{"id":404,"date":"2023-06-03T15:07:37","date_gmt":"2023-06-03T13:07:37","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=404"},"modified":"2024-03-01T17:41:10","modified_gmt":"2024-03-01T16:41:10","slug":"des-cookies-qui-semboitent","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2023\/06\/03\/des-cookies-qui-semboitent\/","title":{"rendered":"Des cookies qui s&#8217;emboitent"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/21187A4F-58BC-44B3-BC2F-11975B1B08EE-768x1024-1.jpeg\" alt=\"\" class=\"wp-image-406\" style=\"width:650px;height:867px\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/21187A4F-58BC-44B3-BC2F-11975B1B08EE-768x1024-1.jpeg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/21187A4F-58BC-44B3-BC2F-11975B1B08EE-768x1024-1-225x300.jpeg 225w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u00ab\u00a0<em>Einstein<\/em>\u00a0\u00bb ou \u00ab\u00a0<em>hat<\/em>\u00a0\u00bb ou \u00ab\u00a0<em>t-shirt<\/em>\u00ab\u00a0, c&rsquo;est une forme de cookie unique (<em>monotile<\/em>) qui permet de remplir une boite inifini de cookie forc\u00e9ment sans jamais pouvoir retrouver le m\u00eame assemblage nullepart (<em>aperiodic<\/em>). Par contre, les cookies doivent parfois \u00eatre retourn\u00e9s \u00e0 l&rsquo;envers). Cette forme de cookie a \u00e9t\u00e9 d\u00e9couvert en 2023  par David Smith, un amateur de maths.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le motif peut \u00eatre facilement dessin\u00e9 sur un carton pour servir de patron pour d\u00e9couper la p\u00e2te:<\/p>\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-e6fb9d1002a5cb071d75ea3089c5d7ce_l3.png\" height=\"95\" width=\"83\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\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-e3475796fcd84877343b89a305a04e03_l3.png\" height=\"187\" width=\"162\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\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-11bfa6bcc1889a1584108afdf077eaaf_l3.png\" height=\"187\" width=\"162\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\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-56c53db51bb4545eaaff6e98dbb9e2c8_l3.png\" height=\"131\" width=\"128\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n\n\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Assemblage de cookies. Le cookie gris est retourn\u00e9, et on en voit le dessous.<\/p>\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-51f82eba966cf7c20203602b360b5fc6_l3.png\" height=\"260\" width=\"266\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">D\u00e9couvert 1 mois plus tard toujours par David Smith, une autre forme unique de cookie permet des assemblages sans retourner les cookies. C&rsquo;est la forme est appel\u00e9e \u00ab\u00a0<em>spectre<\/em>\u00ab\u00a0. L&rsquo;ensemble permet de remplir une boite infinie sans laisser de trou, et sans que l&rsquo;assemblage ne puisse se r\u00e9p\u00e8ter ailleurs (<em>ap\u00e9riodique<\/em>).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1-1024x768.jpeg\" alt=\"\" class=\"wp-image-405\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1-1024x768.jpeg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1-300x225.jpeg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1-768x576.jpeg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1-1536x1152.jpeg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/5786CFB8-FAA4-40D8-9C70-8514EC92ECEE-2048x1536-1.jpeg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u00ab\u00a0Spectre\u00a0\u00bb aperiodic monotile (les cookies ont tous la surface du dessus en haut) d\u00e9couvert 1 mois plus tard en 2023 par David Smith un amateur de maths.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Voici un mod\u00e8le de \u00ab\u00a0<em>cookie cutter<\/em>\u00a0\u00bb \u00e0 imprimer en 3D (<a href=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/Cookie-Cutter.stl\">fichier .stl<\/a>) pour d\u00e9couper les cookies:<\/p>\n\n\n\n<div style='border: 2px solid #AAAA88; background: #FFFFDD; padding:8px;' ><img decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/cuisine.png\" alt=\"\" class=\"wp-image-1120\" width=30 srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/cuisine.png 512w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/cuisine-300x300.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/cuisine-150x150.png 150w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/> <b>Conseil cuisine<\/b><br>Il est plus simple pour \u00e9conomiser de la p\u00e2te et du temps de d\u00e9couper les cookies dans leur agencement optimal, mais c&rsquo;est vrai que c&rsquo;est moins amusant que de d\u00e9couper plein de cookies tous orient\u00e9 de la m\u00eame fa\u00e7on et ensuite les assembler apr\u00e8s cuisson.<\/div>\n\n\n\n<div style='border: 2px solid #AA8888; background: #FFDDDD; padding:8px;' ><img decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/livre.png\" alt=\"\" class=\"wp-image-1123\" width=30 srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/livre.png 512w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/livre-300x300.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/livre-150x150.png 150w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/> <b>Lecture<\/b><br>En Mars 2023, David Smith et des math\u00e9maticien ont d\u00e9couvert ces motifs, et voici leur article publi\u00e9: <i><a target=\"new\" href='https:\/\/arxiv.org\/pdf\/2303.10798.pdf' rel=\"noopener\">An aperiodic Monotile<\/a><\/i>.<\/div>\n\n\n\n<div style='border: 2px solid #88AA88; background: #DDFFDD; padding:8px;' ><img decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/10\/qui.png\" alt=\"\" class=\"wp-image-1123\" width=30 \/> <b>Pour aller plus loin<\/b><br>Thomaths <div><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/glYsmMVwoYI?si=-69tBZruE6hebdhU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>.<\/div>\n\n\n\n<div>\t<div id=\"woo3dv-viewer\" style=\"max-width:500px;max-height:500px;\">\r\n\t\t<div class=\"woo3dv-canvas-wrapper\">\r\n\t\t\t<canvas id=\"woo3dv-cv\" class=\"woo3dv-canvas woo3dv-canvas-border\" width=\"500\" height=\"500\"><\/canvas>\r\n\t\t\t<div id=\"woo3dv-file-loading\">\r\n\t\t\t\t<img decoding=\"async\" alt=\"Loading file\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/plugins\/woo-3d-viewer\/images\/ajax-loader.gif\">\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\r\n\t\t<div id=\"woo3dv-model-controls\">\r\n\t\t<ul id=\"woo3dv-model-controls-list\">\r\n\t\t<li><a href=\"javascript:void(0)\" 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100vw, 726px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Recto-verso ou recto seulement, ces cookies s&#8217;emboitent d&rsquo;une mani\u00e8re forc\u00e9ment unique sans motif.<\/p>\n","protected":false},"author":1,"featured_media":799,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-404","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\/404","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=404"}],"version-history":[{"count":129,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/404\/revisions"}],"predecessor-version":[{"id":3871,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/404\/revisions\/3871"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/799"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}