tag:blogger.com,1999:blog-594878483692603412024-03-19T03:10:59.265+00:00Objectiva.MenteObjectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.comBlogger597125tag:blogger.com,1999:blog-59487848369260341.post-16268371974435945632010-12-18T22:59:00.002+00:002010-12-20T09:37:41.516+00:00LPDJLQH D VHFUHW<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwlDs1Q7mbBmHHI1ueMEEGIDPoeqFUgad1RwbvpbrifeusIKfxTmUIfNRHWyh2ufxGhpOM6kXUIOVViNAFg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>Este foi um dos projectos no qual estive envolvido e trata-se de uma animação de conteúdo científico cujo tema aborda o papel da matemãtica na moderna tecnologia da encriptação.<br />
É um filme que não tem uma leitura fácil para quem não domina os conceitos matemáticos abordados (eu incluido) mas o meu papel foi o da realização e banda sonora, em colaboração com o meu amigo Vitor Fernandes. A ideia original e o guião matemático foi do Prof. José Francisco Rodrigues.<br />
Foi exibido pela 1ª vez em 26 de Setembro em Óbidos numa conferência internacional de matemática.<br />
O texto que aparece no final ajuda a compreender o conteúdo e é o seguinte:<br />
<br />
<div class="MsoNormal" style="mso-hyphenate: auto; mso-pagination: widow-orphan;"><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">"Os triplos pitagóricos, por exemplo (3, 4, 5) ou (4961, 6480, 8161), eram já bem conhecidos na antiga Babilónia, cerca de 1600 A.C., tal como a sua correspondência com o comprimentos dos lados de um triângulo rectângulo e o problema de partir um número quadrado na soma de dois quadrados. Apesar desses triplos terem sido estudados em detalhe no tempo de Euclides (300 A.C.), foi apenas em meados do século XVII que Pierre de Fermat observou: "Nenhum cubo se pode partir em dois cubos, nem nenhum biquadrado em dois biquadrados, nem, em geral, nenhuma potência maior que a segunda em duas outras do mesmo tipo". </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> Esta afirmação tornou-se no famoso "Último Teorema de Fermat", estabelecendo que a equação </span></span></div><div class="MsoNormal" style="mso-hyphenate: auto; mso-pagination: widow-orphan;"><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">A</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">N</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> + B</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> N</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="mso-spacerun: yes;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span><span style="font-family: "Arial", "Helvetica", sans-serif;">= C</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> N</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span></b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="mso-spacerun: yes;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span><span style="font-family: "Arial", "Helvetica", sans-serif;">não tem soluções inteiras não nulas quando </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">N</span></b><span style="font-family: "Arial", "Helvetica", sans-serif;"> é maior que 2, e apenas foi completamente demonstrada em 1994, cerca de três séculos e meio mais tarde, usando a teoria das curvas elípticas do século XX !</span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> As curvas elípticas são curvas planas do tipo </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">y</span></b></span><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 2</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> = x</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 3 </span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">+ a x + b</span></span></b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> que possuem propriedades belas e profundas, bem estudadas desde o século XIX. A essa equação corresponde a equação homogénea de grau três </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">z y</span></b></span><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 2</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> = x</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 3</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> + a x z</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 2</span></span></sup></b><b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> + b z</span></span></b><b><sup><span style="font-size: 10.0pt; mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> 3</span></span></sup></b><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">, a qual descreve no espaço uma família de superfícies algébricas com dois parâmetros </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">a</span></b><span style="font-family: "Arial", "Helvetica", sans-serif;"> e </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">b</span></b><span style="font-family: "Arial", "Helvetica", sans-serif;">. A variação computacional desses parâmetros nessas equações gera belas animações que estimulam a nossa imaginação e evocam a nossa criatividade matemática.</span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> A criptografia trata de métodos seguros para transmitir e salvaguardar informação secreta e valiosa. Desde 1977 o sistema de chave pública RSA tem sido largamente usado e baseia-se na teoria dos números primos e na dificuldade de fatorização de números inteiros muito grandes. Com o impacto do método das curvas elípticas na fatorização de inteiros, os matemáticos inventaram em 1985 um sistema de encriptação por curvas elípticas, o ECC </span><i><span style="font-family: "Arial", "Helvetica", sans-serif;">(Elliptic Curve Cryptography)</span></i><span style="font-family: "Arial", "Helvetica", sans-serif;"> e, desde então, a sofisticação matemática da criptografia foi elevada a um novo nível.</span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> A segurança dos algoritmos ECC é baseada no problema do logaritmo discreto na teoria das curvas elípticas, o qual é atualmente um problema muito mais difícil da aritmética em corpos finitos. Avanços matemáticos recentes implicam que um certo nível de segurança desejada pode ser atingida com chaves significativamente menores, por exemplo, uma chave ECC de 160 bits fornece o mesmo nível de segurança que uma chave RSA de 1024 bits.</span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span><span style="font-family: "Arial", "Helvetica", sans-serif;"><br />
</span><span style="font-family: "Arial", "Helvetica", sans-serif;"> A teoria das curvas elípticas ilustra a beleza das interligações entre a teoria dos números, a álgebra e a geometria, além de que fornece um poderoso instrumento matemático para reforçar a segurança do comércio eletrónico e das comunicações digitais. O velho e inseguro método de César para cifrar mensagens no alfabeto latino, que corresponde à simples operação aritmética </span><b><span style="font-family: "Arial", "Helvetica", sans-serif;">d = c - 3</span></b><span style="font-family: "Arial", "Helvetica", sans-serif;"> (mod 26), está ultrapassado. Mas ainda nos dá a chave para decifrar o título deste filme:</span></span><br />
<span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span><span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span><br />
<span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;">Os créditos são:</span></span><br />
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: PT; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA;">INITIATIVA<br />
<br />
Centro Internacional de Matemática<br />
Casa da Animação <br />
Mathematisches Forschungsinstitut Oberwolfach<br />
<br />
IDEIA ORIGINAL<br />
<br />
José Francisco Rodrigues<br />
<br />
CONCEPÇÃO<br />
<br />
Victor Fernandes<br />
Stephan Klaus<br />
Armindo Moreira<br />
José Francisco Rodrigues<br />
<br />
REALIZAÇÃO E PRODUÇÃO<br />
<br />
Victor Fernandes<br />
Armindo Moreira<br />
<br />
FILMES DO SURFER<br />
<br />
Andreas Matt<br />
Bianca Violet<br />
<br />
MUSICA ORIGINAL<br />
<br />
Victor Fernandes<br />
Armindo Moreira<br />
<br />
AGRADECIMENTOS<br />
<br />
CMAF/Universidade de Lisboa<br />
Fundação Calouste Gulbenkian<br />
IMAGINARY exhibition<br />
Vila de Óbidos<br />
<br />
PATROCÍNIO<br />
<br />
CIÊNCIA VIVA <br style="mso-special-character: line-break;" /> <span style="mso-ansi-language: PT; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: KN; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: JA; mso-font-kerning: 0pt;"><span style="font-family: "Arial", "Helvetica", sans-serif;"> </span></span></span></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-80875931038919224332010-12-18T21:43:00.000+00:002010-12-18T21:43:49.635+00:00Ainda cá andoPara quem ainda vem por aqui espreitar agradeço e comunico que ainda não desisti, embora tenha estado bastante arredado da fotografia por si mesma. A verdade é que outros projectos se meteram no caminho e com eles vai muito do tempo disponível.<br />
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Abraço a todosObjectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com1tag:blogger.com,1999:blog-59487848369260341.post-78546665316889229202010-12-18T21:25:00.002+00:002010-12-18T23:26:46.087+00:00ainda se usa...<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG4T011Mn3e7h1kSKF0zvv0AQklAd7JBvELSAsvrT3fI02w_Ep4WLnnsVVl5TM5q-oTkiKyCFcSulZvWseK6-7T8VCv77ishiussRpzEnE-WI2byV3epvhUGrUXku_e2lO1PU79eAauA/s1600/IMG_9832.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG4T011Mn3e7h1kSKF0zvv0AQklAd7JBvELSAsvrT3fI02w_Ep4WLnnsVVl5TM5q-oTkiKyCFcSulZvWseK6-7T8VCv77ishiussRpzEnE-WI2byV3epvhUGrUXku_e2lO1PU79eAauA/s320/IMG_9832.JPG" width="320" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG0eDmViud1_2WurwDuuyD-KDBfzKVctMhUz3-BQjRk87eiG64ko4kYoPTo7LFEzGG_BeSl5v4TJOmXdAJ-GJJ4mpHSFphFCkqRhnDKlG84aArEZZEy13aqWRIVhSJJpRo75ch06gYyQ/s1600/IMG_9779.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG0eDmViud1_2WurwDuuyD-KDBfzKVctMhUz3-BQjRk87eiG64ko4kYoPTo7LFEzGG_BeSl5v4TJOmXdAJ-GJJ4mpHSFphFCkqRhnDKlG84aArEZZEy13aqWRIVhSJJpRo75ch06gYyQ/s320/IMG_9779.JPG" width="320" /></a></div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-ehgQLi03QjIcxTCgIrprak4t7ngiiuL67bkzrmy9TqUGtO-shqZMUbglQdt5vjxeGHVbLRiIQPAnTICLZAOkiJYKaf0HMuX_96LRwOu2TjfAou305SfmvaIavoMgv7tbiRRRLybkvQ/s1600/IMG_9922.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-ehgQLi03QjIcxTCgIrprak4t7ngiiuL67bkzrmy9TqUGtO-shqZMUbglQdt5vjxeGHVbLRiIQPAnTICLZAOkiJYKaf0HMuX_96LRwOu2TjfAou305SfmvaIavoMgv7tbiRRRLybkvQ/s320/IMG_9922.JPG" width="320" /></a><br />
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Afurada - os homens estão no café porque hoje não se pesca ou porque assim é que é....Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-20887687703824274952010-08-20T13:11:00.000+00:002010-08-20T13:11:29.461+00:00Harry Potter e a fada "Boa"<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWtsT1dt9dsanlzHBGTChtIJyDMvVcVrhUrjMkLnBBaXxWAGIIuxd4rrGahP9TNfTbZFsm7OR4LD3Iv2PIuPPmFLvszOM2LP6YEEcZNVxywAZQLG_4lAmAZPuhyphenhyphenSy1hjkPKRcSxICyow/s1600/N168-20.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWtsT1dt9dsanlzHBGTChtIJyDMvVcVrhUrjMkLnBBaXxWAGIIuxd4rrGahP9TNfTbZFsm7OR4LD3Iv2PIuPPmFLvszOM2LP6YEEcZNVxywAZQLG_4lAmAZPuhyphenhyphenSy1hjkPKRcSxICyow/s320/N168-20.jpg" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-47478434915161612752010-08-19T22:00:00.002+00:002010-08-19T22:00:42.552+00:00Útero<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxtYi_-EJnwvF-fFj8J0nARlmMkatKUPzfqBaP7U5TzpU7VpqCyKzoScnz99PF0RBuucRqlTXkhLyxyGNQo2_BNLvAGXaejU9UGB1LQ-4ux4jTXWsAnT_PEcrrgjCsrSNwawXrfhvGKA/s1600/IMG_9083.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxtYi_-EJnwvF-fFj8J0nARlmMkatKUPzfqBaP7U5TzpU7VpqCyKzoScnz99PF0RBuucRqlTXkhLyxyGNQo2_BNLvAGXaejU9UGB1LQ-4ux4jTXWsAnT_PEcrrgjCsrSNwawXrfhvGKA/s320/IMG_9083.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-72107220369448537502010-08-19T21:59:00.000+00:002010-08-19T21:59:54.372+00:00(des)proporção<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_fJzCUxz5IuWarQZNJqtr6B-gSAnnfkgWBKWaP-mwprInhzNko3Qp3v8YuuAGWMFRjS7WuN8oWxnbaOiHTKmMKejTT_QW8vs95xtXkQmDGUbzyVGq2bMl_GrPeAvv0HUHfbop1AcbUw/s1600/N156_19.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_fJzCUxz5IuWarQZNJqtr6B-gSAnnfkgWBKWaP-mwprInhzNko3Qp3v8YuuAGWMFRjS7WuN8oWxnbaOiHTKmMKejTT_QW8vs95xtXkQmDGUbzyVGq2bMl_GrPeAvv0HUHfbop1AcbUw/s320/N156_19.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-61721567014864233602010-08-05T12:59:00.000+00:002010-08-05T12:59:15.654+00:00...!<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm8tZQy9pQmKYcdLU0pdxZE3guKC9M4dm8yt1AF47HGvzxKmbkpUTyNZlZmv-OLQ81v7-5A6nPYgyQ2he81nIcHjykBeMBk-MOsEDNNuL1K3MN_eu9SFAHCLxYlvnUEu4DiAus7UP8wA/s1600/N168_33.jpg" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" bx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm8tZQy9pQmKYcdLU0pdxZE3guKC9M4dm8yt1AF47HGvzxKmbkpUTyNZlZmv-OLQ81v7-5A6nPYgyQ2he81nIcHjykBeMBk-MOsEDNNuL1K3MN_eu9SFAHCLxYlvnUEu4DiAus7UP8wA/s320/N168_33.jpg" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com4tag:blogger.com,1999:blog-59487848369260341.post-12473539118999148052010-07-23T23:26:00.000+00:002010-07-23T23:26:06.494+00:00A torre<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLEDcMvzJ-PSSOlrvdbAYZ68hY-TkCvTuZHWdDQ_coidUNkHtmPidaEsGVYCL2AAqUyvv1x3s0bqwz9l1BzieB0efamhe2LazvbRwMmRx55e6qXCox2fGrUxZFvbmlmgYzPl6H2RdKVQ/s1600/Picture+058a.jpg" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" hw="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLEDcMvzJ-PSSOlrvdbAYZ68hY-TkCvTuZHWdDQ_coidUNkHtmPidaEsGVYCL2AAqUyvv1x3s0bqwz9l1BzieB0efamhe2LazvbRwMmRx55e6qXCox2fGrUxZFvbmlmgYzPl6H2RdKVQ/s320/Picture+058a.jpg" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com2tag:blogger.com,1999:blog-59487848369260341.post-74132940556724107852010-07-06T22:19:00.000+00:002010-07-06T22:19:15.780+00:00...<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0X4DKvtFjbqqNM2vxl9ViRN0zgS2sX_7DvjeaCxkNgccw84eZrGwaw2GoY7RRfk5jmghRM2_zTZAoJIozzFvL139XQ8HIYbEJ9GpmzNZWVhkQ4CtBRSB1l1JvklkZfLaN1lfZxF8ptQ/s1600/N168_24.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0X4DKvtFjbqqNM2vxl9ViRN0zgS2sX_7DvjeaCxkNgccw84eZrGwaw2GoY7RRfk5jmghRM2_zTZAoJIozzFvL139XQ8HIYbEJ9GpmzNZWVhkQ4CtBRSB1l1JvklkZfLaN1lfZxF8ptQ/s320/N168_24.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com2tag:blogger.com,1999:blog-59487848369260341.post-82808362501015414772010-06-28T01:46:00.000+00:002010-06-28T01:46:55.776+00:00estendal - Afurada<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfhCNbKZVRcjgtpH4bpWqFGnGLxjSDDpQ44LStteBIvxBpCy3FCkyloFRK5Kjco97e5_MyR1wt3R7sRaA_br9vHkSxDHBxMfB7q7dPDDhKZ2rcwWLL9AMbEeCdG3vkv_GLTPUkoE3Ng/s1600/N167_20.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfhCNbKZVRcjgtpH4bpWqFGnGLxjSDDpQ44LStteBIvxBpCy3FCkyloFRK5Kjco97e5_MyR1wt3R7sRaA_br9vHkSxDHBxMfB7q7dPDDhKZ2rcwWLL9AMbEeCdG3vkv_GLTPUkoE3Ng/s320/N167_20.JPG" /></a></div><br />
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ÓbidosObjectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com4tag:blogger.com,1999:blog-59487848369260341.post-69721337368961587172010-05-03T17:05:00.000+00:002010-05-03T17:05:04.135+00:00morfismos<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSIhYAsat7SFd9TYAMbgg_2hagBnUL0GBfr1T7pz66dJdJmu6oOWLWpcyPPY5_zFxOgOjV85oTPUd-35ofERPXZ-kG8SOfgzsv97ttDM6WT6R5sp1AOqQ6gHr3U2Bxjgq_6GtQ0O_xA/s1600/N159_22.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSIhYAsat7SFd9TYAMbgg_2hagBnUL0GBfr1T7pz66dJdJmu6oOWLWpcyPPY5_zFxOgOjV85oTPUd-35ofERPXZ-kG8SOfgzsv97ttDM6WT6R5sp1AOqQ6gHr3U2Bxjgq_6GtQ0O_xA/s320/N159_22.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-4008651920113309472010-04-28T22:47:00.001+00:002010-04-28T22:48:19.259+00:00Pontas soltas II<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrnP3JVLO-5ZSOsKBOHwxYQb6TCOKCss58RS31lqUdXhLZI3-Ka8AeZO7JfDpNDsKgxOE3wB7_ciu90scpi5pxUEtkL8oT55NLaYCmrddlMkn8YXj7JY7LMalDoOpo1wFMDVduiPCYbw/s1600/N159_25.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrnP3JVLO-5ZSOsKBOHwxYQb6TCOKCss58RS31lqUdXhLZI3-Ka8AeZO7JfDpNDsKgxOE3wB7_ciu90scpi5pxUEtkL8oT55NLaYCmrddlMkn8YXj7JY7LMalDoOpo1wFMDVduiPCYbw/s320/N159_25.JPG" /></a></div><br />
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</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTx6IIjz_XLkeQNfYTP68yTyuzizci2Y0nNVy92-5nZ_Ho_cxEz-rHKnvTO_QEcR2sVTn4peGEjZi62Er2_ngiKn36fmUG2kVdGoMTWMIRV9i9SgUoB6h3ihMMEC2ANlYyBQbpG3zVFw/s1600/N159_24.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTx6IIjz_XLkeQNfYTP68yTyuzizci2Y0nNVy92-5nZ_Ho_cxEz-rHKnvTO_QEcR2sVTn4peGEjZi62Er2_ngiKn36fmUG2kVdGoMTWMIRV9i9SgUoB6h3ihMMEC2ANlYyBQbpG3zVFw/s320/N159_24.JPG" /></a> </div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-23427558228966838672010-04-26T16:58:00.000+00:002010-04-26T16:58:03.166+00:00antevisão<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBh1UXIYc9vKSM9RIhwBQCc3xhYo52vXeY1Xko4BMR1PF1UCHXmOJihhSpzHul2wdp9Fv1VK4UKyp_NUyLYRKGkQUG_bHtMTsm3DdAUm67Fk21Yfr6EkNKtuBkZGNMlzR65veToS1CYQ/s1600/IMG_8701.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBh1UXIYc9vKSM9RIhwBQCc3xhYo52vXeY1Xko4BMR1PF1UCHXmOJihhSpzHul2wdp9Fv1VK4UKyp_NUyLYRKGkQUG_bHtMTsm3DdAUm67Fk21Yfr6EkNKtuBkZGNMlzR65veToS1CYQ/s320/IMG_8701.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-44123758383108980692010-04-26T15:13:00.000+00:002010-04-26T15:13:27.293+00:00Enredado...<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgO_b_ZIr10fNcatIG7-gFAdKZMEx7XZEtsypv5arfkwII9i0TAdGpjbxEh904oQm459_ZLorKTqdl6PgS9BHttCxAPwcZ5Ht-iwNuOyLCfytNrsGeJ5gGrKRP0a4qBiqZn9pjzglEAw/s1600/N165_27.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgO_b_ZIr10fNcatIG7-gFAdKZMEx7XZEtsypv5arfkwII9i0TAdGpjbxEh904oQm459_ZLorKTqdl6PgS9BHttCxAPwcZ5Ht-iwNuOyLCfytNrsGeJ5gGrKRP0a4qBiqZn9pjzglEAw/s320/N165_27.JPG" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0l-dFbOkYwsvc_A0OLIfZ7H9me2VCXqNQXg39eQnDsIrH0Jl3-TQscLWltw4orMIvnkfxZV3BAu63fB1qZ4fcjOPiH9Ck4BfXqvjvn3FFLS2YgEeBKbNKiaxw35uvTV4Sn638DOaXkQ/s1600/N165_14.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0l-dFbOkYwsvc_A0OLIfZ7H9me2VCXqNQXg39eQnDsIrH0Jl3-TQscLWltw4orMIvnkfxZV3BAu63fB1qZ4fcjOPiH9Ck4BfXqvjvn3FFLS2YgEeBKbNKiaxw35uvTV4Sn638DOaXkQ/s320/N165_14.JPG" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBoJupqJ2tUk0l1sOAAGPuKPBry_hMM9-puRKOFpyXo_sawmiCmgorbXCzeioupQkKXIB2xOqGV6HPQO-zN5pTCFuDX9w0y0mIJt4vyMsod_iEn8z07hMxQZkqhPkhBSBJX2OL6F8Ymw/s1600/N165_17.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBoJupqJ2tUk0l1sOAAGPuKPBry_hMM9-puRKOFpyXo_sawmiCmgorbXCzeioupQkKXIB2xOqGV6HPQO-zN5pTCFuDX9w0y0mIJt4vyMsod_iEn8z07hMxQZkqhPkhBSBJX2OL6F8Ymw/s320/N165_17.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com1tag:blogger.com,1999:blog-59487848369260341.post-60477803766163255642010-04-26T14:59:00.000+00:002010-04-26T14:59:28.402+00:00Terminais<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX063jib7SpukT4zjzk97HTBgkw_jT5nDddehi4FZURi6AkKIQVGcLpCjCMiOhqv-jpXQr9iKidhGVA7IXwZzY19GqJ-7YgvIylNEWQn20ADpKEvCueCoMlvchyGSnaounHG5_6XCtaQ/s1600/N159_14.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX063jib7SpukT4zjzk97HTBgkw_jT5nDddehi4FZURi6AkKIQVGcLpCjCMiOhqv-jpXQr9iKidhGVA7IXwZzY19GqJ-7YgvIylNEWQn20ADpKEvCueCoMlvchyGSnaounHG5_6XCtaQ/s320/N159_14.JPG" /></a></div><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc5450xjq1dvzVjSR15uwhDI2yXeK2v24YZBCEWB5mPLtBotzoI6eQzMtaQ3Fj_UR646PkKhKWQHWnIvOOEHMbjH4gzn2-leTkYgulpTRFFcQFDhEUM3QqcPI9cafWby9OO7GIueMnsw/s1600/DPP_0008.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc5450xjq1dvzVjSR15uwhDI2yXeK2v24YZBCEWB5mPLtBotzoI6eQzMtaQ3Fj_UR646PkKhKWQHWnIvOOEHMbjH4gzn2-leTkYgulpTRFFcQFDhEUM3QqcPI9cafWby9OO7GIueMnsw/s320/DPP_0008.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com3tag:blogger.com,1999:blog-59487848369260341.post-49104429741629922592010-04-22T03:05:00.000+00:002010-04-22T03:05:51.263+00:00Fora de moda<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidc9aTR-AZWYPomWeHQEqlEYuA8HPBF_Dd9JFr3I2R-UG0kXLmVfOJRcFS0jIMuPCxuFzOyHF0Xi3m_PsUPd3L0M5saJG6LXk4m4V1QSRWgGj0f47FOB2HPiExM4r-aYcwyLXBklTz8g/s1600/N163_07.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidc9aTR-AZWYPomWeHQEqlEYuA8HPBF_Dd9JFr3I2R-UG0kXLmVfOJRcFS0jIMuPCxuFzOyHF0Xi3m_PsUPd3L0M5saJG6LXk4m4V1QSRWgGj0f47FOB2HPiExM4r-aYcwyLXBklTz8g/s320/N163_07.JPG" /></a></div>Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com0tag:blogger.com,1999:blog-59487848369260341.post-39182796677210165472010-04-22T00:09:00.001+00:002010-04-22T00:10:38.542+00:00a figura humana como referência de escala..<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ecfXdSlWyviVc_Y7YDNu_gamr3Ik1_4r7DkpF8tqMbyWcpq4xb4eNSK2ng4milL_XCsm27qQj7UOmrtJcQPs1yvp4OjjKGCw4tFT8tDXRabHEVV26CA3Cv53GOxLBpLsi5a2ASFcQg/s1600/N163_23.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-ecfXdSlWyviVc_Y7YDNu_gamr3Ik1_4r7DkpF8tqMbyWcpq4xb4eNSK2ng4milL_XCsm27qQj7UOmrtJcQPs1yvp4OjjKGCw4tFT8tDXRabHEVV26CA3Cv53GOxLBpLsi5a2ASFcQg/s320/N163_23.JPG" /></a></div><br />
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Ponte Sarmento Rodrigues, Barca D´Alva<br />
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A iluminação da dita gasta mais energia que toda a vila junta. Para além do absurdo estético eis um exemplo de "boa" gestão de recursos da autarquia.Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com2tag:blogger.com,1999:blog-59487848369260341.post-57632089871344389202010-04-13T14:26:00.001+00:002010-04-13T14:30:20.555+00:00Talhado na rocha<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie6UJpX6E9oht7Ai_HiW0qxJDqr2sPI5F-KjdekA8ctE5ggpfwiYVUW5f2V3yU6lGgcWIArK_qO6IH1TrbJl1UGGJ3lvm8G11caWXIdQ9YV6F7RKejzZvA_NLJSl1sWCgLnCvTVBnxFA/s1600/N160_25.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie6UJpX6E9oht7Ai_HiW0qxJDqr2sPI5F-KjdekA8ctE5ggpfwiYVUW5f2V3yU6lGgcWIArK_qO6IH1TrbJl1UGGJ3lvm8G11caWXIdQ9YV6F7RKejzZvA_NLJSl1sWCgLnCvTVBnxFA/s320/N160_25.JPG" /></a></div><br />
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«Desfiladeiro do diabo»Objectiva.Mentehttp://www.blogger.com/profile/15517408883519907901noreply@blogger.com2tag:blogger.com,1999:blog-59487848369260341.post-75447072023308012772010-04-13T14:07:00.002+00:002010-04-13T14:13:31.531+00:00desconstrucção<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh32s5njCb6c7mSUKwmXgzIxVEugqrnngClOEuMMJsImMjpjHRVdQpvuM1pDZLQE4pfeW26TJs7IiBgE61vNNpBP_z0-0Yyk7qS8JxcmJ16tycRlmyf9IeD8NKzhyphenhyphenFBpwufaFv4NsoOYg/s1600/N160_20.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh32s5njCb6c7mSUKwmXgzIxVEugqrnngClOEuMMJsImMjpjHRVdQpvuM1pDZLQE4pfeW26TJs7IiBgE61vNNpBP_z0-0Yyk7qS8JxcmJ16tycRlmyf9IeD8NKzhyphenhyphenFBpwufaFv4NsoOYg/s320/N160_20.JPG" /></a></div><br />
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