[SPAM] [obm-l] Re: [obm-l] Re: [obm-l] perímetro mínimo

[Eder Albuquerque <eder_mat@xxxxxxxxxxxx>]

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Obrigado pelos esclarecimentos. Estou analisando aqui.

--- Em seg, 23/6/08, Luiz Alberto Duran Salom=E3o <salomao@xxxxxx> escreveu=
:

De: Luiz Alberto Duran Salom=E3o <salomao@xxxxxx>
Assunto: [obm-l] Re: [obm-l] per=EDmetro m=EDnimo
Para: obm-l@xxxxxxxxxxxxxx
Data: Segunda-feira, 23 de Junho de 2008, 10:37

Caro Ponce:

Creio que sua inten=E7=E3o foi dizer que C =E9 a interse=E7=E3o de OY com B=
P (e
n=E3o AP) e que B estaria na interse=E7=E3o de OX com CQ (e n=E3o AQ),
n=E3o =E9 mesmo?

Abra=E7os,
Luiz Alberto


----- Original Message -----=20
From: "Rogerio Ponce" <abrlwsky@xxxxxxxxx>
To: <obm-l@xxxxxxxxxxxxxx>
Sent: Sunday, June 22, 2008 6:40 PM
Subject: Re: [obm-l] per=EDmetro m=EDnimo


> Ola'  Eder,
> suponhamos que o ponto B ja' estivesse marcado, e que estamos apenas
> procurando pelo ponto C otimo, sobre OY.
>
> Nesse caso, para minimizar BC + CA , vemos que C e' a intersecao de OY
> com AP , onde P e' o ponto simetrico de A em relacao a OY.
>
> O mesmo aconteceria se C ja' estivesse marcado, e estivessemos
> procurando pelo ponto B otimo, que estaria na intersecao de OX com AQ,
> onde Q e' o simetrico de A em relacao a OX.
>
> Portanto, como cada um dos vertices C e B necessariamente otimiza a
> soma de suas distancias aos outros dois vertices, basta localizar os
> simetricos de A em relacao a OX e OY, e uni-los, de forma a determinar
> os vertices C e B.
>
> []'s
> Rogerio Ponce
>
>
> Em 22/06/08, Eder Albuquerque<eder_mat@xxxxxxxxxxxx> escreveu:
>> Por gentileza, ajudem-me na quest=E3o abaixo
>>
>>
>> Dado um =E2ngulo agudo XOY e um ponto interior A, achar um ponto B
sobre OX=20
>> e
>> um ponto C sobre OY tais que o per=EDmetro do tri=E2ngulo ABC seja
m=EDnimo.
>>
>>
>>       Novos endere=E7os, o Yahoo! que voc=EA conhece. Crie um email novo
com=20
>> a
>> sua cara @ymail.com ou @rocketmail.com.
>> http://br.new.mail.yahoo.com/addresses
>
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=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
> No virus found in this incoming message.
> Checked by AVG.
> Version: 7.5.524 / Virus Database: 270.4.1/1514 - Release Date: 23/6/2008=
=20
> 07:17
>
>=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=0A=0A=
=0A      Novos endere=E7os, o Yahoo! que voc=EA conhece. Crie um email novo=
 com a sua cara @ymail.com ou @rocketmail.com.=0Ahttp://br.new.mail.yahoo.c=
om/addresses
--0-460223670-1214411024=:18959
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<table cellspacing=3D'0' cellpadding=3D'0' border=3D'0' ><tr><td valign=3D'=
top' style=3D'font: inherit;'>Obrigado pelos esclarecimentos. Estou analisa=
ndo aqui.<BR><BR>--- Em <B>seg, 23/6/08, Luiz Alberto Duran Salom=E3o <I>&l=
t;salomao@xxxxxx&gt;</I></B> escreveu:<BR>
<BLOCKQUOTE style=3D"PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: rgb(=
16,16,255) 2px solid">De: Luiz Alberto Duran Salom=E3o &lt;salomao@xxxxxx&g=
t;<BR>Assunto: [obm-l] Re: [obm-l] per=EDmetro m=EDnimo<BR>Para: obm-l@mat.=
puc-rio.br<BR>Data: Segunda-feira, 23 de Junho de 2008, 10:37<BR><BR><PRE>C=
aro Ponce:

Creio que sua inten=E7=E3o foi dizer que C =E9 a interse=E7=E3o de OY com B=
P (e
n=E3o AP) e que B estaria na interse=E7=E3o de OX com CQ (e n=E3o AQ),
n=E3o =E9 mesmo?

Abra=E7os,
Luiz Alberto


----- Original Message -----=20
From: "Rogerio Ponce" &lt;abrlwsky@xxxxxxxxx&gt;
To: &lt;obm-l@xxxxxxxxxxxxxx&gt;
Sent: Sunday, June 22, 2008 6:40 PM
Subject: Re: [obm-l] per=EDmetro m=EDnimo


&gt; Ola'  Eder,
&gt; suponhamos que o ponto B ja' estivesse marcado, e que estamos apenas
&gt; procurando pelo ponto C otimo, sobre OY.
&gt;
&gt; Nesse caso, para minimizar BC + CA , vemos que C e' a intersecao de OY
&gt; com AP , onde P e' o ponto simetrico de A em relacao a OY.
&gt;
&gt; O mesmo aconteceria se C ja' estivesse marcado, e estivessemos
&gt; procurando pelo ponto B otimo, que estaria na intersecao de OX com AQ,
&gt; onde Q e' o simetrico de A em relacao a OX.
&gt;
&gt; Portanto, como cada um dos vertices C e B necessariamente otimiza a
&gt; soma de suas distancias aos outros dois vertices, basta localizar os
&gt; simetricos de A em relacao a OX e OY, e uni-los, de forma a determinar
&gt; os vertices C e B.
&gt;
&gt; []'s
&gt; Rogerio Ponce
&gt;
&gt;
&gt; Em 22/06/08, Eder Albuquerque&lt;eder_mat@xxxxxxxxxxxx&gt; escreveu:
&gt;&gt; Por gentileza, ajudem-me na quest=E3o abaixo
&gt;&gt;
&gt;&gt;
&gt;&gt; Dado um =E2ngulo agudo XOY e um ponto interior A, achar um ponto B
sobre OX=20
&gt;&gt; e
&gt;&gt; um ponto C sobre OY tais que o per=EDmetro do tri=E2ngulo ABC seja
m=EDnimo.
&gt;&gt;
&gt;&gt;
&gt;&gt;       Novos endere=E7os, o Yahoo! que voc=EA conhece. Crie um emai=
l novo
com=20
&gt;&gt; a
&gt;&gt; sua cara @ymail.com ou @rocketmail.com.
&gt;&gt; http://br.new.mail.yahoo.com/addresses
&gt;
&gt; =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
&gt; Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
&gt; http://www.mat.puc-rio.br/~obmlistas/obm-l.html
&gt; =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
&gt;
&gt;
&gt;
&gt; --=20
&gt; No virus found in this incoming message.
&gt; Checked by AVG.
&gt; Version: 7.5.524 / Virus Database: 270.4.1/1514 - Release Date: 23/6/2=
008=20
&gt; 07:17
&gt;
&gt;=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</PRE>=
</BLOCKQUOTE></td></tr></table><br>=0A=0A=0A      <hr size=3D1>Novos endere=
=E7os, o Yahoo! que voc=EA conhece. <a href=3D"http://br.rd.yahoo.com/mail/=
taglines/mail/*http://br.new.mail.yahoo.com/addresses";>Crie um email novo</=
a> com a sua cara @ymail.com ou @rocketmail.com.
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