{"id":4212,"date":"2024-07-05T17:14:09","date_gmt":"2024-07-05T15:14:09","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=4212"},"modified":"2024-08-03T15:02:26","modified_gmt":"2024-08-03T13:02:26","slug":"aire-du-triangle-a-lintegrale","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2024\/07\/05\/aire-du-triangle-a-lintegrale\/","title":{"rendered":"Aire du Triangle, de la pyramide, \u00e0 l&rsquo;int\u00e9grale"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Voici un triangle rempli de billes. SI je le d\u00e9forme avec une aire constante, les billes resteront juste \u00e0 l&rsquo;int\u00e9rieur.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En gardant la base immobile et constante, je peux d\u00e9placer le sommet oppos\u00e9 suivant une parall\u00e8le \u00e0 la base. Je suis ainsi assur\u00e9 de pouvoir d\u00e9former le triangle avec un aire constante.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-930d3512 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.30-972x1024.png\" alt=\"\" class=\"wp-image-4247\" style=\"width:204px;height:auto\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.30-972x1024.png 972w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.30-285x300.png 285w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.30-768x809.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.30.png 1276w\" sizes=\"auto, (max-width: 972px) 100vw, 972px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"693\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.31.08-1024x693.png\" alt=\"\" class=\"wp-image-4250\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.31.08-1024x693.png 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.31.08-300x203.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.31.08-768x520.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.31.08.png 1292w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-930d3512 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"977\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.02-977x1024.png\" alt=\"\" class=\"wp-image-4246\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.02-977x1024.png 977w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.02-286x300.png 286w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.02-768x805.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.27.02.png 1282w\" sizes=\"auto, (max-width: 977px) 100vw, 977px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"977\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/triangle-double.jpg\" alt=\"\" class=\"wp-image-4248\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/triangle-double.jpg 977w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/triangle-double-286x300.jpg 286w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/triangle-double-768x805.jpg 768w\" sizes=\"auto, (max-width: 977px) 100vw, 977px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-930d3512 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"703\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.12-1024x703.png\" alt=\"\" class=\"wp-image-4252\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.12-1024x703.png 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.12-300x206.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.12-768x527.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.12.png 1294w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"714\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.29-1024x714.png\" alt=\"\" class=\"wp-image-4251\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.29-1024x714.png 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.29-300x209.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.29-768x536.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.32.29.png 1282w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" controls src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/v2.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pour bien comprendre comment la surface est d\u00e9form\u00e9e, je peux remplacer les billes par des bandes qui peuvent glisser les unes sur les autres.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On r\u00e9alise ainsi que chaque hauteur de couche reste \u00e0 sa hauteur au cours de la d\u00e9formation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On comprend alors bien pourquoi le th\u00e9or\u00e8me du th\u00e9or\u00e8me gliss\u00e9 est juste.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On peut appliquer cela pour d\u00e9former un triangle en un triangle rectangle. Ce triangle est alors la moiti\u00e9 d&rsquo;un rectangle. D&rsquo;o\u00f9 l&rsquo;aire du triangle qui est la moiti\u00e9 de l&rsquo;aire du rectangle. Comme l&rsquo;aire du rectangle est largeur x hauteur, autrement dit ici base x hauteur, en le divisant par deux, on obtient bien la formule base x hauteur divis\u00e9 par deux.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Volume d&rsquo;une pyramide<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">On peut appliquer le m\u00eame principe pour un volume et une pyramide en particulier. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si on prend une forme quelconque coup\u00e9 en tranche, on peut d\u00e9placer les tranches, sans en changer le voulme.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Les deux volumes suivant ont \u00e9videment le m\u00eame volume. <\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-930d3512 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"684\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-684x1024.jpg\" alt=\"\" class=\"wp-image-4215\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-684x1024.jpg 684w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-200x300.jpg 200w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-768x1150.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-1026x1536.jpg 1026w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-1368x2048.jpg 1368w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06397-gouter-maths-pain-mie-2-1-scaled.jpg 1710w\" sizes=\"auto, (max-width: 684px) 100vw, 684px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"953\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-953x1024.jpg\" alt=\"\" class=\"wp-image-4213\" style=\"width:437px;height:auto\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-953x1024.jpg 953w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-279x300.jpg 279w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-768x825.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-1430x1536.jpg 1430w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/SNY06398-gouter-maths-pain-mie-2-1906x2048.jpg 1906w\" sizes=\"auto, (max-width: 953px) 100vw, 953px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Coupons un cube en 3 parties ainsi. Ce sont trois parties \u00e9gales donc ayant pour volume celui du cube divis\u00e9 par trois.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Prenons une pyramide, et on peut d\u00e9placer les couches pour former n&rsquo;importe quelle pyramide \u00e0 base carr\u00e9 avec pour hauteur le cot\u00e9 du cube. Toutes ces pyramides ont donc pour volume 1\/3 du volume du cube. Base x Hauteur divis\u00e9 par trois.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Volume Pyramide: 1\/3 Base x Hauteur<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si on allonge une pyramide dans une direction d&rsquo;un facteur f, le volume sera agrandi du m\u00eame facteur f. On r\u00e9alise ainsi que le volume d&rsquo;une pyramide quelconque a bien pour formule de volume :<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Volume Pyramide: 1\/3 Base x Hauteur<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Et on peut g\u00e9n\u00e9raliser facilement aux pyramides \u00e0 base triangulaire, (moiti\u00e9 du carr\u00e9 de base). ET \u00e0 toute surface de base (que l&rsquo;on peut d\u00e9couper en petits triangles), y compris le volume d&rsquo;un c\u00f4ne, qu&rsquo;il soit droit ou pench\u00e9.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Aire d&rsquo;une cylo\u00efde<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Au d\u00e9but du si\u00e8cle xx, on probl\u00e8me qui occupait beaucoup \u00e9tait de connaitre l&rsquo;aire sous la courbe d&rsquo;une cycloide.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Int\u00e9grale<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">On d\u00e9coupe en petites tranches que l&rsquo;on ajoute.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Volume d&rsquo;une pyramide en dimensions 4<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Base (du tetrahedre) x Hauteur \/ 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base (du triangle) x Hauteur \/ (3*4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base (=cot\u00e9) x Hauteur \/ (2*3*4)?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hypervolume: <a href=\"https:\/\/fr.wikipedia.org\/wiki\/4-polytope_r%C3%A9gulier_convexe\">https:\/\/fr.wikipedia.org\/wiki\/4-polytope_r%C3%A9gulier_convexe<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.apmep.fr\/IMG\/pdf\/AAA05020.pdf\">https:\/\/www.apmep.fr\/IMG\/pdf\/AAA05020.pdf<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/hal.science\/tel-02459860v1\/file\/Skapin_These_2001.pdf\">https:\/\/hal.science\/tel-02459860v1\/file\/Skapin_These_2001.pdf<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/community.wolfram.com\/groups\/-\/m\/t\/1150337\">https:\/\/community.wolfram.com\/groups\/-\/m\/t\/1150337<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Finding the volume of a simplex (straightforward method, no linear algebra)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/o9hXjCpVB10?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"435\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46-1024x435.png\" alt=\"\" class=\"wp-image-4244\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46-1024x435.png 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46-300x127.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46-768x326.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46-1536x652.png 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/Capture-decran-2024-07-09-a-12.25.46.png 1814w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1024\" data-id=\"4398\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-1021x1024.jpg\" alt=\"\" class=\"wp-image-4398\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-1021x1024.jpg 1021w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-300x300.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-150x150.jpg 150w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-768x770.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche-1531x1536.jpg 1531w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-gauche.jpg 1644w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"966\" data-id=\"4399\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite-1024x966.jpg\" alt=\"\" class=\"wp-image-4399\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite-1024x966.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite-300x283.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite-768x724.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite-1536x1449.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/pyramide-droite.jpg 1723w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"493\" data-id=\"4401\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-1024x493.jpg\" alt=\"\" class=\"wp-image-4401\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-1024x493.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-300x144.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-768x369.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-1536x739.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8079-3-pyramides-2048x985.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"510\" data-id=\"4403\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-1024x510.jpg\" alt=\"\" class=\"wp-image-4403\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-1024x510.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-300x149.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-768x382.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-1536x765.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/IMG_8076-3d-2048x1020.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"845\" height=\"1024\" data-id=\"4400\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube-845x1024.jpg\" alt=\"\" class=\"wp-image-4400\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube-845x1024.jpg 845w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube-248x300.jpg 248w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube-768x931.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube-1268x1536.jpg 1268w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-cube.jpg 1361w\" sizes=\"auto, (max-width: 845px) 100vw, 845px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"673\" data-id=\"4402\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide-1024x673.jpg\" alt=\"\" class=\"wp-image-4402\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide-1024x673.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide-300x197.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide-768x505.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide-1536x1009.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2024\/07\/cube-pyramide.jpg 1928w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Th\u00e9or\u00e8me du triangle<\/p>\n","protected":false},"author":1,"featured_media":4217,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4212","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/4212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/comments?post=4212"}],"version-history":[{"count":20,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/4212\/revisions"}],"predecessor-version":[{"id":4404,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/4212\/revisions\/4404"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/4217"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=4212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=4212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=4212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}