for ; Tue, 25 Dec 2007 08:54:58 -0200 Received: by hs-out-2122.google.com with SMTP id m63so1313656hsc.13 for ; Tue, 25 Dec 2007 03:56:38 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=+oevQmhgyjVRCOOT2XGX3MiFrXBwOx3vLVO6doQhPPw=; b=iJxNJaDs8HO208zePFvtPif+z7NI+zOwUk+xVkmUlWb14w5m4q7V460Be02gOp6Zfc1x4dR+ZTx7lX0I4vT5NJjRyAnc/a3IkcpU684cxpriHuJ+ZIFd2/x88oIoELCf8UxO3CD317zwab+zyrPGdmKFKkniUXZ+L1NGv0jg8bo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=tGMhfoOPW07v5E7J+DkfsZz+53EMr1xWxWs75jHdWO8EGUJPN85UmcEgBn3jDQpraDYsuU5hgMqPfRHX49ksXGldWM2JX65xXkAbF77e+H5dSPedG+P9ilS+JmW4KosZ6QYTzNO8XruQwahMdbpXYRCKZlxDS/2d7XpTqZLLR/E= Received: by 10.150.58.5 with SMTP id g5mr1405196yba.89.1198583797970; Tue, 25 Dec 2007 03:56:37 -0800 (PST) Received: by 10.150.96.3 with HTTP; Tue, 25 Dec 2007 03:56:37 -0800 (PST) Message-ID: <9f4be2240712250356k267b082dg70b10391faec7f8d@mail.gmail.com> Date: Tue, 25 Dec 2007 09:56:37 -0200 From: "Lucas Prado Melo" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Filhos semelhantes... In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <536036.3359.qm@web56312.mail.re3.yahoo.com> <99886d920712190723v23d9a0aft45ff70029d4b5614@mail.gmail.com> X-Google-Sender-Auth: a77f910b7d646ac0 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBPAsx8l020672 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Lucas Prado Melo" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** E tem mais um complicador:o "crossing-over". Às vezes, dois cromossomos trocam algumas partes... On Dec 19, 2007 8:28 PM, Ojesed Mirror wrote: > > > Ruy, está errado, o correto seria (1/2)^46, pois são 23 cromossomos do óvulo > e 23 do espermatozoide. > O 1/2 vem do fato da mitose resultar sempre duas células a partir de uma. > > Ojesed. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 10:03:13 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPC218l032494 for ; Tue, 25 Dec 2007 10:02:01 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPC21TO032492 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 10:02:01 -0200 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.153]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPC1x8l032483 for ; Tue, 25 Dec 2007 10:02:00 -0200 Received: by fg-out-1718.google.com with SMTP id e12so1098794fga.3 for ; Tue, 25 Dec 2007 05:03:38 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=mDHs/wqgl9Wc7r+H5jriLnTEuMUYUYxFvLc0fuEq8N4=; b=gVjfWlAXBGJqn/azLk/vl3cHG/j7/Err/nUPZdeM5Hj36/7zcrDNoIvcLbQimCSSkVO0TN+GR5+y2Js6xKC+0sNSXbttdUTbgQrlMUlOFvCXoFsmFmXFPa84Lo2EeQHSpG9oqSqfJ9dLeGJAWdZK0K159COaPLAxRf2LfkOHgvw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=IjaGv/Sn1fWsoipla5JhOeVzxVvI4Bq8bqVk7RVo2UXClRtdodnUK4JpY+JAhtRjZeYgO4KivnalYvLMc8SHZ1YfDqwmIGyFENJrOpjK1pbEbnrkObw0s4hSnzE69fs/gT6YO3czggZgVEtWfs8qAhwNeZqidu3Tr+rkRY0s5y4= Received: by 10.82.123.16 with SMTP id v16mr8911950buc.18.1198587818652; Tue, 25 Dec 2007 05:03:38 -0800 (PST) Received: by 10.82.189.1 with HTTP; Tue, 25 Dec 2007 05:03:38 -0800 (PST) Message-ID: Date: Tue, 25 Dec 2007 11:03:38 -0200 From: "Marcelo Gomes" To: obm-l@mat.puc-rio.br Subject: [obm-l] =?ISO-8859-1?Q?Demonstra=E7=F5es_Matem=E1ticas?= MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_6913_18681257.1198587818652" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Gomes" X-Spam-Status: No, hits=0.5 required=5.0 tests=SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_6913_18681257.1198587818652 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal, bom Natal a todos os membros da lista e para suas distintas fam=EDlias tamb=E9m. Gostaria que algu=E9m me auxiliasse no seguinte: Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es d= as equa=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros complexos, com= o objetivo de fazer um projeto para o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber : 1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel s= obre sobre a impossibilidade de se estabelecer coeficientes para equa=E7=F5es de= grau maior que 5 2-A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das eq= ua=E7=F5es e seus relacionamentos entre si 3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano) 4-Se algum dos professores da lista, quiser compartilhar comigo alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros co= mplexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda. Muito obrigado a todos e boas festas, Abra=E7os, Marcelo. ------=_Part_6913_18681257.1198587818652 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal, bom Natal a todos os membros da lista e para suas distintas = fam=EDlias tamb=E9m.

Gostaria que algu=E9m me auxiliasse no seguinte:

Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es d= as equa=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros complexos, com o objetivo de fazer um projeto para o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber :

1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel sobre sobre a impossibilidade de se estabelecer coeficientes para equa=E7=F5es de grau maior que 5

2-A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das eq= ua=E7=F5es e seus relacionamentos entre si

3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano)

4-Se algum dos professores da lista, quiser compartilhar comigo alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros complexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda.

Muito obrigado a todos e boas festas,

Abra=E7os, Marcelo.
------=_Part_6913_18681257.1198587818652-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 10:14:52 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCDd8l000588 for ; Tue, 25 Dec 2007 10:13:39 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPCDdY5000586 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 10:13:39 -0200 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCDb8l000579 for ; Tue, 25 Dec 2007 10:13:38 -0200 Received: by fg-out-1718.google.com with SMTP id e12so1100791fga.3 for ; Tue, 25 Dec 2007 05:15:16 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=ua+UszGRX6KCE/XDA0T/brvTQvcKh8scg+StXoUD2Xg=; b=TgVfiub5TTueNDKKMMfMydEBug56Px7jLOvXBwrou9g8QeDhUI8TOFsqlUs5g1caLnbCMyb0lqX7HIxCIs8XhpvdD/k8fm3MrUAwnGxNxr2YbyBF5suSusK37A+FurHX7SONtIhkclNDKFXwYJPaienC/yji0/N8n6SALqj/d1Q= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=gOyXOJKyjrtKEXTVSzhho0Pgkq4+9OVIIBfF1tq8ZrNbNIqBVJx6omPs4pkHDOipbCpqpKnnOzjvSvIfQb9RMhfBKW9W+JJaZYtO0uVyg3d7BNvuQr/NzLVDQ6gVAnD6lLMMohE6Weh8sx5gn+G/mAIvBYOAGfZblf597HP9SI4= Received: by 10.82.149.8 with SMTP id w8mr8954371bud.24.1198588516372; Tue, 25 Dec 2007 05:15:16 -0800 (PST) Received: by 10.82.189.1 with HTTP; Tue, 25 Dec 2007 05:15:16 -0800 (PST) Message-ID: Date: Tue, 25 Dec 2007 11:15:16 -0200 From: "Marcelo Gomes" To: obm-l@mat.puc-rio.br Subject: [obm-l] =?ISO-8859-1?Q?Demonstra=E7=E3o_de_Gaus?= MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_6922_25683814.1198588516364" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Gomes" X-Spam-Status: No, hits=0.5 required=5.0 tests=SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_6922_25683814.1198588516364 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal bom dia de novo. Esqueci de perguntar aos senhores sobre a demosntra=E7=E3o do Teorema fundamental da =E1lgebra feita por Gauss. Se algu=E9m possu=ED-la pro favor= entre em contato comigo, ok ? Forte abra=E7o, Marcelo. ------=_Part_6922_25683814.1198588516364 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal bom dia de novo.

Esqueci de perguntar aos senhores sobre a demosntra=E7=E3o do Teorema fundamental da =E1lgebra feita por Gauss. Se algu=E9m possu=ED-la pro favor entre em contato comigo, ok ?

Forte abra=E7o, Marcelo.
------=_Part_6922_25683814.1198588516364-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 10:19:31 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCIZ8l000995 for ; Tue, 25 Dec 2007 10:18:35 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPCIZWo000993 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 10:18:35 -0200 Received: from bay0-omc2-s32.bay0.hotmail.com (bay0-omc2-s32.bay0.hotmail.com [65.54.246.168]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCIX8l000989 for ; Tue, 25 Dec 2007 10:18:33 -0200 Received: from BAY113-W7 ([65.54.168.107]) by bay0-omc2-s32.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Tue, 25 Dec 2007 05:20:13 -0800 Message-ID: Content-Type: text/plain X-Originating-IP: [201.42.146.224] From: Tales Prates Correia To: Subject: [SPAM] =?iso-8859-1?Q?RE:_[obm-l]_Composi=E7=E3o_de_Fun=E7=F5es?= Date: Tue, 25 Dec 2007 16:20:13 +0300 Importance: Normal In-Reply-To: <000e01c846af$a8cd5830$01fea8c0@microcf7b75528> References: <000e01c846af$a8cd5830$01fea8c0@microcf7b75528> MIME-Version: 1.0 X-OriginalArrivalTime: 25 Dec 2007 13:20:13.0178 (UTC) FILETIME=[E1A80DA0:01C846F8] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Tales Prates Correia X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_FONT_COLOR_BLUE,IN_REP_TO, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="_ae308b00-9721-4623-8c5c-7e1461b6af72_" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 107.168.54.65.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 107.168.54.65.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --_ae308b00-9721-4623-8c5c-7e1461b6af72_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 ! A fun=E7=E3o f, como voc=EA bem disse, tem como dom=EDnio mais ex= tenso o conjunto D =3D R - {2}. Uma vez que a sua lei de correspond=EAncia = =E9 dada por f(x) =3D (2x + 1)/(x - 2) a lei de fof d=E1-se por (fof)(x) =3D x(x - 2)/(x - 2) E seu dom=EDnio ainda =E9 D =3D R - {2}. Essa fun=E7=E3o n=E3o es= t=E1 definida no ponto x =3D 2 e =E9 identica a fun=E7=E3o g real definida = por g(x) =3D x no conjunto D. Por esse motivo, o exerc=EDcio n=E3o apresenta alternativa corret= a. Desconsiderando esse erro dos formuladores, seria sensato apontar como c= orreta a alternativa C. Espero ter ajudado. Abra=E7os! From: ucsjr@uol.com.br To: obm-l@mat.puc-rio.br Subject: [obm-l] Composi=E7=E3o de Fun=E7=F5es Date: Tue, 25 Dec 2007 01:36:03 -0300 Ol=E1, =20 =20 Dada a fun=E7=E3o f(x) =3D (2x + 1)/(x=20 - 2), o valor se fof(2), =E9:=20 a)=20 1/4 b) 1/2 c)=20 2 d)=20 4 e) -4 =20 =20 O problema acima foi aplicado num exame de=20 vestibular e o gabarito oficial apontava a alternativa C como=20 correta. =20 =C9 f=E1cil ver que f(2) n=E3o existe, pois D(f) =3D R - {2}. Desse=20 modo, ser=EDamos levados a concluir que o problema n=E3o apresenta alternat= iva=20 correta, pois f(f(2)) n=E3o existe. =20 Por outro lado, f(f(x)) =3D x, donde f(f(2)) =3D 2. O que parece=20 ter sido levado em considera=E7=E3o pelo examinador. =20 Pergunta: Onde est=E1 o erro? =20 Abra=E7os. =20 =20 =20 _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_ae308b00-9721-4623-8c5c-7e1461b6af72_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable           Ol=E1 !

 = ;         A fun=E7=E3o f, como voc= =EA bem disse, tem como dom=EDnio mais extenso o conjunto D =3D R - {2}. Um= a vez que a sua lei de correspond=EAncia =E9 dada por

  &n= bsp;       f(x) =3D (2x + 1)/(x - 2)

&= nbsp;         a lei de fof d=E1-se = por

          (fof)(x) = =3D x(x - 2)/(x - 2)

        = ;  E seu dom=EDnio ainda =E9 D =3D R - {2}. Essa fun=E7=E3o n=E3o est= =E1 definida no ponto x =3D 2 e =E9 identica a fun=E7=E3o g real definida p= or g(x) =3D x no conjunto D.

      &nb= sp;   Por esse motivo, o exerc=EDcio n=E3o apresenta alternativa = correta. Desconsiderando esse erro dos formuladores, seria sensato apontar = como correta

          = a alternativa C.

        &nb= sp; Espero ter ajudado.

       &n= bsp;  Abra=E7os!

From: ucsjr@uol.com.br
To: = obm-l@mat.puc-rio.br
Subject: [obm-l] Composi=E7=E3o de Fun=E7=F5es
D= ate: Tue, 25 Dec 2007 01:36:03 -0300

Ol=E1,
 
 
     = ;       Dada a fun=E7=E3o f(x) =3D (2x + 1)/(x=20 - 2), o valor se fof(2), =E9:
         = ;   a)=20 1/4     b) 1/2    c)=20 2    d)=20 4      e) -4
 
 
O problema acima foi aplicado num exame&nbs= p;de=20 vestibular e o gabarito oficial apontava a alternativa C como=20 correta.
 
=C9 f=E1cil ver que f(2) n=E3o existe, pois D(f) =3D = R - {2}. Desse=20 modo, ser=EDamos levados a concluir que o problema n=E3o apresenta alternat= iva=20 correta, pois f(f(2)) n=E3o existe.
 
Por outro lado, f(f(x)) =3D x, donde f(f(2)) =3D 2. O= que parece=20 ter sido levado em considera=E7=E3o pelo examinador.
 
Pergunta: Onde est=E1 o erro?
 
Abra=E7os.   
 
 

Receba GR=C1TIS as mensagens do Messenger no seu c= elular quando voc=EA estiver offline. Conhe=E7a o MSN Mobile! Crie = j=E1 o seu! = --_ae308b00-9721-4623-8c5c-7e1461b6af72_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 10:32:19 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCV78l003779 for ; Tue, 25 Dec 2007 10:31:07 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPCV64r003770 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 10:31:06 -0200 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.234]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPCV28l003756 for ; Tue, 25 Dec 2007 10:31:03 -0200 Received: by wx-out-0506.google.com with SMTP id t4so614348wxc.18 for ; Tue, 25 Dec 2007 05:32:42 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; bh=Nk40sTn/9meYc8DUhbRXWj2pvI6sX+yuTH1MlrTgOp8=; b=PMPFoFQ0T3d0kpjNri+APKDfiaJ3w7CWl8eSZ/Ps9gtQcD0o6BOPUDxnWc6eIfPRWPBpCQ14PoGnn4d7Ma2l5wu/tLMjSI7fKSoqu+M6ztC+z5ZTUe3gb2pBnhcqTkD/3eaPQaiPQBH99mcFJ3tyDzGu2A+vlaVwmefzEFgUo08= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:content-type:content-transfer-encoding; b=oFKSTT8AqiYJAcps14EXVX4iNdsBpF6s3MHRF/Xy21rj7FoyI+96J3+tdx2fzHf7l2jBjOU5Q6HS0K4nacmYXZtbBhr0CZh2le1SdVlEqnwTEMm+ypxqvtFTPHUNMUgAlzT/jXoTXRmphzqBt9Hqm69fe/IeyNNri+hkmqlx4/8= Received: by 10.70.55.3 with SMTP id d3mr2602354wxa.79.1198589562732; Tue, 25 Dec 2007 05:32:42 -0800 (PST) Received: from ?201.20.228.254? ( [201.20.228.254]) by mx.google.com with ESMTPS id i10sm8843724wxd.22.2007.12.25.05.32.41 (version=SSLv3 cipher=RC4-MD5); Tue, 25 Dec 2007 05:32:41 -0800 (PST) Message-ID: <47710669.9090806@gmail.com> Date: Tue, 25 Dec 2007 11:32:25 -0200 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Teorema de Elyahu Ripz Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: Yes, hits=5.3 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 234.82.249.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 234.82.249.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Alguém conhece o enunciado teorema de Ripz (Elyahu Ripz) sobre a ação de grupos finitos ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 14:32:57 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPGUM8l000927 for ; Tue, 25 Dec 2007 14:30:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPGUMpW000925 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 14:30:22 -0200 Received: from web63701.mail.re1.yahoo.com (web63701.mail.re1.yahoo.com [69.147.97.86]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBPGUJ8l000918 for ; Tue, 25 Dec 2007 14:30:20 -0200 Received: (qmail 25072 invoked by uid 60001); 25 Dec 2007 17:31:59 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=pGLyISbBtgFpQyFGrBd3drw6noTItODNy85fI8Iy3DMrBpya9Mfwyav1AO4wzATe1fwQ1t9AkdUlrfDfOPp/g3yfsjsHgTYuWPytHKZRj+m/31J+QjOkEnDHbyyfkqL9i+IhxcsjVvTsJ5Yb4hD/8tVgQtMh62wYplwCzBEy4w8=; X-YMail-OSG: peiRcEIVM1n_10uCqjMM5WvhdxYIADidiwU5pnco1L8_n4AD03U6Se6vMsfHXEzX9d7B_tSa9pT3WxRzAbNseNmLi2HzhdJIUvxpFIaBA.05dp_.s9sw3w-- Received: from [189.24.118.87] by web63701.mail.re1.yahoo.com via HTTP; Tue, 25 Dec 2007 14:31:59 ART Date: Tue, 25 Dec 2007 14:31:59 -0300 (ART) From: fagner almeida Subject: [SPAM] RE: [obm-l] Geometria . 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Já que os segmentos AO e BO são congruentes (pois possuem o mesmo comprimento R) e os pontos A, O e B são colineares, O é o ponto médio da corda (diâmetro) AB. Consecutivamente, a reta perpendicular ao segmento AB conduzida por seu ponto médio passa pelo centro O de C. 2° caso: a corda não passa pelo centro Nesse caso, a reunião dos segmentos determinados pelos pontos A, O e B corresponde a um triângulo. Haja visto que AO = OB, AM = MB e OM é comum aos dois triângulos AOM e BOM, em que M é o ponto médio da corda AB, conclui-se pelo critério de congruência de triângulos LLL que o polígono AOM é congruente ao polígono BOM. Dessa congruência, decorre que os ângulos AMO e BMO são congruentes. Porém eles também são suplementares e adjacentes. Por definição, os ângulos AMO e BMO são retos. Assim, a reta OM é a mediatriz da corda AB, pois OM é perpendicular ao segmento AB e passa pelo seu ponto médio. Tendo em vista que a mediatriz de um segmento existe e é única (na geometria plana), concluímos, enfim, que a proposição da questão cinco é verdadeira. --------------------------------- Date: Fri, 21 Dec 2007 20:31:59 -0300 From: fagner_mat23@yahoo.com.br Subject: RE: [obm-l] Geometria . To: obm-l@mat.puc-rio.br obrigado ,Muito boa suas soluções. Na 5 o Iezzi da a seguinte dica : Usando o caso de congruencia LLL pode se provar a propriedade como seria essa prova ? Tales Prates Correia escreveu: .ExternalClass .EC_hmmessage P {padding:0px;} .ExternalClass EC_body.hmmessage {font-size:10pt;font-family:Tahoma;} 4 - A afirmação propõe um novo caso de congruência, a saber, o caso "lado-lado-ângulo". Usando a figura fornecida, é possível mostrar porque esse critério não é válido: segundo esse novo caso, os triângulos ROP e QOP deveriam ser congruentes, porém isto é uma inverdade, uma vez que o teorema do angulo externo aplicado ao triângulo QOR nos permite afirmar que o ângulo PQO é maior do que PRO. 5 - Por definição, uma corda de uma circunferência é um segmento de reta cujas extremidades pertencem a essa circunferência. A mediatriz de um segmento de reta é o lugar geométrico dos pontos eqüidistantes das extremidades desse segmento. Ora, uma vez que as extremidades da corda pertencem à circunferência, as distâncias desses pontos ao centro desta são iguais e congruentes ao raio. Por conseguinte, a mediatriz "passará" pelo centro da circunferência. Q.E.D. 6 - Todas as afirmações são verdadeiras. Item a: Propriedade fundamental dos paralelogramos que decorre do teorema angular de Tales. Item b: Por definição, um losango é um quadrilátero plano convexo cujos quatro lados são congruentes entre si. Usando essa definição e a propriedade característica dos paralelogramos referida no item anterior, pode-se demonstrar essa afirmação. Item c: Propriedade dos retângulos que pode ser demonstrada usando a definição dessa figura geométrica e as propriedade dos paralelogramos, uma vez que todo retângulo é um paralelogramo (fato também justificável). Item d: Propriedade decorrente da definição de losango e das propriedades do paralelogramo, já que esta figura geométrica também um paralelogramo. Item e: A veracidade dessa afirmação decorre da definição de losango e do seguinte teorema: Todo losango é um paralelogramo. --------------------------------- Date: Thu, 20 Dec 2007 18:26:46 -0300 From: fagner_mat23@yahoo.com.br Subject: [obm-l] Geometria . To: obm-l@mat.puc-rio.br http://imagetoker.com/viewer.php?id=890318geometria.JPG http://imagetoker.com/viewer.php?id=541398geometria2.JPG Quem puder ajudar valeu --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Encontre o que você procura com mais eficiência! Instale já a Barra de Ferramentas com Windows Desktop Search! É GRÁTIS! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Notícias direto do New York Times, gols do Lance, videocassetadas e muitos outros vídeos no MSN Videos! Confira já! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1799879019-1198603919=:23495 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
 
muito bom  cara , não é  atoa  que seu  nome é  tales , obrigada
 
 


Tales Prates Correia <tales1337@hotmail.com> escreveu:
           A fim de mostrar a validade de tal afirmação, simbolizaremos pela letra C a circunferência, pela letra O o seu centro e pela letra R o seu raio.

          1º caso: a corda passa pelo centro

          Sejam A e B as extremidades da corda. Já que os segmentos AO e BO são congruentes (pois possuem o mesmo comprimento R) e os pontos

          A, O e B são colineares, O é o ponto médio da corda (diâmetro) AB. Consecutivamente, a reta perpendicular ao segmento AB conduzida por seu

          ponto médio passa pelo centro O de C.

          2° caso: a corda não passa pelo centro

          Nesse caso, a reunião dos segmentos determinados pelos pontos A, O e B corresponde a um triângulo. Haja visto que AO = OB, AM = MB e OM

          é comum aos dois triângulos AOM e BOM, em que M é o ponto médio da corda AB, conclui-se pelo critério de congruência de triângulos LLL que

          o polígono AOM é congruente ao polígono BOM.

          Dessa congruência, decorre que os ângulos AMO e BMO são congruentes. Porém eles também são suplementares e adjacentes. Por definição,

          os ângulos AMO e BMO são retos. Assim, a reta OM é a mediatriz da corda AB, pois OM é perpendicular ao segmento AB e passa pelo seu ponto

          médio. Tendo em vista que a mediatriz de um segmento existe e é única (na geometria plana), concluímos, enfim, que a proposição da questão

          cinco é verdadeira.
Date: Fri, 21 Dec 2007 20:31:59 -0300
From: fagner_mat23@yahoo.com.br
Subject: RE: [obm-l] Geometria .
To: obm-l@mat.puc-rio.br

obrigado ,Muito boa  suas  soluções.
 
Na  5  o    Iezzi  da  a seguinte dica :
Usando o caso de congruencia  LLL pode se  provar a propriedade
como  seria  essa  prova ?

Tales Prates Correia <tales1337@hotmail.com> escreveu:

          4 - A afirmação propõe um novo caso de congruência, a saber, o caso "lado-lado-ângulo". Usando a figura fornecida, é possível mostrar porque

          esse critério não é válido: segundo esse novo caso, os triângulos ROP e QOP deveriam ser congruentes, porém isto é uma inverdade, uma vez

          que o teorema do angulo externo aplicado ao triângulo QOR nos permite afirmar que o ângulo PQO é maior do que PRO.

          5 - Por definição, uma corda de uma circunferência é um segmento de reta cujas extremidades pertencem a essa circunferência. A mediatriz de

          um segmento de reta é o lugar geométrico dos pontos eqüidistantes das extremidades desse segmento. Ora, uma vez que as extremidades da

          corda pertencem à circunferência, as distâncias desses pontos ao centro desta são iguais e congruentes ao raio. Por conseguinte, a mediatriz

          "passará" pelo centro da circunferência.                                                                                                                                         Q.E.D.

          6 - Todas as afirmações são verdadeiras.

          Item a: Propriedade fundamental dos paralelogramos que decorre do teorema angular de Tales.

          Item b: Por definição, um losango é um quadrilátero plano convexo cujos quatro lados são congruentes entre si. Usando essa definição e a

          propriedade característica dos paralelogramos referida no item anterior, pode-se demonstrar essa afirmação.

          Item c: Propriedade dos retângulos que pode ser demonstrada usando a definição dessa figura geométrica e as propriedade dos paralelogramos,

          uma vez que todo retângulo é um paralelogramo (fato também justificável).

          Item d: Propriedade decorrente da definição de losango e das propriedades do paralelogramo, já que esta figura geométrica também um

          paralelogramo.

          Item e: A veracidade dessa afirmação decorre da definição de losango e do seguinte teorema: Todo losango é um paralelogramo.


Date: Thu, 20 Dec 2007 18:26:46 -0300
From: fagner_mat23@yahoo.com.br
Subject: [obm-l] Geometria .
To: obm-l@mat.puc-rio.br



http://imagetoker.com/viewer.php?id=890318geometria.JPG

http://imagetoker.com/viewer.php?id=541398geometria2.JPG
 
Quem puder  ajudar  valeu
 
 



Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Encontre o que você procura com mais eficiência! Instale já a Barra de Ferramentas com Windows Desktop Search! É GRÁTIS!




Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Notícias direto do New York Times, gols do Lance, videocassetadas e muitos outros vídeos no MSN Videos! Confira já!



Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1799879019-1198603919=:23495-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Dec 25 14:34:51 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPGX18l001042 for ; Tue, 25 Dec 2007 14:33:01 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPGWxmx001038 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 14:32:59 -0200 Received: from web63710.mail.re1.yahoo.com (web63710.mail.re1.yahoo.com [69.147.97.95]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBPGWc8l000985 for ; Tue, 25 Dec 2007 14:32:39 -0200 Received: (qmail 7182 invoked by uid 60001); 25 Dec 2007 17:34:18 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=0kARbklPQidds4C46VgKlBmi3VXkmegi6/4Qzf98ed2yFP3QXst9meIJbxZDZ06W3mnZE41EtlhhLTQEnX+Fhcr9vRE5CWZV6a+6jQYDJ9mnZZrBLvj7kcPyZSn4Bn+PFkqDaP3TIJz2Q0dDkV5FQUlb0jC4K/58R/1u6wXAvT4=; X-YMail-OSG: 4KQbQIAVM1nCQNpKIhzN.6vdLsYvAiB1bor7jGImNMMIQgbP4BjS_eqGCt540a2aBdlnMLVLA97edagGh95TcWQ2nEWV0ODnE4KNRFGEN475iwS34Qii Received: from [189.24.118.87] by web63710.mail.re1.yahoo.com via HTTP; Tue, 25 Dec 2007 14:34:18 ART Date: Tue, 25 Dec 2007 14:34:18 -0300 (ART) From: fagner almeida Subject: [SPAM] [obm-l] =?iso-8859-1?q?quest=E3o=20C.N?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <569307.1157.qm@web63710.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=8.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-734118781-1198604058=:1157" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 95.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 95.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-734118781-1198604058=:1157 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit http://imagetoker.com/viewer.php?id=610307imagem.JPG na 10 o gabarito não bate e 18 não sei fazer --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-734118781-1198604058=:1157 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
na 10 o gabarito não bate e 18 não sei fazer


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-734118781-1198604058=:1157-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 26 00:27:55 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQ2JeHZ003816 for ; Wed, 26 Dec 2007 00:26:02 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBPNMl6W024498 for obm-l-MllGbsmmN; Tue, 25 Dec 2007 21:22:47 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBPNMe8l024438 for ; Tue, 25 Dec 2007 21:22:41 -0200 Received: by rv-out-0910.google.com with SMTP id c27so1571488rvf.9 for ; Tue, 25 Dec 2007 16:24:21 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=PaekJNblvaymDCu7holIxT8CgxM47jtHZ/HvKUoXvjU=; b=S5vZ7q6wefdq4BoaSOJiuuPAmWw6jl5XzIDn+kp55ALX6D11v6eZz/gjwTmEOG9YBoO/03vzLKiC55UNnH1W/bc5DOUGvS0ZvzTFGHqfgYrLCJU7Ln5cYMZJ6aC5yy9PI4K++JaR4rdCibmhaJX2f05nOWbkffXtfI7Is2W+THU= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=O9a/QH9ULwgt5oiSZl0jVuN4t9db2EwKS/R9gGu6iXWTe+JUWYeoC+At9fwUE9zILJRTWeK/brDK6b1x3/EV7vVLTMXeSxM9We3li7ApQ/r8qYYTPn3QibJjdOl5re7IXQnMVXXf/s5pAbW68jK9X3NZaGxnzRmyvB71MqlDJCE= Received: by 10.141.122.20 with SMTP id z20mr3020300rvm.93.1198628660959; Tue, 25 Dec 2007 16:24:20 -0800 (PST) Received: by 10.141.190.10 with HTTP; Tue, 25 Dec 2007 16:24:20 -0800 (PST) Message-ID: Date: Tue, 25 Dec 2007 22:24:20 -0200 From: "Marcelo Costa" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_quest=E3o_C.N?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_6706_29785350.1198628660952" References: <569307.1157.qm@web63710.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Costa" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_6706_29785350.1198628660952 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Antes que me esque=E7a, esta quest=E3o j=E1 foi resolvida e esta solu=E7=E3= o enviada n=E3o =E9 a minha solu=E7=E3o. Em 25/12/07, Marcelo Costa escreveu: > > Solu=E7=E3o da quest=E3o 18 do CN segue em anexo. > > 2007/12/25, fagner almeida : > > > > http://imagetoker.com/viewer.php?id=3D610307imagem.JPG > > na 10 o gabarito n=E3o bate e 18 n=E3o sei fazer > > > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > ------=_Part_6706_29785350.1198628660952 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Antes que me esque=E7a, esta quest=E3o j=E1 foi resolvida e esta solu=E7=E3= o enviada n=E3o =E9 a minha solu=E7=E3o.

Em 25/12/07, Marcelo Costa < mat.moura@gmail.com> escreveu:
Solu=E7=E3o da quest=E3o 18 do CN segue em anexo= .

2007/12/25, fagner almeida <fagner_mat23@yahoo.com.br>:=
na 10 o gabarito n=E3o bate e 18 n=E3o sei fazer

=20

Abra sua conta no Yahoo! Mail, o =FAnic= o sem limite de espa=E7o para armazenamento!=20




------=_Part_6706_29785350.1198628660952-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 26 01:32:41 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQ3VF8l010433 for ; Wed, 26 Dec 2007 01:31:15 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBQ3VE5M010431 for obm-l-MllGbsmmN; Wed, 26 Dec 2007 01:31:14 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQ3VC8l010421 for ; Wed, 26 Dec 2007 01:31:13 -0200 Received: by wa-out-1112.google.com with SMTP id m28so3965641wag.13 for ; Tue, 25 Dec 2007 20:32:52 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Q+DlJPQZ8QSxqZkN6cTl/l3XHwd75KR/Ebq8Wi0Iz+I=; b=Mb2Ihqag6JqbhDmK8wMzpnjB1NhSwCsY4HE1KLZZxwz21nZIb/KSRPvj0VgqBIMIDrJI4DsYGWzWSVaDzHh1JsSwa4wnlx4Ojii5nTWuXeRbgLMeakOigzhtxwK+ekxdsss+EURNCZt7lERDwNuVDQaSq6DrIZMIreROWCQsOTg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=fpAEtBIX3meVa+Y6oNyJowSMTVVAaUGgkFPpjO+SUkY9YvKWYYkrEtR/q/3mKhXPOMDZ2dwftdgIcyVDJYbUAFo83GNEkmOJEwy411+MfcUKP0UITboW9sxxqI5+Ncsl0Gmp4gt5KYOql+CwbZIl/1CAfMTBKNz7KtayYdsnluw= Received: by 10.114.184.7 with SMTP id h7mr4661753waf.28.1198643572914; Tue, 25 Dec 2007 20:32:52 -0800 (PST) Received: by 10.114.136.9 with HTTP; Tue, 25 Dec 2007 20:32:52 -0800 (PST) Message-ID: <3bd00efc0712252032r7c1850dcreef954c0b2f15a6c@mail.gmail.com> Date: Wed, 26 Dec 2007 02:32:52 -0200 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_quest=E3o_C.N?= In-Reply-To: <569307.1157.qm@web63710.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_10286_23505465.1198643572886" References: <569307.1157.qm@web63710.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_10286_23505465.1198643572886 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1, para a quest=E3o 18, ele j=E1 te diz que =E9 uma circunferencia.. desenhe uma circunferencia com centro em O, marque um ponto P externo. trace a tangente PT, ela mede 8... trace a reta que liga PO... trace OT, que mede 6 (raio) pelo triangulo retangulo OTP, temos que PO =3D 10 trace a outra reta tangente PH... o centro da circunferencia procurada esta ne mediatriz do segmento TH.. mas ele tbem esta na mediatriz do segmento OT.. a reta PO esta contida na mediatriz do segmento TH, entao, trace a mediatri= z da reta OT por semelhanca de triangulos, vc tira que o raio =E9 5 espero que tenha dado pra entender.. um abra=E7o, Salhab On Dec 25, 2007 3:34 PM, fagner almeida wrote: > http://imagetoker.com/viewer.php?id=3D610307imagem.JPG > na 10 o gabarito n=E3o bate e 18 n=E3o sei fazer > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_10286_23505465.1198643572886 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1,

para a quest=E3o 18, ele j=E1 te diz que =E9 uma circunferenc= ia..
desenhe uma circunferencia com centro em O, marque um ponto P exter= no.
trace a tangente PT, ela mede 8...
trace a reta que liga PO...trace OT, que mede 6 (raio)
pelo triangulo retangulo OTP, temos que PO =3D 10
trace a outra reta= tangente PH...
o centro da circunferencia procurada esta ne mediatriz d= o segmento TH..
mas ele tbem esta na mediatriz do segmento OT..
a ret= a PO esta contida na mediatriz do segmento TH, entao, trace a mediatriz da = reta OT
por semelhanca de triangulos, vc tira que o raio =E9 5

espero qu= e tenha dado pra entender..

um abra=E7o,
Salhab



On Dec 25, 2007 3:34 PM, fagner almeida < fagner_mat23@yahoo.com.br> wrote:
na 10 o gabarito n= =E3o bate e 18 n=E3o sei fazer


=20

Abra sua conta no Yahoo! M= ail, o =FAnico sem limite de espa=E7o para armazenamento!=20

------=_Part_10286_23505465.1198643572886-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 26 08:36:47 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQAWI8l027917 for ; Wed, 26 Dec 2007 08:32:18 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBQAWIcE027915 for obm-l-MllGbsmmN; Wed, 26 Dec 2007 08:32:18 -0200 Received: from web63712.mail.re1.yahoo.com (web63712.mail.re1.yahoo.com [69.147.97.97]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id lBQAWF8l027908 for ; Wed, 26 Dec 2007 08:32:16 -0200 Received: (qmail 5874 invoked by uid 60001); 26 Dec 2007 11:33:56 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=I1Y1gG0f5iR50pF2rU0zjmWhqHgGb/NnHfdHDCw9/Tmi/BAWh/h/ketK0QURmgg4ctiUBSHkERKc8DWja0W0yAnY3m8r9fUJwF1E/cuF1feyYwUAjag//penA10iUHzbLKz3RbdKVPYVkG47HvyODX/5k73Sx9BIrsb4VRIDVHI=; X-YMail-OSG: RVcgvFUVM1mhxySAB8o.d6zge9ijtK3RkHeCqdLGTJDy7Em.LAznDRcWq1eQKN9ulRNAcak0r0hvmbDt1Mmw5TSekEAuT8Y6fW6qVMz79bnxA8yb5ajb6Q-- Received: from [189.24.111.202] by web63712.mail.re1.yahoo.com via HTTP; Wed, 26 Dec 2007 08:33:56 ART Date: Wed, 26 Dec 2007 08:33:56 -0300 (ART) From: fagner almeida Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20quest=E3o=20C.N?= To: obm-l@mat.puc-rio.br In-Reply-To: <3bd00efc0712252032r7c1850dcreef954c0b2f15a6c@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <474587.5189.qm@web63712.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: fagner almeida X-Spam-Status: Yes, hits=8.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,IN_REP_TO, MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2003389095-1198668836=:5189" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 97.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 97.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2003389095-1198668836=:5189 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit não entendi ? porque vc afirmou ''que o centro da circunferencia procurada esta na mediatriz do segmento TH..'' e tambem ''mas ele tbem esta na mediatriz do segmento OT..'' como chegou a essa conclusão Marcelo Salhab Brogliato escreveu: Olá, para a questão 18, ele já te diz que é uma circunferencia.. desenhe uma circunferencia com centro em O, marque um ponto P externo. trace a tangente PT, ela mede 8... trace a reta que liga PO... trace OT, que mede 6 (raio) pelo triangulo retangulo OTP, temos que PO = 10 trace a outra reta tangente PH... o centro da circunferencia procurada esta ne mediatriz do segmento TH.. mas ele tbem esta na mediatriz do segmento OT.. a reta PO esta contida na mediatriz do segmento TH, entao, trace a mediatriz da reta OT por semelhanca de triangulos, vc tira que o raio é 5 espero que tenha dado pra entender.. um abraço, Salhab On Dec 25, 2007 3:34 PM, fagner almeida < fagner_mat23@yahoo.com.br> wrote: http://imagetoker.com/viewer.php?id=610307imagem.JPG na 10 o gabarito não bate e 18 não sei fazer --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2003389095-1198668836=:5189 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
não entendi ?  porque  vc  afirmou ''que o centro da circunferencia procurada esta na mediatriz do segmento TH..''
e  tambem  
''mas ele tbem esta na mediatriz do segmento OT..''
como  chegou  a  essa conclusão

Marcelo Salhab Brogliato <msbrogli@gmail.com> escreveu:
Olá,

para a questão 18, ele já te diz que é uma circunferencia..
desenhe uma circunferencia com centro em O, marque um ponto P externo.
trace a tangente PT, ela mede 8...
trace a reta que liga PO...
trace OT, que mede 6 (raio)
pelo triangulo retangulo OTP, temos que PO = 10
trace a outra reta tangente PH...
o centro da circunferencia procurada esta ne mediatriz do segmento TH..
mas ele tbem esta na mediatriz do segmento OT..
a reta PO esta contida na mediatriz do segmento TH, entao, trace a mediatriz da reta OT
por semelhanca de triangulos, vc tira que o raio é 5

espero que tenha dado pra entender..

um abraço,
Salhab



On Dec 25, 2007 3:34 PM, fagner almeida < fagner_mat23@yahoo.com.br> wrote:
na 10 o gabarito não bate e 18 não sei fazer


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!




Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2003389095-1198668836=:5189-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 26 16:22:32 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQIK48l019281 for ; Wed, 26 Dec 2007 16:20:05 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBQIK3ap019273 for obm-l-MllGbsmmN; Wed, 26 Dec 2007 16:20:03 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.176]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQIJt8l019175 for ; Wed, 26 Dec 2007 16:19:56 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4432511wag.13 for ; Wed, 26 Dec 2007 11:21:36 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=dirGcTIlguV2UF7G2xOSdjsyTsOJWcJgXTGzXk7eFA0=; b=D1lG8DUlOrHqKmsHaLlz+czGa7Y8DixowP8PTr2W6s0m3rCfMTymo0xhIwBrUyOkbWbYKfQ8gfqapS6zZpNrYkhyXkdHq/79tOcjT2wQSj5WO2Q5YdO5B6yh5qTYKE1fi0eoHe6meobO529k+fdjwHLNtS26hyyj3sAzx+LYDGs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=q5zawbl6SDXP2PjtbQucSlWjO7R4LWVaAd+5zJZ4wUzOTpUvXvihlJpQnoRlXeII8p+Q2SLakKKW2HxIbstTGykcQMOMs3e4tQT3UhfISy8Tl1n/ZA4Q7qhNu0KjVTVsPHCKJfdkqC9RMCMP3UOs48sakDuMMKSN5Kzp7RO1odc= Received: by 10.114.210.2 with SMTP id i2mr4981648wag.36.1198696895966; Wed, 26 Dec 2007 11:21:35 -0800 (PST) Received: by 10.114.137.2 with HTTP; Wed, 26 Dec 2007 11:21:35 -0800 (PST) Message-ID: <71c5e1520712261121q6fdbee56v934832949ed5262c@mail.gmail.com> Date: Wed, 26 Dec 2007 17:21:35 -0200 From: "Nicolau C. Saldanha" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Mostrar que sequenciais subaditivas convergem In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <5bb472220712190629u74ee42acld034384c749a3f76@mail.gmail.com> X-Google-Sender-Auth: c27f1ce874b207bc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBQIJx8l019231 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Nicolau C. Saldanha" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Não sei se entendi bem, não ficou claro qual o domínio de seq, i.e., para quais valores de n está definido x_n. Será que é {0,1,2,3,...}? Ou talvez {1,2,3,...}? Em qualquer um dos dois casos a seq x_n = 3+n é subaditiva, não? Temos x_(m+n) = 3+m+n < x_m + x_n = 6+m+n. Mas lim (x_n)/n = 1 e infimo x_n = 3 se 0 pertencer ao domínio ou 4 caso contrário. De qualquer forma não vale a conclusão. N. On Dec 19, 2007 1:37 PM, Artur Costa Steiner wrote: > Acho este interessante: > > Seja x_n uma sequencias de números positivos tais que, para todos m e n, tenhamos > > x_(m + n) <= x_m + x_n. Tais sequencia sao denominadas de subaditivas. > > Mostre que lim (x_n)/n = infimo x_n > > Artur > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Dec 26 17:30:03 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQJJgHZ023318 for ; Wed, 26 Dec 2007 17:28:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBQIQ0EW020992 for obm-l-MllGbsmmN; Wed, 26 Dec 2007 16:26:00 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBQIPB8l020930 for ; Wed, 26 Dec 2007 16:25:14 -0200 Received: by wa-out-1112.google.com with SMTP id m28so4435158wag.13 for ; Wed, 26 Dec 2007 11:26:52 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; bh=uFXRk3sJHBopE3Q4401t5z0oUL/EALxI1DsD2DFARcM=; b=uNmN+lbthHK062KWNKXbnen7PeEsd9CL6eV3lp9mspO/Wciw75SIwJA4YySrV/Pv7+2gtcbWYmC1OgZlGd6Z1nMfONb0QbL/G+4YBl6RRLXnUkAlPPOyDd0s2bVYqCg9dIGJ+g8awbatxEDIiL0jfao3My3xJEpglA7oa9zKfT0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:sender:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references:x-google-sender-auth; b=DA/61svMr1R5U8bFjfsfSu9QWnLX1vbt/5lm8hrPFoO8ygJQ97p8p4qFc5X4s26H3//ANXxbN1LE8jlwzDCn/9OG1mT6mhgzzQjF84dobblj+8ka6HMHCbRVroV5ZTgh0KU4ZBI47e8BdnX8daGfImYGpNGZpf+4x0ZlaooiL2U= Received: by 10.114.154.1 with SMTP id b1mr3506587wae.118.1198697212626; Wed, 26 Dec 2007 11:26:52 -0800 (PST) Received: by 10.114.137.2 with HTTP; Wed, 26 Dec 2007 11:26:52 -0800 (PST) Message-ID: <71c5e1520712261126n4510fda8ia17a1f60971602da@mail.gmail.com> Date: Wed, 26 Dec 2007 17:26:52 -0200 From: "Nicolau C. Saldanha" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_N=FAmero_de_Pol=EDgonos_Regulare?= =?ISO-8859-1?Q?s_(estrelados_inclusive)_n=E3o_Semelhantes?= In-Reply-To: <000801c84459$373509a0$01fea8c0@microcf7b75528> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <000801c84459$373509a0$01fea8c0@microcf7b75528> X-Google-Sender-Auth: 0c17330e08ca5fd6 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBQIPS8l020960 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Nicolau C. Saldanha" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Basta escolher de quantos em quantos vértices pular. Você pode pular 1 (para obter o único polígono convexo regular), 5, 7, 11, 13, 17, 19 ou 23. Assim, temos 8 opções. Em geral, temos phi(n)/2 polígonos regulares com n vértices (onde phi é a função de Euler). N. On Dec 22, 2007 3:12 AM, Ulysses Coelho de Souza Jr. wrote: > > > Olá, > > Quantos polígonos regulares não semelhantes existem com 48 lados? > > > > Abraços. > > > Ulysses Coelho de Souza. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Dec 27 16:55:11 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBRIrM8l006271 for ; Thu, 27 Dec 2007 16:53:22 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBRIrMPb006269 for obm-l-MllGbsmmN; Thu, 27 Dec 2007 16:53:22 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.191]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBRIrJ8l006266 for ; Thu, 27 Dec 2007 16:53:20 -0200 Received: by rv-out-0910.google.com with SMTP id c27so2187988rvf.9 for ; Thu, 27 Dec 2007 11:55:01 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=wfkoSLA4Ks8sbEyHvN/8vM9mUdtehgt+rd9Y4K3OtPQ=; b=v1tH0jEx4ebXbgEK64K2Erniq7CcEU8yYWmilSslul/r4hmNcPR15Ifqy+pfT5qBcj51GrdAQh6QJSyEa6R3Y8mcKC5jnEdaJ9m8JrGPEZ8mNLiFJeRXkPNMATf6m+nncZp0OUXJmNRcdcfWHm11Y6FTsog/HJPPKL/zgZ7JUyc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=jSsjq5Twp5XhpFnKCceUARDyu5EKZvmhCxKWkzCd8jv+5F6DNhiThDXGYcZspd4ZSILXRYa8hMSMaQ+kEgfnnDEINMHAgBbyzbArtv/Bfpk3nr+qTWjh57dCsj78GJtVGSwpZj8jshv6t/YTGOY8qoxvkAcEh5CKG3Foq0pPGMg= Received: by 10.141.96.21 with SMTP id y21mr4277539rvl.132.1198785301618; Thu, 27 Dec 2007 11:55:01 -0800 (PST) Received: by 10.141.190.10 with HTTP; Thu, 27 Dec 2007 11:55:01 -0800 (PST) Message-ID: Date: Thu, 27 Dec 2007 17:55:01 -0200 From: "Marcelo Costa" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Provas do IME, versao 13 In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_9808_23614544.1198785301619" References: <20071123122255.K17965@loghost01.lps.ufrj.br> <43bea1ef0711230728o34d327eat3baecbba34919c28@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Costa" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_9808_23614544.1198785301619 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline o link n=E3o apresenta nada?? Algu=E9m pode me ajudar? Em 24/11/07, Anselmo Alves de Sousa escreveu: > > sim, =E9 isso a=ED. > > > > ------------------------------ > Date: Fri, 23 Nov 2007 13:28:17 -0200 > From: fabio.henrique.araujo@gmail.com > To: obm-l@mat.puc-rio.br > Subject: Re: [obm-l] Provas do IME, versao 13 > CC: sergioln@lps.ufrj.br > > Qual o Link das Provas ??? > > On 11/23/07, *Sergio Lima Netto* wrote: > > Caros colegas, > Disponibilizei hoje a versao 13 do material > com as provas de matematica do vetibular do IME. > Nesta nova versao incluo as provas de 2007/2008 > e algumas pequenas correcoes. > Abraco, > sergio > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > -- > Be Free > Use LINUX > Linux #244712 > > > ------------------------------ > Receba as =FAltimas not=EDcias do Brasil e do mundo direto no seu Messeng= er! =C9 > GR=C1TIS! Assine j=E1! > ------=_Part_9808_23614544.1198785301619 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline o link n=E3o apresenta nada??
Algu=E9m pode me ajudar?

Em 24/11/07, Anselmo A= lves de Sousa <anselmo_rj@= hotmail.com > escreveu:
sim, =E9 isso a=ED.



Date: Fri, 23 Nov 2007 13:28:17 -0200
From: fabio.henrique.araujo@gmail.com
To: obm-l@mat.puc-rio.br
Subject: Re: [obm-l] Provas do IME, versao 13
CC: sergioln@lps.ufrj.br
=

Qual o Link das Provas ???

On 11/23/07, Sergio Lima Netto <sergioln@lps.ufrj.br> wrote:=20
Caros colegas,
Disponibilizei hoje a versao 13 do material
c= om as provas de matematica do vetibular do IME.
Nesta nova versao inclu= o as provas de 2007/2008
e algumas pequenas correcoes.
Abraco,
sergio
=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es pa= ra entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
<= br>

--
Be Free
Use LINUX
Linux #244712=20

Receba as =FAltimas not=EDcias do Brasil = e do mundo direto no seu Messenger! =C9 GR=C1TIS! Assine j=E1!

------=_Part_9808_23614544.1198785301619-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 28 01:03:56 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBS32Q8l029379 for ; Fri, 28 Dec 2007 01:02:26 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBS32QQI029377 for obm-l-MllGbsmmN; Fri, 28 Dec 2007 01:02:26 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBS32O8l029373 for ; Fri, 28 Dec 2007 01:02:25 -0200 Received: by wa-out-1112.google.com with SMTP id m28so5434954wag.13 for ; Thu, 27 Dec 2007 20:04:06 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=H/OEFjOS6wTgwCnu7lUW8LJ5J4vk6MZHghmMQ2DPuOQ=; b=q6zWjxNAzEXGYz0NPFG9cfzVH20T0vUzgJ0We8iBu2o7/hujsI8Gv+m07OVd+82QDBn1LNWp4PMIVyFZJ9LtEvD3E41b8hSCdCGcNj0GiXfSUosad3H8t5PmAMzZDWZs6Vhcaad1d0DlhYHvOahoCCqesorWgDXG3JCC8NrmOTA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=T6pa7wcdlaH067NuOXjpUEp5yJ95OSNdNR7C7e9+pdNLGOEAXvc7jWRq1T9PiqvRhdHGtFb4TRhpz1LimY/m4exi/nCxQqVvTQ3GzSArqbzJ4Ci7jlWB0EoxKrxPkyr7Sl8CHTFxb5o/cx5NMlDtccsyuuRi35Wc7KAEKbFfvo8= Received: by 10.114.26.1 with SMTP id 1mr8923044waz.80.1198814646943; Thu, 27 Dec 2007 20:04:06 -0800 (PST) Received: by 10.114.72.5 with HTTP; Thu, 27 Dec 2007 20:04:06 -0800 (PST) Message-ID: <20b75f630712272004g368f32cfvf4d51697f42787cf@mail.gmail.com> Date: Fri, 28 Dec 2007 02:04:06 -0200 From: "Ivan lopes" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Provas do IME, versao 13 In-Reply-To: <20071123154750.D17965@loghost01.lps.ufrj.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Content-Disposition: inline References: <20071123122255.K17965@loghost01.lps.ufrj.br> <20071123154750.D17965@loghost01.lps.ufrj.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ivan lopes" X-Spam-Status: No, hits=1.7 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SIGNATURE_LONG_DENSE,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Caro sergio, o link encontra-se out ivan -- [ ]'s Ivan Carlos Da Silva Lopes Engenheiro Eletronico e Computacao lopesivan@poli.ufrj.br UFRJ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 28 09:36:13 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBSBXm8l008163 for ; Fri, 28 Dec 2007 09:33:48 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBSBXlsx008161 for obm-l-MllGbsmmN; Fri, 28 Dec 2007 09:33:47 -0200 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBSBXj8l008157 for ; Fri, 28 Dec 2007 09:33:46 -0200 Received: by rv-out-0910.google.com with SMTP id c27so2423614rvf.9 for ; Fri, 28 Dec 2007 04:35:28 -0800 (PST) Received: by 10.142.148.7 with SMTP id v7mr63694wfd.153.1198845328293; Fri, 28 Dec 2007 04:35:28 -0800 (PST) Received: by 10.142.49.15 with HTTP; Fri, 28 Dec 2007 04:35:28 -0800 (PST) Message-ID: Date: Fri, 28 Dec 2007 10:35:28 -0200 From: "Marcelo Rodrigues" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Gauss,Abel,Tartaglia-Eq._3=BA_Grau-Complexos?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Rodrigues" X-Spam-Status: Yes, hits=5.8 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_5717_17733006.1198845328278" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 186.198.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 186.198.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_5717_17733006.1198845328278 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal, bom Natal a todos os membros da lista e para suas distintas fam=EDlias tamb=E9m. Gostaria que algu=E9m me auxiliasse no seguinte: Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es d= as equa=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros complexos, com= o objetivo de fazer um projeto para o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber : 1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel s= obre sobre a impossibilidade de se estabelecer coeficientes para equa=E7=F5es de= grau maior que 5 2-A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das eq= ua=E7=F5es e seus relacionamentos entre si 3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano) 4-Se algum dos professores da lista, quiser compartilhar comigo alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros co= mplexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda. Muito obrigado a todos e boas festas, Abra=E7os, Marcelo. ------=_Part_5717_17733006.1198845328278 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal, bom Natal a todos os membros da lista e para suas distintas = fam=EDlias tamb=E9m.

Gostaria que algu=E9m me auxiliasse no seguinte:

Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es d= as equa=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros complexos, com o objetivo de fazer um projeto para o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber :

1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel sobre sobre a impossibilidade de se estabelecer coeficientes para equa=E7=F5es de grau maior que 5

2-A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das eq= ua=E7=F5es e seus relacionamentos entre si

3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano)

4-Se algum dos professores da lista, quiser compartilhar comigo alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros complexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda.

Muito obrigado a todos e boas festas,

Abra=E7os, Marcelo. ------=_Part_5717_17733006.1198845328278-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Dec 28 09:45:51 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBSBiY8l009589 for ; Fri, 28 Dec 2007 09:44:34 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBSBiX26009586 for obm-l-MllGbsmmN; Fri, 28 Dec 2007 09:44:33 -0200 Received: from mailhost.lps.ufrj.br (colchester.lps.ufrj.br [146.164.99.16]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBSBiV8l009565 for ; Fri, 28 Dec 2007 09:44:31 -0200 Received: from localhost (localhost.lps.ufrj.br [127.0.0.1]) by mailhost.lps.ufrj.br (Postfix) with ESMTP id C503350DF9C for ; Fri, 28 Dec 2007 10:46:14 -0200 (BRST) X-Virus-Scanned: amavisd-new at lps.ufrj.br Received: from mailhost.lps.ufrj.br ([127.0.0.1]) by localhost (colchester.lps.ufrj.br [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id rXprChZ2zgP7 for ; Fri, 28 Dec 2007 10:46:14 -0200 (BRST) Received: from loghost1.lps.ufrj.br (loghost1.lps.ufrj.br [146.164.99.27]) by mailhost.lps.ufrj.br (Postfix) with ESMTP id 9071C50DF94 for ; Fri, 28 Dec 2007 10:46:14 -0200 (BRST) Date: Fri, 28 Dec 2007 10:46:14 -0200 (BRST) From: Sergio Lima Netto To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Provas do IME, versao 13 In-Reply-To: Message-ID: <20071228104349.Y84931@loghost01.lps.ufrj.br> References: <20071123122255.K17965@loghost01.lps.ufrj.br> <43bea1ef0711230728o34d327eat3baecbba34919c28@mail.gmail.com> MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="0-612879148-1198845974=:84931" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Sergio Lima Netto X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MIME_EXCESSIVE_QP, MIME_NULL_BLOCK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. --0-612879148-1198845974=:84931 Content-Type: TEXT/PLAIN; charset=X-UNKNOWN; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE Caros colegas, Foram feitas algumas mudancas no servidor do LPS (Laboratorio de Processamento de Sinais). Infelizmente, soh vou conseguir resolver isto na minha volta - jah em 2008. Quem nao quiser esperar, me manda um email diretamente para sergioln@lps.ufrj.br que eu envio o arquivo imev13.pdf, jah que nao posso e nem devo anexar este arquivo a uma mensagem para a lista. Abracos, sergio On Thu, 27 Dec 2007, Marcelo Costa wrote: > o link n=E3o apresenta nada?? > Algu=E9m pode me ajudar? > > Em 24/11/07, Anselmo Alves de Sousa escreveu: >> >> sim, =E9 isso a=ED. >> >> >> >> ------------------------------ >> Date: Fri, 23 Nov 2007 13:28:17 -0200 >> From: fabio.henrique.araujo@gmail.com >> To: obm-l@mat.puc-rio.br >> Subject: Re: [obm-l] Provas do IME, versao 13 >> CC: sergioln@lps.ufrj.br >> >> Qual o Link das Provas ??? >> >> On 11/23/07, *Sergio Lima Netto* wrote: >> >> Caros colegas, >> Disponibilizei hoje a versao 13 do material >> com as provas de matematica do vetibular do IME. >> Nesta nova versao incluo as provas de 2007/2008 >> e algumas pequenas correcoes. >> Abraco, >> sergio >> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D >> Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D >> >> >> >> >> -- >> Be Free >> Use LINUX >> Linux #244712 >> >> >> ------------------------------ >> Receba as =FAltimas not=EDcias do Brasil e do mundo direto no seu Messen= ger! =C9 >> GR=C1TIS! Assine j=E1! >> > --0-612879148-1198845974=:84931-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 29 11:35:56 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTDWS8l004989 for ; Sat, 29 Dec 2007 11:32:28 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBTDWRDQ004987 for obm-l-MllGbsmmN; Sat, 29 Dec 2007 11:32:27 -0200 Received: from smtpi01s.infolink.com.br (smtpi01s.infolink.com.br [200.187.64.121]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTDWQ8l004970 for ; Sat, 29 Dec 2007 11:32:26 -0200 Received: from smtpi01s.infolink.com.br (localhost [127.0.0.1]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 9F8281A7810 for ; Sat, 29 Dec 2007 12:34:10 -0200 (EDT) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 7FDAB1AD129 for ; Sat, 29 Dec 2007 12:34:10 -0200 (EDT) Message-ID: <47765AB3.3080604@infolink.com.br> Date: Sat, 29 Dec 2007 12:33:23 -0200 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.9 (Windows/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Dica de um livro maravilhoso Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 071228-0, 28/12/2007), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: Yes, hits=5.2 required=5.0 tests=AWL,CTYPE_JUST_HTML,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.20 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 176.112.60.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 176.112.60.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: CTYPE_JUST_HTML (0.4 points) HTML-only mail, with no text version SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Oi, gente,

Ando sumido por falta de tempo, mas dou uma dica para quem adora livros bem escritos e fascinantes sobre matemática.

Saiu pela Zahar a tradução (muito bem feita) do maravilhoso livro  "A música dos números primos", do matemático (de Oxford) Marcus du Sautoy - achei na livraria Timbre.

Para quem não o conhece, o livro é absolutamente fascinante e não se consegue parar de lê-lo.  É uma linda aula de história da matemática, contendo fascinantes observações da vida pessoal e profissional de dezenas de matemáticos,  especialmente os que se debruçaram sobre os primos, desde Euclides até os dias de hoje...   A linha mestra são (naturalmente) os números primos e o problema (ainda em aberto) que foi mencionado recentemente aqui na lista: A conjectura de Riemman.    Um livro imperdível para todos: curiosos, alunos, professores de matemática, física ou ciências, em geral, Ciência da Computação (passa por Goedel, Turing, e muito mais)...

Sem querer comparar mas já comparando, muito mais gostoso de ler que "O último teorema de Fermat"... ou "Chaos and Fractals"... :-)

Divirtam-se e abraços a todos e um produtivo e feliz ano novo,
Nehab
 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 29 15:43:58 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTHeL8l020349 for ; Sat, 29 Dec 2007 15:40:21 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBTHeKBT020347 for obm-l-MllGbsmmN; Sat, 29 Dec 2007 15:40:20 -0200 Received: from bay0-omc2-s25.bay0.hotmail.com (bay0-omc2-s25.bay0.hotmail.com [65.54.246.161]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTHeJ8l020340 for ; Sat, 29 Dec 2007 15:40:19 -0200 Received: from BAY137-W24 ([64.4.48.59]) by bay0-omc2-s25.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sat, 29 Dec 2007 10:42:03 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_b821bf7a-afc7-4624-b42a-72bee88d0fa6_" X-Originating-IP: [201.32.101.1] From: Fabio Honorato To: Subject: [obm-l] =?iso-8859-1?Q?RE:_[obm-l]_Gauss,Abel,Tartaglia-Eq._3=BA_Grau-Complexos?= Date: Sat, 29 Dec 2007 18:42:02 +0000 Importance: Normal In-Reply-To: References: MIME-Version: 1.0 X-OriginalArrivalTime: 29 Dec 2007 18:42:03.0016 (UTC) FILETIME=[80DE8080:01C84A4A] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Fabio Honorato X-Spam-Status: No, hits=4.5 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_b821bf7a-afc7-4624-b42a-72bee88d0fa6_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_b821bf7a-afc7-4624-b42a-72bee88d0fa6_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Receba GR=C1TIS as mensagens do Messenger no seu celular quando= voc=EA estiver offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! = --_b821bf7a-afc7-4624-b42a-72bee88d0fa6_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 29 16:58:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTItu8l025861 for ; Sat, 29 Dec 2007 16:55:56 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBTItthZ025852 for obm-l-MllGbsmmN; Sat, 29 Dec 2007 16:55:55 -0200 Received: from hs-out-2122.google.com (hs-out-0708.google.com [64.233.178.251]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTItq8l025826 for ; Sat, 29 Dec 2007 16:55:52 -0200 Received: by hs-out-2122.google.com with SMTP id m63so2704629hsc.13 for ; Sat, 29 Dec 2007 11:57:36 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=9zc2ROqft7gl/4o6rnnMhTRNinwWC4gWzaMJSxBh86g=; b=aO7lpdhqHU1kiX3YY6fE/TTgLzivEiG5Zvk9utsNzrbrs0pIMn3BVeSMKivRoAjFodoV42EW7Bok/Z03PN6FyAYmJXGo7byodaopZ91CZ9V2yl2b0b5pGAcRggaZSyBsuGR21KHSLuqT1/UJs34GyUMwRrgNHllGdyZns+mP5PY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=lHFPZhiL2pMoohgp+gxAi2DEieZgF/GGUgp8Z3pwP8VXBINlg+PxLHpIoRM4F3ji3v4CJAx4etk0GCW86gvva+V/s6pwpR5p06CFpEn6WeUmJzdGqadiZcRKwwCQ0rJW4xOD7nrUwxl8INbwKuNlicF9FhBvL3TB6wfKyHGgL0E= Received: by 10.150.199.21 with SMTP id w21mr3000185ybf.129.1198958255880; Sat, 29 Dec 2007 11:57:35 -0800 (PST) Received: by 10.150.96.3 with HTTP; Sat, 29 Dec 2007 11:57:35 -0800 (PST) Message-ID: <9f4be2240712291157r2ea0d15ag51e10f3943650009@mail.gmail.com> Date: Sat, 29 Dec 2007 17:57:35 -0200 From: "Lucas Prado Melo" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Composi=E7=E3o_de_Fun=E7=F5es?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <000e01c846af$a8cd5830$01fea8c0@microcf7b75528> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id lBTItr8l025844 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Lucas Prado Melo" X-Spam-Status: No, hits=4.4 required=5.0 tests=IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Se tivermos duas funções: f e g. Tal que f: A->B e g: B->C então fog:A->C Logo, no caso, acho que fof:R-{2}->R O que anularia a questão. Alguém discorda? On Dec 25, 2007 11:20 AM, Tales Prates Correia wrote: > > Olá ! > > A função f, como você bem disse, tem como domínio mais extenso o > conjunto D = R - {2}. Uma vez que a sua lei de correspondência é dada por > > > f(x) = (2x + 1)/(x - 2) > > a lei de fof dá-se por > > (fof)(x) = x(x - 2)/(x - 2) > > E seu domínio ainda é D = R - {2}. Essa função não está definida > no ponto x = 2 e é identica a função g real definida por g(x) = x no > conjunto D. > > Por esse motivo, o exercício não apresenta alternativa correta. > Desconsiderando esse erro dos formuladores, seria sensato apontar como > correta > > a alternativa C. > > Espero ter ajudado. > > Abraços! > > ________________________________ > From: ucsjr@uol.com.br > To: obm-l@mat.puc-rio.br > Subject: [obm-l] Composição de Funções > Date: Tue, 25 Dec 2007 01:36:03 -0300 > > > > > Olá, > > > Dada a função f(x) = (2x + 1)/(x - 2), o valor se fof(2), é: > > a) 1/4 b) 1/2 c) 2 d) 4 e) -4 > > > O problema acima foi aplicado num exame de vestibular e o gabarito oficial > apontava a alternativa C como correta. > > É fácil ver que f(2) não existe, pois D(f) = R - {2}. Desse modo, seríamos > levados a concluir que o problema não apresenta alternativa correta, pois > f(f(2)) não existe. > > Por outro lado, f(f(x)) = x, donde f(f(2)) = 2. O que parece ter sido levado > em consideração pelo examinador. > > Pergunta: Onde está o erro? > > Abraços. > > > > > ________________________________ > Receba GRÁTIS as mensagens do Messenger no seu celular quando você estiver > offline. Conheça o MSN Mobile! Crie já o seu! > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Dec 29 18:31:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTKSj8l032629 for ; Sat, 29 Dec 2007 18:28:45 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBTKSjhC032627 for obm-l-MllGbsmmN; Sat, 29 Dec 2007 18:28:45 -0200 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBTKSg8l032623 for ; Sat, 29 Dec 2007 18:28:43 -0200 Received: by wa-out-1112.google.com with SMTP id m28so6706746wag.13 for ; Sat, 29 Dec 2007 13:30:26 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=CfC19IWBRaG6HZXq5c3Nkx/ueZgNLbXarVPmokG3Iw0=; b=JfUnBJbzO5wkW6IVL2mYnJEDhfWsRrtu2Oub8a8HsEMWKVqY1MzZLOkRCjVWv6PM8UWzD573d7EAae/SDwqrSAQRFM+w6Ex0pJXhsSBIbEmbjTt9P4AatcR420TBrNdSBkHE4lk/owvWwdqjdx6gvN/bvbxMTz8KMYQ91e3ArS0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=KeRkAPwkB7aWe9yQ++l8+Xvusq/Q2NUtkqnCsXZpF/0jtqckUf1Z0Q1+wRaGnLt+fH5XdnGAb9rNgb4R3HoTVrkxWifRs5hg5GzJmo55FprS3GSwBm2JxNe3rY+S0fzJyDtXTuFD8WDdCxJbGmvFegZy0jbH/8nwccje/JywfsU= Received: by 10.114.26.1 with SMTP id 1mr11254796waz.80.1198963465086; Sat, 29 Dec 2007 13:24:25 -0800 (PST) Received: by 10.114.136.9 with HTTP; Sat, 29 Dec 2007 13:24:25 -0800 (PST) Message-ID: <3bd00efc0712291324s23cab20r4abd8a4593d78c8@mail.gmail.com> Date: Sat, 29 Dec 2007 22:24:25 +0100 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_quest=E3o_C.N?= In-Reply-To: <474587.5189.qm@web63712.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_20205_30629639.1198963465070" References: <3bd00efc0712252032r7c1850dcreef954c0b2f15a6c@mail.gmail.com> <474587.5189.qm@web63712.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=2.7 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_20205_30629639.1198963465070 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Fagner, os pontos T e H pertencem a circunferencia procurada... e todos os pontos equidistantes de ambos pertencem a mediatriz (e somente a mediatriz). O mesmo vale para o segmento OT. abracos, Salhab On 12/26/07, fagner almeida wrote: > > n=E3o entendi ? porque vc afirmou ''que o centro da circunferencia > procurada esta na mediatriz do segmento TH..'' > e tambem > ''mas ele tbem esta na mediatriz do segmento OT..'' > como chegou a essa conclus=E3o > > *Marcelo Salhab Brogliato * escreveu: > > Ol=E1, > > para a quest=E3o 18, ele j=E1 te diz que =E9 uma circunferencia.. > desenhe uma circunferencia com centro em O, marque um ponto P externo. > trace a tangente PT, ela mede 8... > trace a reta que liga PO... > trace OT, que mede 6 (raio) > pelo triangulo retangulo OTP, temos que PO =3D 10 > trace a outra reta tangente PH... > o centro da circunferencia procurada esta ne mediatriz do segmento TH.. > mas ele tbem esta na mediatriz do segmento OT.. > a reta PO esta contida na mediatriz do segmento TH, entao, trace a > mediatriz da reta OT > por semelhanca de triangulos, vc tira que o raio =E9 5 > > espero que tenha dado pra entender.. > > um abra=E7o, > Salhab > > > > On Dec 25, 2007 3:34 PM, fagner almeida < fagner_mat23@yahoo.com.br> > wrote: > > > http://imagetoker.com/viewer.php?id=3D610307imagem.JPG > > na 10 o gabarito n=E3o bate e 18 n=E3o sei fazer > > > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_20205_30629639.1198963465070 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Fagner,

os pontos T e H pertencem a circunferencia procurada..= . e todos os pontos equidistantes de ambos pertencem a mediatriz (e somente= a mediatriz). O mesmo vale para o segmento OT.


abracos,
Salh= ab


On 12/26/07, fagner almeida <fagner_mat23@yahoo.com.br> wrote:
n=E3o entendi ?  porque  vc  afirmou ''que o ce= ntro da circunferencia procurada esta na mediatriz do segmento TH..'= 9;
e  tambem  
''mas ele tbem esta n= a mediatriz do segmento OT..''
como  chegou  a  essa conclus=E3o

= Marcelo Salhab Brogliato <msbrog= li@gmail.com> escreveu:
Ol=E1,

para a quest=E3o 18, ele j=E1 te diz q= ue =E9 uma circunferencia..
desenhe uma circunferencia com centro em O, marque um ponto P externo.<= br>trace a tangente PT, ela mede 8...
trace a reta que liga PO...
tra= ce OT, que mede 6 (raio)
pelo triangulo retangulo OTP, temos que PO =3D= 10
trace a outra reta tangente PH...
o centro da circunferencia procura= da esta ne mediatriz do segmento TH..
mas ele tbem esta na mediatriz do = segmento OT..
a reta PO esta contida na mediatriz do segmento TH, entao, trace a mediatriz da reta OT
por semelhanca de tri= angulos, vc tira que o raio =E9 5

espero que tenha dado pra entender= ..

um abra=E7o,
Salhab



On Dec 25, 2007 3:34 PM, fagner almeida < fagner_mat23@yahoo.com.br> wrote:
na 10 o gabarito n=E3o bate e 18 n=E3o sei fazer


Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamento!




=20

Abra sua conta no Yahoo!= Mail , o =FAnico sem limite de espa=E7o para armazenamento!=20


------=_Part_20205_30629639.1198963465070-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 30 02:05:45 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBU43o8l027789 for ; Sun, 30 Dec 2007 02:03:50 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBU43oSu027781 for obm-l-MllGbsmmN; Sun, 30 Dec 2007 02:03:50 -0200 Received: from bay0-omc2-s38.bay0.hotmail.com (bay0-omc2-s38.bay0.hotmail.com [65.54.246.174]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBU43l8l027770 for ; Sun, 30 Dec 2007 02:03:48 -0200 Received: from BAY137-W10 ([64.4.48.45]) by bay0-omc2-s38.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sat, 29 Dec 2007 21:05:31 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_58329edc-b85a-4716-bdf1-3555de670c7e_" X-Originating-IP: [201.32.95.240] From: Fabio Honorato To: Subject: [obm-l] =?iso-8859-1?Q?RE:_[obm-l]_Gauss,Abel,Tartaglia-Eq._3=BA_Grau-Complexos?= Date: Sun, 30 Dec 2007 05:05:31 +0000 Importance: Normal In-Reply-To: References: MIME-Version: 1.0 X-OriginalArrivalTime: 30 Dec 2007 05:05:31.0964 (UTC) FILETIME=[9A56F7C0:01C84AA1] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Fabio Honorato X-Spam-Status: No, hits=4.5 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_58329edc-b85a-4716-bdf1-3555de670c7e_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oi Marcelo , sobre o assunto "3-Demonstra=E7=E3o da F=F3rmula de Tartaglia = (Cardano)" eu encontrei esse link http://www2.dm.ufscar.br/~sampaio/eq123g= raus.PDF na p=E1gina do Prof Jo=E3o C V Sampaio e vc pode encontrar tamb=E9= m algumas informa=E7=F5es sobre esse mesmo assunto na Revista Eureka n 15. = Um exerc=EDcio muito interessante que relaciona Equa=E7=F5es de 3=BA Grau = com N=FAmeros complexos eh que: =20 Dada a equa=E7=E3o x^3+px+q=3D0, onde uma das ra=EDzes eh dada por \sqrt [3= ]{-q/2+\sqrt {D}}+ \sqrt [3]{-q/2 - \sqrt {D}}, D =3D 1/4*q^2+1/27*p^3. Pro= ve que se a equa=E7=E3o possui 3 ra=EDzes reais entaum D<0. =20 Ateh + =20 =20 Date: Fri, 28 Dec 2007 10:35:28 -0200From: geo3d@ibest.com.brTo: obm-l@mat.= puc-rio.brSubject: [obm-l] Gauss,Abel,Tartaglia-Eq. 3=BA Grau-ComplexosOl= =E1 pessoal, bom Natal a todos os membros da lista e para suas distintas fa= m=EDlias tamb=E9m.Gostaria que algu=E9m me auxiliasse no seguinte:Estou des= envolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es das equa= =E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros compl= exos, com o objetivo de fazer um projeto para o ensino m=E9dio sobre esta = =E1rea da matem=E1tica, e desejaria saber :1-Algum site que contivesse a de= monstra=E7=E3o da F=F3rmula de Niels Abel sobre sobre a impossibilidade de = se estabelecer coeficientes para equa=E7=F5es de grau maior que 52-A demons= tra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das equa=E7=F5es= e seus relacionamentos entre si3-Demonstra=E7=E3o da F=F3rmula de Tartagli= a (Cardano)4-Se algum dos professores da lista, quiser compartilhar comigo = alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAm= eros complexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda.Mu= ito obrigado a todos e boas festas,Abra=E7os, Marcelo.=20 _________________________________________________________________ Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA esti= ver offline. Conhe=E7a o MSN Mobile! http://mobile.live.com/signup/signup2.aspx?lc=3Dpt-br= --_58329edc-b85a-4716-bdf1-3555de670c7e_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oi Marcelo , sobre o assunto "3-Demonstra=E7=E3o da F=F3rmula de Tartag= lia (Cardano)" eu encontrei esse link  http://www2.dm.ufscar.br/~sampaio/eq123graus.= PDF na p=E1gina do Prof Jo=E3o C V Sampaio e vc pode encontrar tamb=E9m= algumas informa=E7=F5es sobre esse mesmo assunto na Revista Eureka n 15.&n= bsp; Um exerc=EDcio muito interessante que relaciona Equa=E7=F5es de 3=BA G= rau com N=FAmeros complexos  eh que:
 
Dada a equa=E7=E3o x^3+px+q=3D0, onde uma das ra=EDzes eh dada por \sqrt [3= ]{-q/2+\sqrt {D}}+ \sqrt [3]{-q/2 - \sqrt {D}}, D =3D 1/4*q^2+1/27*p^3. Pro= ve que se a equa=E7=E3o possui 3 ra=EDzes reais entaum D<0.
 
Ateh +
 

 
Date: Fri, 28 Dec 2007 10:35:28 -0200
From: geo3d@ibest.com.br
To: ob= m-l@mat.puc-rio.br
Subject: [obm-l] Gauss,Abel,Tartaglia-Eq. 3=BA Grau-C= omplexos

Ol=E1 pessoal, bom Natal a todos os membros da lista e para= suas distintas fam=EDlias tamb=E9m.

Gostaria que algu=E9m me auxili= asse no seguinte:

Estou desenvolvendo um trabalho de p=F3s gradua=E7= =E3o sobre solu=E7=F5es das equa=E7=F5es de terceiro grau com radicais e o = aparecimento dos n=FAmeros complexos, com o objetivo de fazer um projeto pa= ra o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber :<= BR>
1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels= Abel sobre sobre a impossibilidade de se estabelecer coeficientes para equ= a=E7=F5es de grau maior que 5

2-A demonstra=E7=E3o da F=F3rmula de A= lbert Girard sobre as ra=EDzes das equa=E7=F5es e seus relacionamentos entr= e si

3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano)

4= -Se algum dos professores da lista, quiser compartilhar comigo alguma exper= i=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros comp= lexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda.

= Muito obrigado a todos e boas festas,

Abra=E7os, Marcelo.
Receba GR=C1TIS as mensagens do Messenger no seu celular qua= ndo voc=EA estiver offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu= ! = --_58329edc-b85a-4716-bdf1-3555de670c7e_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Dec 30 17:57:43 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBUJuC8l022250 for ; Sun, 30 Dec 2007 17:56:12 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBUJuBhu022248 for obm-l-MllGbsmmN; Sun, 30 Dec 2007 17:56:11 -0200 Received: from sr03-05.mta.terra.com.br (sr03-05.mta.terra.com.br [200.154.152.44]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBUJuA8l022245 for ; Sun, 30 Dec 2007 17:56:10 -0200 Received: from quebec.hst.terra.com.br (quebec.hst.terra.com.br [200.176.10.31]) by bungunia.hst.terra.com.br (Postfix) with ESMTP id D947821B4161 for ; Sun, 30 Dec 2007 18:57:55 -0200 (BRST) X-Terra-Karma: -2% X-Terra-Hash: 8b0b4d76440f7196cde5822e2d19ea58 Received-SPF: pass (quebec.hst.terra.com.br: domain of terra.com.br designates 200.176.10.31 as permitted sender) client-ip=200.176.10.31; envelope-from=fgb1@terra.com.br; helo=bernardechbqji; Received: from bernardechbqji (unknown [189.24.19.220]) (authenticated user fgb1) by quebec.hst.terra.com.br (Postfix) with ESMTP id 0E5046804E for ; Sun, 30 Dec 2007 18:57:54 -0200 (BRST) Message-ID: <008c01c840ef$69f6ea10$0501010a@bernardechbqji> From: "Bernardo" To: Subject: [SPAM] [obm-l] Concurso professor RJ Date: Mon, 17 Dec 2007 18:54:48 -0200 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-Antivirus: avast! (VPS 071230-0, 30/12/2007), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Bernardo" X-Spam-Status: Yes, hits=7.5 required=5.0 tests=DATE_IN_PAST_96_XX,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0018_01C840DE.4C4C10F0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.50 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: DATE_IN_PAST_96_XX (1.5 points) Date: is 96 hours or more before Received: date SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 31.10.176.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 31.10.176.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0018_01C840DE.4C4C10F0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Amigos me ajudem nesses dois, foram da =FAltima prova p/ professor do = estado do RJ Ab=E7 a todos e Um grande 2008 tb No intervalo [0, 2pi], a soma das solu=E7=F5es da equa=E7=E3o sen(2x+30) = =3D cos(x) =E9: a) 480 b) 420 c) 260 d) 160 e) 20 Seja N =3D {0,1,2,3,...} o conj dos naturais. O n=FAmero de elementos do = conj NxN que satisfazem =E0 condi=E7=E3o=20 y < x =3D 6 =E9: a) 21 b) 22 c) 23 d) 24 e) 26 ------=_NextPart_000_0018_01C840DE.4C4C10F0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

 

Amigos me ajudem nesses dois, foram da =FAltima = prova p/=20 professor do estado do RJ

 

Ab=E7 a todos e Um grande 2008 tb

 

No intervalo [0, 2pi], a soma das solu=E7=F5es da = equa=E7=E3o=20 sen(2x+30) =3D cos(x) =E9:

a) 480

b) 420

c) 260

d) 160

e) 20

 

Seja N =3D {0,1,2,3,...} o conj dos naturais. O = n=FAmero de=20 elementos do conj NxN que satisfazem =E0 condi=E7=E3o

y < x =3D 6 =E9:

a) 21

b) 22

c) 23

d) 24

e) 26

 

 

------=_NextPart_000_0018_01C840DE.4C4C10F0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Dec 31 11:56:00 2007 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBVDrD8l013704 for ; Mon, 31 Dec 2007 11:53:13 -0200 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id lBVDrDVJ013702 for obm-l-MllGbsmmN; Mon, 31 Dec 2007 11:53:13 -0200 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id lBVDrA8l013698 for ; Mon, 31 Dec 2007 11:53:11 -0200 Received: by fk-out-0910.google.com with SMTP id 22so5711635fkq.13 for ; Mon, 31 Dec 2007 06:54:55 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=336qvWJrLqscmxl7xzX4SUpgDBqAQpv9yEGx632dZ54=; b=gFgkttyD02DNFMyGZeXE27bXPppupWWPT4Om7qOur+RSGjsL0oDOThmCy6qgE/CnaiH+FVOQLI9kU8D3Wt69Z0i1+2IgTHoKhZziZGdLmj9YNAKq/l3ii01U/tSx4zb+F2JnPBqMHNmSZmyAIeo1DmOyJdgMVDFMttKBM7NNENo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Xcscm7abi7Z6dmtj91d9aJg7mmvcONTjfGEyi5FiUCtgDeZ7sMyLRegvrVu75N8FMQU8utu2oMRYZZrKsUZYW6sZ16Hd7ce7YEj9xMJgTITMpV1RkD5Ydx/MJBg6+CtMvEngeFeYQP9WzZxwWoFqJrpKA5pGhyxuAHCWjAMIfJ8= Received: by 10.82.186.5 with SMTP id j5mr22173640buf.16.1199112894395; Mon, 31 Dec 2007 06:54:54 -0800 (PST) Received: by 10.82.189.1 with HTTP; Mon, 31 Dec 2007 06:54:54 -0800 (PST) Message-ID: Date: Mon, 31 Dec 2007 12:54:54 -0200 From: "Marcelo Gomes" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RE:_[obm-l]_Gauss,Abe?= =?ISO-8859-1?Q?l,Tartaglia-Eq._3=BA_Grau-Complexos?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_20589_10323915.1199112894394" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Gomes" X-Spam-Status: No, hits=2.3 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_20589_10323915.1199112894394 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Oi Fabinho...boa tarde. Muito obrigado pela ajuda..chegou em uma =F3tima hora, valeu mesmo pelo seu interesse em ajudar. Ainda estou ca=E7ando as demonstra=E7=F5es dos outros. Mais uma vez muito o= brigado pela aten=E7=E3o e um excelente 2008 para voc=EA e toda sua fam=EDlia, um = abra=E7=E3o, Marcelo. Em 30/12/07, Fabio Honorato escreveu: > > > Oi Marcelo , sobre o assunto "3-Demonstra=E7=E3o da F=F3rmula de Tartagli= a > (Cardano)" eu encontrei esse link > http://www2.dm.ufscar.br/~sampaio/eq123graus.PDFna p=E1gina do Prof Jo=E3o C V Sampaio e vc pode= encontrar tamb=E9m algumas > informa=E7=F5es sobre esse mesmo assunto na Revista Eureka n 15. Um exer= c=EDcio > muito interessante que relaciona Equa=E7=F5es de 3=BA Grau com N=FAmeros = complexos > eh que: > > Dada a equa=E7=E3o x^3+px+q=3D0, onde uma das ra=EDzes eh dada por \sqrt > [3]{-q/2+\sqrt {D}}+ \sqrt [3]{-q/2 - \sqrt {D}}, D =3D 1/4*q^2+1/27*p^3. > Prove que se a equa=E7=E3o possui 3 ra=EDzes reais entaum D<0. > > Ateh + > > > > > ------------------------------ > Date: Fri, 28 Dec 2007 10:35:28 -0200 > From: geo3d@ibest.com.br > To: obm-l@mat.puc-rio.br > Subject: [obm-l] Gauss,Abel,Tartaglia-Eq. 3=BA Grau-Complexos > > Ol=E1 pessoal, bom Natal a todos os membros da lista e para suas distinta= s > fam=EDlias tamb=E9m. > > Gostaria que algu=E9m me auxiliasse no seguinte: > > Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es= das > equa=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros > complexos, com o objetivo de fazer um projeto para o ensino m=E9dio sobre= esta > =E1rea da matem=E1tica, e desejaria saber : > > 1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel= sobre > sobre a impossibilidade de se estabelecer coeficientes para equa=E7=F5es = de grau > maior que 5 > > 2-A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das = equa=E7=F5es > e seus relacionamentos entre si > > 3-Demonstra=E7=E3o da F=F3rmula de Tartaglia (Cardano) > > 4-Se algum dos professores da lista, quiser compartilhar comigo alguma > experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros = complexos-> > sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda. > > Muito obrigado a todos e boas festas, > > Abra=E7os, Marcelo. > > > ------------------------------ > Receba GR=C1TIS as mensagens do Messenger no seu celular quando voc=EA es= tiver > offline. Conhe=E7a o MSN Mobile! Crie j=E1 o seu! > ------=_Part_20589_10323915.1199112894394 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Oi Fabinho...boa tarde.

Muito obrigado pela ajuda..chegou em uma =F3tima hora, valeu mesmo pelo seu= interesse em ajudar.

Ainda estou ca=E7ando as demonstra=E7=F5es dos outros. Mais uma vez muito obrigado pela aten=E7=E3o e um excelente 2008 para voc=EA e toda sua fam=EDlia,  um abra=E7=E3o, Marcelo.

Em 30/12/07, Fabio Honorato <fabinho_g3@hotmail.com> escr= eveu:

Oi Marcelo , sobre o assunto "3-Demonstra=E7=E3o da F=F3rmula de T= artaglia (Cardano)" eu encontrei esse link  http://www2.dm.ufscar.br/~sampaio/eq123graus.PDF na p=E1gina do Prof Jo=E3o C V Sampaio e vc pode encontrar tamb=E9m algumas informa=E7=F5es sobre esse mesmo assunto na Revista Eureka n 15.  Um exerc=EDcio muito interessante que relaciona Equa=E7=F5es de 3=BA Grau com N=FAmeros complexos  eh que:
 
Dada a equa=E7=E3o x^3+px+q=3D0, onde uma das ra=EDzes eh dada por \sqrt [3]{-q/2+\sqrt {D}}+ \sqrt [3]{-q/2 - \sqrt {D}}, D =3D 1/4*q^2+1/27*p^3. Prove que se a equa=E7=E3o possui 3 ra=EDzes reais entaum D<0.
 
Ateh +
 

 
Date: Fri, 28 Dec 2007 10:35:28 -0200
From: geo3d@ibest.com.br
To: obm-l@mat.puc-rio.br
Subject: [obm-l] Gauss,Abel,Tartaglia-Eq. 3=BA = Grau-Complexos


Ol= =E1 pessoal, bom Natal a todos os membros da lista e para suas distintas fa= m=EDlias tamb=E9m.

Gostaria que algu=E9m me auxiliasse no seguinte:

Estou desenvolvendo um trabalho de p=F3s gradua=E7=E3o sobre solu=E7=F5es das equ= a=E7=F5es de terceiro grau com radicais e o aparecimento dos n=FAmeros complexos, com o objetivo de fazer um projeto para o ensino m=E9dio sobre esta =E1rea da matem=E1tica, e desejaria saber :

1-Algum site que contivesse a demonstra=E7=E3o da F=F3rmula de Niels Abel sobre sobre a impossibilidade d= e se estabelecer coeficientes para equa=E7=F5es de grau maior que 5

2-= A demonstra=E7=E3o da F=F3rmula de Albert Girard sobre as ra=EDzes das equa= =E7=F5es e seus relacionamentos entre si

3-Demonstra=E7=E3o da F=F3r= mula de Tartaglia (Cardano)

4-Se algum dos professores da lista, quiser compartilhar comigo alguma experi=EAncia nesta =E1rea de equa=E7=F5es de terceiro grau -> n=FAmeros complexos-> sua hist=F3ria e ensino m=E9dio, ser=E1 muito bem vinda.
=
Muito obrigado a todos e boas festas,

Abra=E7os, Marcelo.

Receba GR=C1TIS as mensagens = do Messenger no seu celular quando voc=EA estiver offline. Conhe=E7a o MSN= Mobile!=20 Crie j=E1= o seu!

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