{"id":7011,"date":"2015-12-03T19:00:02","date_gmt":"2015-12-03T21:00:02","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=7011"},"modified":"2015-12-03T19:00:02","modified_gmt":"2015-12-03T21:00:02","slug":"a-cela-da-abelha","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2015\/12\/a-cela-da-abelha\/","title":{"rendered":"A cela da abelha"},"content":{"rendered":"<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone\" src=\"http:\/\/cerapura.com.br\/wp-content\/uploads\/2014\/05\/bigstock-Macro-of-working-bee-on-honey-25963553-900x444.jpg\" alt=\"\" width=\"900\" height=\"444\" \/><\/p>\n<p style=\"padding-left: 30px\" align=\"justify\"><span style=\"font-family: Georgia\">Quando contemplamos a Abelha a construir sua cela para armazenar seu estoque de inverno, construindo-a de forma que seja a mais resistente e conveniente, deve ser evidente a qualquer um que tenha dado o m\u00ednimo de aten\u00e7\u00e3o \u00e0s diferentes propriedades das figuras o seguinte: que h\u00e1 apenas tr\u00eas que admitem a justaposi\u00e7\u00e3o de seus lados sem qualquer espa\u00e7o vacante entre eles, sendo todas as figuras iguais e similares. A saber, o quadrado, o tri\u00e2ngulo equil\u00e1tero e o hex\u00e1gono. Este \u00faltimo \u00e9 o mais resistente e mais conveniente. Assim, \u00e9 em sua forma que percebemos que as celas [das abelhas] s\u00e3o constru\u00eddas. Isso \u00e9 um fato maravilhoso! Igualmente not\u00e1vel \u00e9 que o ponto central de cada cela, de um lado, est\u00e1 diretamente oposto pelo ponto de encontro de tr\u00eas parti\u00e7\u00f5es do lado oposto. Por essa posi\u00e7\u00e3o a cela recebe um refor\u00e7o adicional. Isso n\u00e3o \u00e9 tudo. Se a engenhosidade humana tivesse que conceber uma cela que demandasse o menor gasto de material e trabalho, haveria a quest\u00e3o, n\u00e3o facilmente sol\u00favel: qual o \u00e2ngulo preciso em que os tr\u00eas planos que comp\u00f5em o fundo devem se encontrar? <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Colin_Maclaurin\">[Colin] Maclaurin [1698-1746]<\/a>, o c\u00e9lebre matem\u00e1tico, atrav\u00e9s de um c\u00e1lculo fluxion\u00e1rio [<em>sic; i.e, c\u00e1lculo integral<\/em>] determinou precisamente o \u00e2ngulo necess\u00e1rio. E descobriu, pela mais exata mensura\u00e7\u00e3o requerida pelo assunto, que \u00e9 o mesmo \u00e2ngulo com o qual se encontram exatamente os tr\u00eas planos do fundo de uma c\u00e9lula de um favo de mel. <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Ren%C3%A9-Antoine_Ferchault_de_R%C3%A9aumur\">R\u00e9amur [1683-1757]<\/a>, por sua vez, supondo que os \u00e2ngulos tivessem sido adotados com o prop\u00f3sito de economizar material, prop\u00f4s a <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Johann_Samuel_K%C3%B6nig\">[Johann Samuel] K\u00f6nig [1712-1757]<\/a>, o matem\u00e1tico, que determinasse quais seriam os \u00e2ngulos de uma cela hexagonal, de base piramidal, que demandariam menos material. Atrav\u00e9s do c\u00e1lculo infinitesimal, ele assegurou que o maior \u00e2ngulo seria de 109\u00ba 26&#8242; e o menor de 70\u00ba 34&#8242;, os mesm\u00edssimos \u00e2ngulos adotados pelas abelhas. Que incr\u00edvel coincid\u00eancia! Foi preciso um profundo matem\u00e1tico para resolver um problema bastante dif\u00edcil. E ele descobriu que sua conclus\u00e3o \u2014 encontrada \u00e0s custas de consider\u00e1vel engenhosidade e pensamento profundo \u2014 era praticamente a mesma exibida nas opera\u00e7\u00f5es das abelhas.<\/span><\/p>\n<p style=\"padding-left: 30px\" align=\"justify\"><span style=\"font-family: Georgia\">Os h\u00e1bitos das abelhas s\u00e3o extremamente dif\u00edceis de serem revelados, gra\u00e7as \u00e0 sua invari\u00e1vel determina\u00e7\u00e3o de trabalhar no escuro. Fil\u00f3sofos de todas as \u00e9pocas devotaram muito tempo ao assunto: de Arist\u00f4maco, de Soli, na Cil\u00edcia \u2014 que, segundo Pl\u00ednio, por 58 anos estudou apenas as abelhas; passando por Fil\u00edsco, o Tr\u00e1cio \u2014 que passou a vida nas florestas, investigando os h\u00e1bitos das abelhas \u2014, at\u00e9 Swammerdam, R\u00e9amur, Hunter e Huber, nos tempos modernos. A constru\u00e7\u00e3o de uma colmeia continua a ser um milagre que sobrepuja nossas faculdades.<\/span><\/p>\n<p style=\"padding-left: 30px\" align=\"justify\"><span style=\"font-family: Georgia\">\u2014 TIMBS, John., <em><strong>Things not Generally Known, Familiarly Explained<\/strong>. A book for old and young<\/em> [<em><strong>Coisas pouco conhecidas ordinariamente, com explica\u00e7\u00f5es familiares<\/strong>. Um livro para jovens e velhos<\/em>] 11a. edi\u00e7\u00e3o. Londres: Lockwood &amp; Co., 1867.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quando contemplamos a Abelha a construir sua cela para armazenar seu estoque de inverno, construindo-a de forma que seja a mais resistente e conveniente, deve ser evidente a qualquer um que tenha dado o m\u00ednimo de aten\u00e7\u00e3o \u00e0s diferentes propriedades das figuras o seguinte: que h\u00e1 apenas tr\u00eas que admitem a justaposi\u00e7\u00e3o de seus lados [&hellip;]<\/p>\n","protected":false},"author":486,"featured_media":7875,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[17,34,53,78,79,151,160,279,333],"tags":[],"class_list":["post-7011","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-animais","category-biologia","category-ciencia","category-cultura","category-curiosidades","category-geometria","category-historia","category-quotes","category-zoologia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A cela da abelha - 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