{"id":2855,"date":"2012-07-04T16:00:03","date_gmt":"2012-07-04T19:00:03","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=2855"},"modified":"2012-07-04T16:00:03","modified_gmt":"2012-07-04T19:00:03","slug":"mesa-professor-universitrio","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/07\/mesa-professor-universitrio\/","title":{"rendered":"A mesa do professor universit\u00e1rio"},"content":{"rendered":"

\"\"<\/p>\n

A seguir, a resposta do Prof. Konhauser para o problema da escrivaninha atulhada de artigos n\u00e3o-lidos<\/span> papel. Se voc\u00ea ainda n\u00e3o leu o enigma, leia-o<\/a> antes de prosseguir.<\/p>\n

\n

Imagine que a escrivaninha tenha sido pintada pouco antes de colocarmos os papeis sobre ela. Assim, algumas folhas v\u00e3o pegar alguma tinta quando forem colocadas sobre a mesa. Mais precisamente, cada folha de papel ter\u00e1 uma mancha de tinta de qualquer parte da mesa que ela cobre e que n\u00e3o \u00e9 coberta por qualquer outra folha que esteja embaixo dela. Uma vez que a escrivaninha \u00e9 completamente coberta pelos papeis, a \u00e1rea total da tinta em todos as folhas \u00e9 exatamente igual \u00e0 \u00e1rea da mesa. Se removermos as cinco folhas com menos tinta, ent\u00e3o claramente a \u00e1rea total das folhas restantes \u00e9 de pelo menos dois ter\u00e7os da \u00e1rea da mesa. Portanto, pelo menos dois ter\u00e7os da escrivaninha s\u00e3o cobertos pelas folhas que sobram.<\/span><\/p>\n<\/blockquote>\n

Como se v\u00ea, a resposta era mais simples do que parecia. Apenas quatro comentaristas se arriscaram. N\u00e3o precisavam ter quebrado a cabe\u00e7a com equa\u00e7\u00f5es \u2014 como fez, de novo, o Takata<\/a>. Bastava um racioc\u00ednio anal\u00f3gico \u2014 como o do Vin\u00edcius Makoto Mori \u2014 para se destacar:<\/p>\n

\n

Para mostrar que \u00e9 poss\u00edvel, basta demonstrar um \u00fanico caso. A estrat\u00e9gia \u00e9 retirar as 5 menores folhas e configurar um cen\u00e1rio extremo, o caso em que as 5 menores folhas assumem a maior \u00e1rea e \u00e9 obtido quando todas as folhas tem tamanho uniforme e n\u00e3o h\u00e1 margem alguma ou nenhuma sobreposi\u00e7\u00e3o. O resultado da extra\u00e7\u00e3o das 5 folhas \u00e9 imediato 2\/3 da superf\u00edcie. A partir deste cen\u00e1rio, os outros s\u00e3o facilmente configur\u00e1veis atrav\u00e9s de uma composi\u00e7\u00e3o de sobreposi\u00e7\u00e3o e deixando partes pairando \u00e0 beira da mesa. Mesmo no caso de uma \u00fanica folha do tamanho da escrivaninha ou maior e as outras folhas tendendo \u00e0 superf\u00edcie 0, h\u00e1 uma configura\u00e7\u00e3o poss\u00edvel.<\/span><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"

A seguir, a resposta do Prof. Konhauser para o problema da escrivaninha atulhada de artigos n\u00e3o-lidos papel. Se voc\u00ea ainda n\u00e3o leu o enigma, leia-o antes de prosseguir.<\/p>\n","protected":false},"author":486,"featured_media":3093,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[152],"tags":[],"class_list":["post-2855","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geral"],"yoast_head":"\nA mesa do professor universit\u00e1rio - hypercubic<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/07\/mesa-professor-universitrio\/\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Renato Pincelli\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/07\\\/mesa-professor-universitrio\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/07\\\/mesa-professor-universitrio\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\"A mesa do professor 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