{"id":59,"date":"2018-02-13T18:29:52","date_gmt":"2018-02-13T17:29:52","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=59"},"modified":"2018-03-03T11:07:50","modified_gmt":"2018-03-03T10:07:50","slug":"pythagore-belle-demonstration-de-leonard-de-vinci","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/","title":{"rendered":"Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci"},"content":{"rendered":"<p>En page 72 de mon livre, <em>Toutes les math\u00e9matiques du monde<\/em>, je laisse le lecteur d\u00e9couvrir la belle d\u00e9monstration du th\u00e9or\u00e8me de Pythagore par L\u00e9onard de Vinci \u00e0 travers un simple dessin. ABC y est un triangle rectangle original, ACDE le carr\u00e9 construit sur son hypot\u00e9nuse, ABFG et BCIH les carr\u00e9s construits sur les c\u00f4t\u00e9s de l\u2019angle droit.<\/p>\n<h2>L&#8217;id\u00e9e de L\u00e9onard<\/h2>\n<p>L\u2019id\u00e9e originale de L\u00e9onard de Vinci est d\u2019introduire deux triangles rectangles \u00e9gaux \u00e0 ABC suppl\u00e9mentaires DEJ et FHB. Voici un expos\u00e9 d\u00e9taill\u00e9 de sa fa\u00e7on de s\u2019en servir.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-60\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-01-300x227.png\" alt=\"\" width=\"300\" height=\"227\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-01-300x227.png 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-01-768x580.png 768w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-01-1024x774.png 1024w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-01.png 1133w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Les deux quadrilat\u00e8res ABJE (en bleu) et DJBC (en vert) sont \u00e9gaux car ils se superposent au moyen d\u2019une rotation de 180\u00b0. La somme de leurs aires est \u00e9gale \u00e0 celle du carr\u00e9 construit sur l\u2019hypot\u00e9nuse plus deux fois celle du triangle rectangle.<\/p>\n<p>On retrouve les m\u00eames quadrilat\u00e8res en AGIC et FGIH sur le c\u00f4t\u00e9 droit. Dans ce cas, ils se superposent par sym\u00e9trie d\u2019axe IBG. La somme de leurs aires est \u00e9gale \u00e0 la somme des aires des carr\u00e9s construits sur les c\u00f4t\u00e9s de l\u2019angle droit plus deux fois celles du triangle rectangle. On en d\u00e9duit que l\u2019aire du carr\u00e9 construit sur l\u2019hypot\u00e9nuse est \u00e9gale \u00e0 la somme des aires des carr\u00e9s construits sur les c\u00f4t\u00e9s de l\u2019angle droit, c\u2019est-\u00e0-dire le th\u00e9or\u00e8me de Pythagore.<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-61\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-02-300x227.png\" alt=\"\" width=\"300\" height=\"227\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-02-300x227.png 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-02-768x580.png 768w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-02-1024x774.png 1024w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/Maths-2018-01-02.png 1133w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>En page 72 de mon livre, Toutes les math\u00e9matiques du monde, je laisse le lecteur d\u00e9couvrir la belle d\u00e9monstration du th\u00e9or\u00e8me de Pythagore par L\u00e9onard de Vinci \u00e0 travers un simple dessin. ABC y est un triangle rectangle original, ACDE le carr\u00e9 construit sur son hypot\u00e9nuse, ABFG et BCIH les carr\u00e9s construits sur les c\u00f4t\u00e9s &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":12,"featured_media":77,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[29],"tags":[34,35,33],"class_list":["post-59","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths-2","tag-demonstration","tag-esthetique","tag-pythagore"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"En page 72 de mon livre, Toutes les math\u00e9matiques du monde, je laisse le lecteur d\u00e9couvrir la belle d\u00e9monstration du th\u00e9or\u00e8me de Pythagore par L\u00e9onard de Vinci \u00e0 travers un simple dessin. ABC y est un triangle rectangle original, ACDE le carr\u00e9 construit sur son hypot\u00e9nuse, ABFG et BCIH les carr\u00e9s construits sur les c\u00f4t\u00e9s &hellip; Continuer la lecture de Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci &rarr;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\" \/>\n<meta property=\"og:site_name\" content=\"MATH&#039;MONDE, le blog d&#039;Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\" \/>\n<meta property=\"article:published_time\" content=\"2018-02-13T17:29:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-03-03T10:07:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/leonardvinci.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"750\" \/>\n\t<meta property=\"og:image:height\" content=\"1027\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\",\"name\":\"Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci, par Herv\u00e9 Lehning\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/leonardvinci.jpg\",\"datePublished\":\"2018-02-13T17:29:52+00:00\",\"dateModified\":\"2018-03-03T10:07:50+00:00\",\"author\":{\"@id\":\"\"},\"breadcrumb\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/#primaryimage\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/leonardvinci.jpg\",\"contentUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2018\/02\/leonardvinci.jpg\",\"width\":750,\"height\":1027},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/02\/13\/pythagore-belle-demonstration-de-leonard-de-vinci\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Pythagore : la belle d\u00e9monstration de L\u00e9onard de Vinci\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\",\"name\":\"MATH&#039;MONDE, le blog d&#039;Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\",\"description\":\"Comment comprendre le monde moderne sans culture math\u00e9matique ? 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