{"id":6393,"date":"2021-08-11T14:19:01","date_gmt":"2021-08-11T12:19:01","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=6393"},"modified":"2021-10-26T16:03:57","modified_gmt":"2021-10-26T14:03:57","slug":"crible-deratosthene-animation-avec-python-et-manim","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2021\/08\/11\/crible-deratosthene-animation-avec-python-et-manim\/","title":{"rendered":"Crible d\u2019\u00c9ratosth\u00e8ne: animation avec Python et manim"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Nous allons nous pencher dans cet article sur le crible d\u2019\u00c9ratosth\u00e8ne, et plus particuli\u00e8rement la fa\u00e7on dont on peut cr\u00e9er une animation avec Python et manim.<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_89 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/08\/11\/crible-deratosthene-animation-avec-python-et-manim\/#La_video\" >La vid\u00e9o<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/08\/11\/crible-deratosthene-animation-avec-python-et-manim\/#Crible_dEratosthene_animation_avec_Python_et_manim_le_code_source\" >Crible d\u2019\u00c9ratosth\u00e8ne, animation avec Python et manim: le code source<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/08\/11\/crible-deratosthene-animation-avec-python-et-manim\/#Cest_quoi_le_crible_dEratosthene\" >C&rsquo;est quoi le crible d\u2019\u00c9ratosth\u00e8ne ?<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"La_video\"><\/span>La vid\u00e9o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">D&rsquo;abord, voici la vid\u00e9o obtenue:<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" controls src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/Crible.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Elle vous pla\u00eet ? Ok, on peut continuer&#8230; Notez que la musique, c&rsquo;est cadeau, c&rsquo;est pour moi! Parce que l&rsquo;extension <em>manim<\/em>, elle n&rsquo;ajoute pas la musique hein?!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-1024x576.png\" alt=\"animation crible \u00c9ratosth\u00e8ne python manim\" class=\"wp-image-6396\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-1024x576.png 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-300x169.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-600x338.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-768x432.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre-1536x864.png 1536w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/cribre.png 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Crible_dEratosthene_animation_avec_Python_et_manim_le_code_source\"><\/span>Crible d\u2019\u00c9ratosth\u00e8ne, animation avec Python et manim: le code source<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Je vous avez parl\u00e9 du crible dans <a href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/24\/le-crible-deratosthene-en-python\/\" target=\"_blank\" rel=\"noreferrer noopener\">cet article<\/a>, donc je ne vais pas revenir dessus. Je vais juste donner le code source utilisant <em>manim<\/em>.<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter um_article\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/eratosthene.py\">eratosthene<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/08\/eratosthene.py\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Le code est assez bien comment\u00e9 pour que chacun\u00b7e puisse comprendre \u00e0 quoi correspondent les diff\u00e9rentes partie.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cest_quoi_le_crible_dEratosthene\"><\/span>C&rsquo;est quoi le crible d\u2019\u00c9ratosth\u00e8ne ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Le principe est simple: on souhaite obtenir la liste de tous les nombres premiers de 2 \u00e0 100 (par exemple).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Un <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Nombre_premier\" target=\"_blank\" rel=\"noreferrer noopener\">nombre premier<\/a> \u00e9tant un nombre divisible uniquement par 1 lui-m\u00eame, il suffit de supprimer tous les nombres entiers qui poss\u00e8dent un diviseur.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>On commence donc par dresser la liste de tous les nombres entiers de 2 \u00e0 100 (on ne commence pas par \u00ab\u00a01\u00a0\u00bb car ce dernier n&rsquo;est pas un nombre premier, contrairement \u00e0 \u00ab\u00a02\u00a0\u00bb);<\/li><li>disposons maintenant les nombre dans une grille carr\u00e9e (pour plus de lisibilit\u00e9);<\/li><li>s\u00e9lectionnons le premier nombre disponible (ici, \u00ab\u00a02\u00a0\u00bb), et on supprime tous les autres nombres de la grille qui sont divisibles par \u00ab\u00a02\u00a0\u00bb (car, s&rsquo;ils sont divisibles par 2, par d\u00e9finition, ils ne sont pas premiers);<\/li><li>le nombre entier suivant qui n&rsquo;est pas supprim\u00e9 est \u00ab\u00a03\u00a0\u00bb, puis on supprime tous les multiples de 3 qui suivent;<\/li><li>le suivant: ce n&rsquo;est pas \u00ab\u00a04\u00a0\u00bb (car il a \u00e9t\u00e9 supprim\u00e9), mais \u00ab\u00a05\u00a0\u00bb. On supprime alors tous les multiples de 5 qui suivent;<\/li><li>le nombre qui vient apr\u00e8s est alors \u00ab\u00a07\u00a0\u00bb; on le s\u00e9lectionne et on supprime tous les multiples de 7 qui suivent;<\/li><li>on continue ainsi jusqu&rsquo;au dernier nombre possible, \u00e0 savoir \u00ab\u00a097\u00a0\u00bb.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c0 la fin, ne restent que les nombres premiers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nous allons nous pencher dans cet article sur le crible d\u2019\u00c9ratosth\u00e8ne, et plus particuli\u00e8rement la fa\u00e7on dont on peut cr\u00e9er une animation avec Python et manim.<\/p>\n","protected":false},"author":1,"featured_media":6406,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,6,5],"tags":[261,303,101],"class_list":["post-6393","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-enseignement","category-mathematiques","category-python","tag-crible","tag-manim","tag-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Crible d\u2019\u00c9ratosth\u00e8ne: animation avec Python et manim - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"Nous allons voir une fa\u00e7on de cr\u00e9er une animation avec Python et manim pour le crible d\u2019\u00c9ratosth\u00e8ne. 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