{"id":2819,"date":"2023-12-28T16:23:07","date_gmt":"2023-12-28T15:23:07","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=2819"},"modified":"2024-07-24T10:02:10","modified_gmt":"2024-07-24T08:02:10","slug":"gateau-geodesique-et-cercles","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2023\/12\/28\/gateau-geodesique-et-cercles\/","title":{"rendered":"G\u00e2teau g\u00e9od\u00e9sique"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"916\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-1024x916.jpg\" alt=\"\" class=\"wp-image-2820\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-1024x916.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-300x268.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-768x687.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-1536x1374.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-copie-2048x1832.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Les <a href=\"https:\/\/mathcurve.com\/courbes3d\/lignes\/geodesictore.shtml\">g\u00e9od\u00e9siques<\/a> du tore<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Les courbes enroul\u00e9es et les non enroul\u00e9es.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il est agr\u00e9able de pouvoir manipuler, faire le tour, manger, couper le mod\u00e8le g\u00e9om\u00e9trique pour bien dig\u00e9rer la g\u00e9om\u00e9trie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D&rsquo;autres g\u00e9od\u00e9siques sont possible. Ici exemple de g\u00e9od\u00e9sique qui ne rentre pas dans le tore avec une sym\u00e9trie 4:<\/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=\"1024\" height=\"897\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-1024x897.jpg\" alt=\"\" class=\"wp-image-2873\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-1024x897.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-300x263.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-768x673.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-1536x1345.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-recto-2048x1794.jpg 2048w\" 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=\"878\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-1024x878.jpg\" alt=\"\" class=\"wp-image-2875\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-1024x878.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-300x257.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-768x658.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-1536x1317.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-geodesique-4-verso-2048x1755.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Voici encore 3 autres g\u00e9od\u00e9siques:<\/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=\"1024\" height=\"1013\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-1024x1013.jpg\" alt=\"\" class=\"wp-image-2908\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-1024x1013.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-300x297.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-768x759.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-1536x1519.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-1-1-2048x2025.jpg 2048w\" 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=\"994\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-1024x994.jpg\" alt=\"\" class=\"wp-image-2909\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-1024x994.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-300x291.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-768x746.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-1536x1491.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Tore-3-2048x1988.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-58505613-1919-42ee-acb7-91992885e529\"><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\n\n  <p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/ql-cache\/quicklatex.com-b83862f4cfd3fe9885c6495d24345e6c_l3.png\" height=\"59\" width=\"120\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/ql-cache\/quicklatex.com-c9a0e8d52d708e53ac0311012e6b93d8_l3.png\" height=\"274\" width=\"345\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<pre id=\"block-f233d81b-fe54-4766-8985-7d5c12ca87a8\" class=\"wp-block-code\"><code><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/ql-cache\/quicklatex.com-66a57cf7b4f2af34acbf3958d685418f_l3.png\" height=\"281\" width=\"465\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/ql-cache\/quicklatex.com-65c37b8788ed893224e4c778d88f050e_l3.png\" height=\"281\" width=\"465\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Bonus<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Le symbole infini cach\u00e9 dans une coupe du tore.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-1006x1024.jpg\" alt=\"\" class=\"wp-image-2870\" style=\"width:650px;height:auto\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-1006x1024.jpg 1006w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-295x300.jpg 295w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-768x782.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-1509x1536.jpg 1509w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/tore-infini-2013x2048.jpg 2013w\" sizes=\"auto, (max-width: 1006px) 100vw, 1006px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>G\u00e9od\u00e9sique du tore pour bien d\u00e9corer le g\u00e2teau ? et Combien de familles de cercles peut-on dessiner sur le g\u00e2teau torique ?<\/p>\n","protected":false},"author":1,"featured_media":2898,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2819","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\/2819","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=2819"}],"version-history":[{"count":25,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/2819\/revisions"}],"predecessor-version":[{"id":4359,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/2819\/revisions\/4359"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/2898"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=2819"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=2819"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=2819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}