{"id":750,"date":"2017-03-17T16:05:47","date_gmt":"2017-03-17T15:05:47","guid":{"rendered":"http:\/\/www2.mathnique.com\/site\/?page_id=750"},"modified":"2019-01-30T14:51:36","modified_gmt":"2019-01-30T13:51:36","slug":"les-classiques","status":"publish","type":"page","link":"https:\/\/www.mathnique.com\/site\/les-classiques\/","title":{"rendered":"Les Classiques"},"content":{"rendered":"<ul>\n<li style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>Le nombre $\\pi$<\/strong><\/span><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-756 aligncenter\" src=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/ramanujan.jpg\" alt=\"\" width=\"180\" height=\"216\" \/>\u00a0<em>Srinivasa RAMANUJAN<\/em><em><em> (22\/12\/1887-26\/04\/1920 Inde)<br \/>\nL'un des plus grands\u00a0math\u00e9maticiens mondiaux<\/em><\/em><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: left;\">$\\int_{-\\infty}^{+\\infty} \\frac{dt}{1 + t^2} \\ dt = 2 \\int_0^{+\\infty} \\frac{dt}{1 + t^2} \\\u00a0dt = \\pi$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: left;\">$ 2 \\int_0^1 \\frac{dt}{\\sqrt{1 - t^2}}\u00a0\\ dt = \\pi$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: left;\">$\\int_a^b \\frac{dt}{\\sqrt{(t -a)(t -b)}}\u00a0\\\u00a0dt = \\pi$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: left;\">Approximations d\u00e9cimales ou rationnelles de $\\pi$ depuis l'Antiquit\u00e9 : Capes interne 1995<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"text-align: left;\">Approximation par la m\u00e9thode des isop\u00e9rim\u00e8tres<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"color: #ff0000;\"><strong>Des lapins de Fibonacci (alias Leonard de Pise) au Nombre d'Or $\\Phi$<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\" wp-image-1635 aligncenter\" src=\"http:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2017\/02\/fibonacci-249x300.png\" alt=\"\" width=\"126\" height=\"152\" srcset=\"https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2017\/02\/fibonacci-249x300.png 249w, https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2017\/02\/fibonacci.png 262w\" sizes=\"auto, (max-width: 126px) 85vw, 126px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2318 aligncenter\" src=\"http:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/lapins.gif\" alt=\"\" width=\"220\" height=\"161\" \/><br \/>\n<\/strong><\/span><\/p>\n<ul>\n<li>Sujet :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/Fibonacci.pdf\">Fibonacci<\/a><\/li>\n<li>Corrig\u00e9 :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/fibonaccicorrige.pdf\">fibonaccicorrige<\/a><\/li>\n<\/ul>\n<\/li>\n<li><strong><strong><span style=\"color: #ff0000;\">les 7 relations m\u00e9triques d'un triangle rectangle \u00a0et quelques relations m\u00e9triques d'un triangle quelconque.<\/span><\/strong><\/strong><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2319 aligncenter\" src=\"http:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet1.png\" alt=\"\" width=\"290\" height=\"117\" \/><strong><span style=\"color: #ff0000;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2320 aligncenter\" src=\"http:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet3-300x165.png\" alt=\"\" width=\"300\" height=\"165\" srcset=\"https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet3-300x165.png 300w, https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet3-768x423.png 768w, https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet3-1024x564.png 1024w, https:\/\/www.mathnique.com\/site\/wp-content\/uploads\/2018\/03\/relmet3.png 1132w\" sizes=\"auto, (max-width: 300px) 85vw, 300px\" \/><\/span><\/strong>\n<ul>\n<li>Sujet :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/Relationsmetriques.pdf\">Relationsmetriques<\/a><\/li>\n<li>Corrig\u00e9 :<\/li>\n<\/ul>\n<\/li>\n<li>Autres relations m\u00e9triques<\/li>\n<li><strong><strong><span style=\"color: #ff0000;\">Thal\u00e8s, Menelaus et Ceva<\/span><\/strong><\/strong>\n<ul>\n<li>Sujet :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/thalesmenelaus.pdf\">thalesmenelaus<\/a><\/li>\n<li>Corrig\u00e9 :<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"color: #ff0000;\"><span style=\"color: #ff0000;\"><strong>Puissance d'un point par rapport \u00e0 un cercle<\/strong><\/span><\/span>\n<ul>\n<li>Sujet :<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/puissancept.pdf\">puissance<\/a><\/li>\n<li>Corrig\u00e9 :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/puissanceptcor.pdf\">puissanceptcor<\/a><\/li>\n<\/ul>\n<\/li>\n<li><strong><strong><span style=\"color: #ff0000;\">L'inversion<\/span><\/strong><\/strong>\n<ul>\n<li>Sujet :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/inversion.pdf\">inversion<\/a><\/li>\n<li>Corrig\u00e9 :\u00a0<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/inversionseul.pdf\">inversionseul<\/a><\/li>\n<\/ul>\n<\/li>\n<li><strong><strong><span style=\"color: #ff0000;\">Irrationnalit\u00e9 de $\\zeta(2)$<\/span><\/strong><\/strong><\/li>\n<li><span style=\"color: #ff0000;\"><strong>Les fonctions eul\u00e9riennes $\\beta$ et $\\Gamma$<\/strong><\/span>\n<ul>\n<li>$Gamma$ et loi du $\\chi_2$ :\n<ul>\n<li>Sujet capes agricole 08 :<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/capesagricole08c1.pdf\">capesagricole08c1<\/a><\/li>\n<li>Corrig\u00e9 capes agricole 08 :<a href=\"http:\/\/www2.mathnique.com\/site\/wp-content\/uploads\/2017\/03\/capesagricole08e1scor.pdf\">capesagricole08e1scor<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Les fonctions trigonom\u00e9triques et hyperboliques inverses :<\/li>\n<li>La fonction\u00a0$\\chi_2$<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Le nombre $\\pi$ \u00a0Srinivasa RAMANUJAN (22\/12\/1887-26\/04\/1920 Inde) L'un des plus grands\u00a0math\u00e9maticiens mondiaux $\\int_{-\\infty}^{+\\infty} \\frac{dt}{1 + t^2} \\ dt = 2 \\int_0^{+\\infty} \\frac{dt}{1 + t^2} \\\u00a0dt = \\pi$ $ 2 \\int_0^1 \\frac{dt}{\\sqrt{1 - t^2}}\u00a0\\ dt = \\pi$ $\\int_a^b \\frac{dt}{\\sqrt{(t -a)(t -b)}}\u00a0\\\u00a0dt = \\pi$ Approximations d\u00e9cimales ou rationnelles de $\\pi$ depuis l'Antiquit\u00e9 : Capes interne 1995 Approximation &hellip; <a href=\"https:\/\/www.mathnique.com\/site\/les-classiques\/\" class=\"more-link\">Continuer la lecture<span class=\"screen-reader-text\"> de &laquo;&nbsp;Les Classiques&nbsp;&raquo;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-750","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/pages\/750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/comments?post=750"}],"version-history":[{"count":21,"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/pages\/750\/revisions"}],"predecessor-version":[{"id":2587,"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/pages\/750\/revisions\/2587"}],"wp:attachment":[{"href":"https:\/\/www.mathnique.com\/site\/wp-json\/wp\/v2\/media?parent=750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}