{"id":189,"date":"2018-04-29T17:56:25","date_gmt":"2018-04-29T15:56:25","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=189"},"modified":"2018-05-29T19:24:57","modified_gmt":"2018-05-29T17:24:57","slug":"abeilles-avaient-raison-logarithmes-tort","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/04\/29\/abeilles-avaient-raison-logarithmes-tort\/","title":{"rendered":"Les abeilles avaient raison et les logarithmes, tort !"},"content":{"rendered":"<p><span style=\"color: #000000;font-family: Times New Roman\">Les abeilles seraient-elles math\u00e9maticiennes\u00a0? Sans doute non mais elles sont \u00e9tonnantes. Le g\u00e2teau de cire qu\u2019elles construisent pour y d\u00e9poser leur miel est form\u00e9 par deux couches d\u2019alv\u00e9oles oppos\u00e9es par leur fond. D\u00e8s l\u2019antiquit\u00e9, on avait remarqu\u00e9 que les alv\u00e9oles ressemblaient \u00e0 des prismes droits \u00e0 base hexagonale r\u00e9guli\u00e8re. Ce n\u2019est qu\u2019au XVIII<sup><span style=\"font-size: small\">e<\/span><\/sup> si\u00e8cle que l\u2019on remarqua que le fond \u00e9tait l\u2019assemblage de trois losanges identiques appartenant chacun \u00e0 deux alv\u00e9oles oppos\u00e9es.<\/span><\/p>\n<figure id=\"attachment_190\" aria-describedby=\"caption-attachment-190\" style=\"width: 229px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-190 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Abeilles-01-229x300.jpg\" alt=\"\" width=\"229\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Abeilles-01-229x300.jpg 229w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Abeilles-01.jpg 244w\" sizes=\"auto, (max-width: 229px) 100vw, 229px\" \/><figcaption id=\"caption-attachment-190\" class=\"wp-caption-text\">Les alv\u00e9oles des abeilles sont des prismes de base hexagonale termin\u00e9s par trois losanges inclin\u00e9s, un peu comme un crayon taill\u00e9.<\/figcaption><\/figure>\n<h2>Une mesure, une hypoth\u00e8se &#8230;<\/h2>\n<p><span style=\"margin: 0px;font-family: 'Times New Roman',serif;font-size: 12pt\"><span style=\"color: #000000\">En 1712, Giacomo Filippo<b> <\/b>Maraldi (1665\u00a0\u2013\u00a01729), un astronome de l\u2019observatoire de Paris, mesura l\u2019angle des losanges et trouva\u00a0: 109 degr\u00e9s et 28 minutes. En 1739, Ren\u00e9-Antoine R\u00e9aumur (\u00a01683\u00a0\u2013\u00a01757) soup\u00e7onna les abeilles de construire le fond de fa\u00e7on \u00e0 utiliser le minimum de cire possible. <\/span><\/span><\/p>\n<h2>Et un calcul<\/h2>\n<figure id=\"attachment_191\" aria-describedby=\"caption-attachment-191\" style=\"width: 232px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-191 size-medium\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Konig_Samuel-232x300.jpg\" alt=\"\" width=\"232\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Konig_Samuel-232x300.jpg 232w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/04\/Konig_Samuel.jpg 309w\" sizes=\"auto, (max-width: 232px) 100vw, 232px\" \/><figcaption id=\"caption-attachment-191\" class=\"wp-caption-text\">Samuel K\u00f6nig<\/figcaption><\/figure>\n<p><span style=\"margin: 0px;font-family: 'Times New Roman',serif;font-size: 12pt\"><span style=\"color: #000000\">Sans lui donner l\u2019origine de son probl\u00e8me, il demanda de le r\u00e9soudre \u00e0 Samuel K\u00f6nig (1712\u00a0\u2013\u00a01757), le math\u00e9maticien allemand connu pour avoir enseign\u00e9 les math\u00e9matiques \u00e0 la marquise \u00c9milie du Ch\u00e2telet (1706\u00a0\u2013\u00a01749), traductrice de Newton en fran\u00e7ais. K\u00f6nig traita le probl\u00e8me par le calcul diff\u00e9rentiel et, en utilisant une table de logarithmes, il en d\u00e9duisit la valeur de 109 degr\u00e9s et 26 minutes. L\u2019erreur des abeilles \u00e9tait n\u00e9gligeable. On s\u2019\u00e9merveilla de cette pr\u00e9cision.<\/span><\/span><\/p>\n<h2>Un naufrage<\/h2>\n<p><span style=\"color: #000000;font-family: Times New Roman\">\u00c0 l\u2019\u00e9poque, les marins utilisaient la m\u00eame table que K\u00f6nig pour leurs calculs. Malheureusement, il fallut un naufrage quelques ann\u00e9es plus tard pour que l\u2019on y d\u00e9couvre quelques erreurs. En 1743, Colin Mac Laurin (1698\u00a0\u2013\u00a01746) corrigea la valeur trouv\u00e9e par K\u00f6nig\u00a0: il s\u2019agissait bien de 109 degr\u00e9s et 28 minutes. La table de logarithmes avait tort et les abeilles, raison\u00a0!<\/span><\/p>\n<p>&nbsp;<\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Les abeilles seraient-elles math\u00e9maticiennes\u00a0? Sans doute non mais elles sont \u00e9tonnantes. Le g\u00e2teau de cire qu\u2019elles construisent pour y d\u00e9poser leur miel est form\u00e9 par deux couches d\u2019alv\u00e9oles oppos\u00e9es par leur fond. D\u00e8s l\u2019antiquit\u00e9, on avait remarqu\u00e9 que les alv\u00e9oles ressemblaient \u00e0 des prismes droits \u00e0 base hexagonale r\u00e9guli\u00e8re. Ce n\u2019est qu\u2019au XVIIIe si\u00e8cle que &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/04\/29\/abeilles-avaient-raison-logarithmes-tort\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Les abeilles avaient raison et les logarithmes, tort !<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":12,"featured_media":193,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[67,29],"tags":[90,92,91,40,93,94],"class_list":["post-189","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ecologie","category-maths-2","tag-abeilles","tag-konig","tag-logarithmes","tag-mathematiques","tag-reaumur","tag-ruche"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Les abeilles avaient raison et les logarithmes, tort !, par Herv\u00e9 Lehning<\/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:\/\/blogs.futura-sciences.com\/lehning\/2018\/04\/29\/abeilles-avaient-raison-logarithmes-tort\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les abeilles avaient raison et les logarithmes, tort !, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Les abeilles seraient-elles math\u00e9maticiennes\u00a0? 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