{"id":208,"date":"2018-06-08T11:09:22","date_gmt":"2018-06-08T09:09:22","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=208"},"modified":"2018-06-16T11:09:17","modified_gmt":"2018-06-16T09:09:17","slug":"chiliogone-de-descartes","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/06\/08\/chiliogone-de-descartes\/","title":{"rendered":"Le chiliogone de Descartes"},"content":{"rendered":"

Dans ses M\u00e9ditations m\u00e9taphysiques<\/em>, Ren\u00e9 Descartes utilise l’exemple des chiliogones, c’est-\u00e0-dire des polygones \u00e0 1000 c\u00f4t\u00e9s, pour montrer qu’il existe des choses faciles \u00e0 concevoir sans pour autant qu’il soit possible de les repr\u00e9senter. Essayons de le faire dans le cas du chiliogone r\u00e9gulier convexe !<\/p>\n

Les polygones r\u00e9guliers convexes<\/h2>\n

Si nous nous limitons aux polygones r\u00e9guliers convexes, les premiers sont le triangle \u00e9quilat\u00e9ral, le carr\u00e9, le pentagone r\u00e9gulier convexe et l’hexagone r\u00e9gulier convexe.<\/p>\n

\"\"
Les polygones convexes r\u00e9guliers de 3, 4, 5 et 6 c\u00f4t\u00e9s.<\/figcaption><\/figure>\n

Le chiliogone r\u00e9gulier convexe<\/h2>\n

\u00c0 partir de l\u00e0, il est facile d’imaginer le chiliogone r\u00e9gulier convexe : en pratique, il est indiscernable du cercle.<\/span><\/p>\n

\"\"
Le chiliogone r\u00e9gulier convexe est indiscernable du cercle<\/figcaption><\/figure>\n

Si on supprime la condition de r\u00e9gularit\u00e9 et si les longueurs des c\u00f4t\u00e9s restent de m\u00eame ordre de grandeur, on obtient une courbe ferm\u00e9e convexe. Si la condition de convexit\u00e9 est supprim\u00e9e et\u00a0les longueurs des c\u00f4t\u00e9s restent de m\u00eame ordre de grandeur, on obtient une courbe ferm\u00e9e … qui peut ressembler \u00e0 un inf\u00e2me gribouillis.<\/p>\n

\"\"
Un polygone \u00e0 20 c\u00f4t\u00e9s peut d\u00e9j\u00e0 \u00eatre tr\u00e8s embrouill\u00e9, \u00e0 1000 c\u00f4t\u00e9s il peut devenir un inf\u00e2me gribouillis<\/figcaption><\/figure>\n

<\/h2>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Dans ses M\u00e9ditations m\u00e9taphysiques, Ren\u00e9 Descartes utilise l’exemple des chiliogones, c’est-\u00e0-dire des polygones \u00e0 1000 c\u00f4t\u00e9s, pour montrer qu’il existe des choses faciles \u00e0 concevoir sans pour autant qu’il soit possible de les repr\u00e9senter. Essayons de le faire dans le cas du chiliogone r\u00e9gulier convexe ! Les polygones r\u00e9guliers convexes Si nous nous limitons aux … Continuer la lecture de Le chiliogone de Descartes<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":217,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[63,104,15],"tags":[103,101,99,102,96,100],"class_list":["post-208","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-histoire","category-philosophie","category-reflexions","tag-brownien","tag-chiliogone","tag-descartes","tag-metaphysique","tag-philosophie","tag-rene-descartes"],"yoast_head":"\nLe chiliogone de Descartes, 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\/06\/08\/chiliogone-de-descartes\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le chiliogone de Descartes, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Dans ses M\u00e9ditations m\u00e9taphysiques, Ren\u00e9 Descartes utilise l’exemple des chiliogones, c’est-\u00e0-dire des polygones \u00e0 1000 c\u00f4t\u00e9s, pour montrer qu’il existe des choses faciles \u00e0 concevoir sans pour autant qu’il soit possible de les repr\u00e9senter. 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