{"id":3538,"date":"2020-09-15T09:52:40","date_gmt":"2020-09-15T07:52:40","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=3538"},"modified":"2021-02-04T16:00:34","modified_gmt":"2021-02-04T15:00:34","slug":"trouver-pi-python","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/","title":{"rendered":"Trouver dans Pi avec Python sa date de naissance"},"content":{"rendered":"\n<p>Trouver dans Pi, \u00e0 l&#8217;aide de Python, un nombre quelconque, par exemple sa date de naissance, serait en th\u00e9orie possible car Pi serait un nombre <em><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Nombre_univers\" target=\"_blank\" rel=\"noreferrer noopener\">univers<\/a><\/em>. <\/p>\n\n\n\n<!--more-->\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"324\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi-univers.jpg\" alt=\"trouver dans pi avec Python un nombre\" class=\"wp-image-3539\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi-univers.jpg 548w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi-univers-300x177.jpg 300w\" sizes=\"auto, (max-width: 548px) 100vw, 548px\" \/><\/figure><\/div>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 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\/2020\/09\/15\/trouver-pi-python\/#Trouver_dans_Pi_un_nombre_fini_avec_Python_prouver_que_cest_possible\" >Trouver dans Pi un nombre fini avec Python: prouver que c&#8217;est possible<\/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\/2020\/09\/15\/trouver-pi-python\/#Trouver_dans_Pi_un_nombre_fini_avec_Python_le_programme\" >Trouver dans Pi un nombre fini avec Python: le programme<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#Trouver_dans_Pi_un_nombre_fini_avec_Python_il_nous_faut_dabord_beaucoup_de_decimales_de_Pi\" >Trouver dans Pi un nombre fini avec Python: il nous faut d&#8217;abord beaucoup de d\u00e9cimales de Pi<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#Le_programme_Python\" >Le programme Python<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#Un_constant_eloquent_ca_cest_bien_un_titre_a_la_%E2%80%9CVoici%E2%80%9D\" >Un constant \u00e9loquent (\u00e7a, c&#8217;est bien un titre \u00e0 la &#8220;Voici&#8221;!)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#Pour_aller_plus_loin%E2%80%A6\" >Pour aller plus loin&#8230;<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#En_2019\" >En 2019<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.mathweb.fr\/euclide\/2020\/09\/15\/trouver-pi-python\/#Nouveau_record_en_2020\" >Nouveau record en 2020<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trouver_dans_Pi_un_nombre_fini_avec_Python_prouver_que_cest_possible\"><\/span>Trouver dans Pi un nombre fini avec Python: prouver que c&#8217;est possible<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Pi est un nombre univers, c&#8217;est-\u00e0-dire un nombre ayant une partie d\u00e9cimale dans laquelle on peut toujours trouver, en th\u00e9orie, n&#8217;importe quel nombre fini.<\/p>\n\n\n\n<p>S&#8217;il est relativement facile de <a  href=\"https:\/\/famille-chazal.pagesperso-orange.fr\/articles\/piirrationnel.pdf\" target=\"_blank\" rel=\"noreferrer noopener\" data-fancybox data-type=\"iframe\" data-width=\"90%\" data-height=\"100%\" data-preload=\"false\">d\u00e9montrer que Pi est irrationnel<\/a> (par l&#8217;absurde), il est assez <a  href=\"http:\/\/www.pi314.net\/sitepdf\/lindemann.PDF\" target=\"_blank\" rel=\"noreferrer noopener\" data-fancybox data-type=\"iframe\" data-width=\"90%\" data-height=\"100%\" data-preload=\"false\">difficile de prouver qu&#8217;il est transcendant<\/a> (c&#8217;est-\u00e0-dire qu&#8217;il n&#8217;est pas solution d&#8217;une \u00e9quation polynomiale \u00e0 coefficients entiers).<\/p>\n\n\n\n<p>Mais d\u00e9montrer que Pi est un nombre univers, l\u00e0, c&#8217;est maousse costaud ! D&#8217;ailleurs, ce n&#8217;est pas encore fait&#8230; On ne fait que supposer qu&#8217;il est univers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trouver_dans_Pi_un_nombre_fini_avec_Python_le_programme\"><\/span>Trouver dans Pi un nombre fini avec Python: le programme<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trouver_dans_Pi_un_nombre_fini_avec_Python_il_nous_faut_dabord_beaucoup_de_decimales_de_Pi\"><\/span>Trouver dans Pi un nombre fini avec Python: il nous faut d&#8217;abord beaucoup de d\u00e9cimales de Pi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Ben oui ! Trouver dans Pi un nombre avec Python n&#8217;est possible que si l&#8217;on dispose du nombre Pi.<\/p>\n\n\n\n<p>Alors, c&#8217;est cadeau : voici un fichier texte contenant les 131 072 d\u00e9cimales de Pi. Oui, j&#8217;ai bien dit 131 072&#8230; Je ne les ai pas trouv\u00e9 moi-m\u00eame, mais repris du site <a href=\"http:\/\/jlsigrist.com\/pi.html\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/jlsigrist.com\/pi.html<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi.txt\">pi<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi.txt\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_programme_Python\"><\/span>Le programme Python<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">with open('pi.txt' , 'r' , encoding='utf8') as f:\n    for line in f:\n        pi = line.replace('\\n','')\n        \ndef trouve(txt):\n    pos = pi.find(txt)\n    if pos > -1:\n        print('{} est trouv\u00e9 \u00e0 la {}-i\u00e8me d\u00e9cimale de Pi'.format(txt,pos-1))\n    else:\n        print(\"{} n'a pas \u00e9t\u00e9 trouv\u00e9 dans Pi\".format(txt))\n        \ntrouve('1973')<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">&gt;&gt;&gt; 1973 est trouv\u00e9 \u00e0 la 1641-i\u00e8me d\u00e9cimale de Pi<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Un_constant_eloquent_ca_cest_bien_un_titre_a_la_%E2%80%9CVoici%E2%80%9D\"><\/span>Un constant \u00e9loquent (\u00e7a, c&#8217;est bien un titre \u00e0 la &#8220;Voici&#8221;!)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Si vous tentez de trouver votre date de naissance avec ce programme, vous allez \u00eatre d\u00e9\u00e7u\u00b7e\u00b7s ! Par exemple:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">trouve('01071973')<\/pre>\n\n\n\n<p>ne donne rien&#8230; Vous vous rendez compte ? Plus de 130 000 d\u00e9cimales de Pi, et je ne peux m\u00eame pas trouver ma date de naissance ! (au passage, n&#8217;oubliez pas de la noter quelque part pour mon futur cadeau&#8230;).<\/p>\n\n\n\n<p>Comme je suis obstin\u00e9 de naissance, je ne me suis pas arr\u00eat\u00e9 \u00e0 cet \u00e9chec. J&#8217;ai donc calcul\u00e9 500 000 000 de d\u00e9cimales! Fallait pas me faire chier !<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi-500000000.zip\">T\u00e9l\u00e9charger le fichier (217 Mo). Mot de passe : sue9rIUG$fisjeh$!9Rth<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/pi-500000000.zip\" class=\"wp-block-file__button\" download=\"\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Et pour info, je trouve ma date de naissance \u00e0 la 228.239.362-i\u00e8me d\u00e9cimale de Pi ! Je suis super content !&#8230;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pour_aller_plus_loin%E2%80%A6\"><\/span>Pour aller plus loin&#8230;<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"En_2019\"><\/span>En 2019<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>En 2019, 31 415 926 535 897 d\u00e9cimales de Pi ont \u00e9t\u00e9 trouv\u00e9es par <strong>Emma Haruka Iwao<\/strong>, une employ\u00e9e de Google: voir cet <a href=\"https:\/\/blog.google\/products\/google-cloud\/most-calculated-digits-pi\/\" target=\"_blank\" rel=\"noreferrer noopener\">article de Google<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"550\" height=\"417\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/Emma-Haruka-Iwao.jpg\" alt=\"Emma Haruka Iwao trouver d\u00e9cimales pi\" class=\"wp-image-3541\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/Emma-Haruka-Iwao.jpg 550w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/09\/Emma-Haruka-Iwao-300x227.jpg 300w\" sizes=\"auto, (max-width: 550px) 100vw, 550px\" \/><\/figure><\/div>\n\n\n\n<p>On peut se demander, alors que l&#8217;on ne se sert que d&#8217;une centaine de d\u00e9cimales en pratique dans diverses sciences, pourquoi s&#8217;acharner \u00e0 trouver de plus en plus de d\u00e9cimales.<\/p>\n\n\n\n<p>Et bien, c&#8217;est tout simplement pour tester la puissance des ordinateurs.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Nouveau_record_en_2020\"><\/span>Nouveau record en 2020<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>On n&#8217;arr\u00eate plus les acharn\u00e9s du bit ! Voil\u00e0 t&#8217;y pas que le petit Timothy Mullican a trouv\u00e9 50 trillions de d\u00e9cimales&#8230; (31,4 trillion avaient \u00e9t\u00e9 d\u00e9couvertes par Emma en 2019, la nulos !).<\/p>\n\n\n\n<p>Comme <a href=\"https:\/\/www.lemonde.fr\/sciences\/article\/2013\/05\/13\/la-marge-est-trop-petite-une-forfanterie-feconde_3176464_1650684.html\" target=\"_blank\" rel=\"noreferrer noopener\">aurait pu le dire<\/a> approximativement Pierre de Fermat:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>D\u00e9sol\u00e9, mais je n&#8217;ai plus de place pour les \u00e9crire ici&#8230;<\/p><cite>Pierre de Fermat (\u00e0 peu pr\u00e8s)<\/cite><\/blockquote>\n\n\n\n<p>Tout ceci a \u00e9t\u00e9 possible \u00e0 l&#8217;aide du logiciel <a href=\"http:\/\/www.numberworld.org\/y-cruncher\/#Download\" target=\"_blank\" rel=\"noreferrer noopener\">y-cruncher<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trouver dans Pi, \u00e0 l&#8217;aide de Python, un nombre quelconque, par exemple sa date de naissance, serait en th\u00e9orie possible car Pi serait un nombre univers.<\/p>\n","protected":false},"author":1,"featured_media":3719,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,5],"tags":[35],"class_list":["post-3538","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","category-python","tag-pi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - 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