{"id":158,"date":"2021-04-12T14:00:00","date_gmt":"2021-04-12T12:00:00","guid":{"rendered":"http:\/\/samuserensemble.fr\/?p=158"},"modified":"2021-05-24T22:46:55","modified_gmt":"2021-05-24T20:46:55","slug":"pythagore-concretement","status":"publish","type":"post","link":"http:\/\/samuserensemble.fr\/?p=158","title":{"rendered":"Pythagore, concr\u00e8tement"},"content":{"rendered":"\n<p>Le th\u00e9or\u00e8me de Pythagore, tout le monde connait ? Dans un triangle rectangle, le carr\u00e9 de la longueur de l&rsquo;hypot\u00e9nuse est \u00e9gal \u00e0 la somme des carr\u00e9s des longueurs des deux autres c\u00f4t\u00e9s. J&rsquo;ai voulu m&rsquo;assurer que mes enfants n&rsquo;avaient pas fait qu&rsquo;apprendre ce th\u00e9or\u00e8me par c\u0153ur, mais puisqu&rsquo;ils devaient l&rsquo;utiliser, qu&rsquo;ils l&rsquo;avaient vraiment compris. Pour cela, il nous fallait moins un cours qu&rsquo;une approche tr\u00e8s visuelle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-1-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en briques Lego\" class=\"wp-image-3628\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-1-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-1-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p>Ils ont alors construit les carr\u00e9s des c\u00f4t\u00e9s.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-2-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en briques Lego\" class=\"wp-image-3629\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-2-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-2-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p>De l\u00e0, la v\u00e9rification est facile : il suffit de superposer les briques des carr\u00e9s des deux petits c\u00f4t\u00e9s sur celles du carr\u00e9 du grand c\u00f4t\u00e9.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-3-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en briques Lego\" class=\"wp-image-3630\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-3-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-3-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p><strong>Pythagore en r\u00e9glettes<\/strong><\/p>\n\n\n\n<p>Comme ils en voulaient encore, je me suis inspir\u00e9e du blog <a href=\"http:\/\/iam-like-iam.blogspot.com\/2017\/09\/puissances-et-racines-carrees-et.html?m=1\" target=\"_blank\" rel=\"noreferrer noopener\">Je suis comme je suis<\/a> pour une manipulations avec les r\u00e9glettes Cuisenaire. De la m\u00eame mani\u00e8re, il s&rsquo;agit de reproduire les c\u00f4t\u00e9s du triangle (m\u00eames dimensions) avec les r\u00e9glettes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-4-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en r\u00e9glettes\" class=\"wp-image-3637\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-4-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-4-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p>Puis on les met au carr\u00e9.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-5-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en r\u00e9glettes\" class=\"wp-image-3638\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-5-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-5-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p>Et on v\u00e9rifie facilement.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-6-scaled.jpg\" alt=\"Th\u00e9or\u00e8me de Pythagore en r\u00e9glettes\" class=\"wp-image-3639\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-6-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-6-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p><strong>Pythagore en papier<\/strong><\/p>\n\n\n\n<p>Nous aurions largement pu nous arr\u00eater l\u00e0, mais nous avons d\u00e9cid\u00e9 de faire une version papier afin de la garder sous la main en cas d&rsquo;oubli du th\u00e9or\u00e8me. L&rsquo;aspect visuel est pr\u00e9sent aussi, m\u00eame s&rsquo;il n&rsquo;est pas possible de v\u00e9rifier par la manipulation, sauf \u00e0 d\u00e9couper les carr\u00e9s. Mais on voit bien que le grand carr\u00e9 contient les deux petits.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" width=\"2560\" height=\"1920\" src=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-7-scaled.jpg\" alt=\"\" class=\"wp-image-3641\" srcset=\"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-7-scaled.jpg 2560w, http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/Pythagore-7-300x225.jpg 300w\" sizes=\"(max-width: 739px) 94vw, (max-width: 969px) 88vw, (max-width: 1199px) 860px, 850px\" \/><\/figure>\n\n\n\n<p><strong>Pythagore en vid\u00e9os<\/strong><\/p>\n\n\n\n<p>Pour le plaisir ! La vid\u00e9o de Micka\u00ebl Launay est tr\u00e8s claire, avec une autre d\u00e9monstration (mais c&rsquo;est beaucoup plus scolaire que ses vid\u00e9os ult\u00e9rieures) :<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarques wp-block-embed-prise-en-charge-des-contenus-embarques wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"jetpack-video-wrapper\"><iframe title=\"Le th\u00e9or\u00e8me de Pythagore 3 (La d\u00e9monstration)\" width=\"850\" height=\"478\" src=\"https:\/\/www.youtube.com\/embed\/yMp2PYBSGHk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<p>Et cette version avec des carr\u00e9s pleins d&rsquo;eau est particuli\u00e8rement concr\u00e8te pour les esprits visuels :<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarques wp-block-embed-prise-en-charge-des-contenus-embarques wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"jetpack-video-wrapper\"><iframe title=\"Une tr\u00e8s belle conjecture du th\u00e9or\u00e8me de Pythagore avec de l&#039;eau\" width=\"850\" height=\"638\" src=\"https:\/\/www.youtube.com\/embed\/3SlqdCRoTas?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Le th\u00e9or\u00e8me de Pythagore, tout le monde connait ? Dans un triangle rectangle, le carr\u00e9 de la longueur [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3624,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[699],"tags":[35,731,275,413,660],"class_list":["post-158","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-en-samusant","tag-apprendre-en-samusant","tag-article-demenage","tag-geometrie","tag-mathematiques","tag-video"],"aioseo_notices":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"http:\/\/samuserensemble.fr\/wp-content\/uploads\/2021\/05\/pythagorean-theorem-5974278_1920.jpg","_links":{"self":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/158","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=158"}],"version-history":[{"count":2,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/158\/revisions"}],"predecessor-version":[{"id":3644,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/posts\/158\/revisions\/3644"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=\/wp\/v2\/media\/3624"}],"wp:attachment":[{"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=158"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=158"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/samuserensemble.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}