{"id":3748,"date":"2018-05-26T11:14:05","date_gmt":"2018-05-26T10:14:05","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=3748"},"modified":"2018-05-29T09:05:02","modified_gmt":"2018-05-29T08:05:02","slug":"triplets-pythagoriciens","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/triplets-pythagoriciens\/","title":{"rendered":"Triplets pythagoriciens"},"content":{"rendered":"<h2><strong>R\u00e9sum\u00e9<\/strong><\/h2>\n<p>Recherche de triplets d\u2019entiers cons\u00e9cutifs a, b, c v\u00e9rifiant c\u00b2 = a\u00b2 + b\u00b2\u00a0 \u00e0 l\u2019aide d\u2019un programme.<\/p>\n<p>Conjecture \u00e0 l\u2019aide d\u2019un algorithme programm\u00e9 en Python\u00a0: il n\u2019y a que le triplet 3, 4, 5 qui convient (Python permet de chercher pour les 1000, 10000, 1000000, \u2026 premiers entiers).<\/p>\n<p>D\u00e9monstration math\u00e9matique \u00e0 l\u2019aide d\u2019une mise en \u00e9quation, des identit\u00e9s remarquables, des \u00e9quations produit nul.<\/p>\n<h2><strong>Th\u00e8mes math\u00e9matiques mis en jeu<\/strong><\/h2>\n<p>Calcul litt\u00e9ral<\/p>\n<p>Mise en \u00e9quation<\/p>\n<p>D\u00e9veloppement<\/p>\n<p>Identit\u00e9s remarquables<\/p>\n<p>\u00c9quations produit nul<\/p>\n<h2><strong>Notions d\u2019algorithmique\/programmation mises en jeu<\/strong><\/h2>\n<p>Test d\u2019\u00e9galit\u00e9<\/p>\n<p>Utilisation des bool\u00e9ens<\/p>\n<p>Cr\u00e9ation d\u2019une fonction qui teste si une \u00e9galit\u00e9 est vraie et qui renvoie un bool\u00e9en<\/p>\n<p>Cr\u00e9ation d\u2019un script qui teste tous les triplets possibles jusqu\u2019\u00e0 un certain nombre donn\u00e9 par l\u2019utilisateur et qui renvoie les triplets solutions.<\/p>\n<p>Triple boucle \u00ab\u00a0for a in range\u00a0\u00bb qui se simplifie en une boucle simple\u00a0; cette simplification permet de constater efficacement que le programme \u00ab\u00a0tourne\u00a0\u00bb plus vite. On pourra \u00e0 cette occasion \u00e9voquer le nombre de calculs effectu\u00e9s par le programme (complexit\u00e9 temporelle).<\/p>\n<h2><strong>Fichiers<\/strong><\/h2>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2018\/05\/Triplets-pythagoriciens.pdf\">Triplets pythagoriciens Fiche \u00e9l\u00e8ve en PDF<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2018\/05\/Triplets-pythagoriciens.docx\">Triplets pythagoriciens Fiche \u00e9l\u00e8ve en WORD<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2018\/05\/Triplets-pythagoriciens-Fichiers-PYTHON.zip\">Fichiers PYTHON<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>R\u00e9sum\u00e9 Recherche de triplets d\u2019entiers cons\u00e9cutifs a, b, c v\u00e9rifiant c\u00b2 = a\u00b2 + b\u00b2\u00a0 \u00e0 l\u2019aide d\u2019un programme. Conjecture \u00e0 l\u2019aide d\u2019un algorithme programm\u00e9 en Python\u00a0: il n\u2019y a que le triplet 3, 4, 5 qui convient (Python permet de chercher pour les 1000, 10000, 1000000, \u2026 premiers entiers). D\u00e9monstration math\u00e9matique \u00e0 l\u2019aide d\u2019une &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/triplets-pythagoriciens\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":38,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3748","post","type-post","status-publish","format-standard","hentry","category-non-classe","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/3748","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/38"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=3748"}],"version-history":[{"count":5,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/3748\/revisions"}],"predecessor-version":[{"id":3867,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/3748\/revisions\/3867"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=3748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=3748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=3748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}