{"id":2388,"date":"2023-12-16T10:23:01","date_gmt":"2023-12-16T09:23:01","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=2388"},"modified":"2024-01-22T09:45:30","modified_gmt":"2024-01-22T08:45:30","slug":"partage-de-cookies","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2023\/12\/16\/partage-de-cookies\/","title":{"rendered":"Partage de cookies en 7"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">6 cookies carr\u00e9s \u00e0 partager en 42.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"982\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-1024x982.jpg\" alt=\"\" class=\"wp-image-2520\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-1024x982.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-300x288.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-768x736.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-1536x1472.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-orig-7-2048x1963.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>Voici un cookie carr\u00e9 d\u00e9cor\u00e9\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-8cb6e05e936da7ad8babce4338194614_l3.png\" height=\"186\" width=\"186\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">On veut le partager en 7. Voici un partage possible.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1) 7 bandes<\/h2>\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-bd28fa7dec4e12376b48433e55914128_l3.png\" height=\"186\" width=\"186\" 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\">Mais comment d\u00e9couper 1\/7\u00e8me ?<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\">2) \u00e0 partir de d\u00e9coupes en 2 et aux nombres binaires:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><blockquote class=\"wp-embedded-content\" data-secret=\"NBDfipmH9t\"><a href=\"https:\/\/interstices.info\/un-algorithme-de-decoupe-de-gateau\/\">Un algorithme de d\u00e9coupe de g\u00e2teau<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;Un algorithme de d\u00e9coupe de g\u00e2teau&#8221; &#8212; Interstices\" src=\"https:\/\/interstices.info\/un-algorithme-de-decoupe-de-gateau\/embed\/#?secret=bPG4Z0o0x0#?secret=NBDfipmH9t\" data-secret=\"NBDfipmH9t\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\/7\u00e8me s&rsquo;\u00e9crit en d\u00e9cimal: 1\/7&nbsp;=&nbsp;0,142857 142857 142857&#8230;<sub>10<\/sub> et en binaire: 1\/7&nbsp;=&nbsp;0,001 001 001 001 &#8230;<sub>2<\/sub>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En effet, il n&rsquo;y a qu&rsquo;\u00e0 poser la division de 1 par 7 en binaire:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code> 1     |   111\n       +---------\n       | 0\n       |\n\n 1     |   111\n 10    +---------\n       | 0,0\n       |\n\n 1     |   111\n 10    +---------\n 100   | 0,00\n       |\n\n 1     |   111\n 10    +---------\n 100   | 0,001 0...\n 1000  |\n- 111  |\n=   1  |\n    10<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">D&rsquo;o\u00f9 l&rsquo;algorithme pour donner \u00e0 la premi\u00e8re personne 1\/\u00e8me du gateau:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>On coupe en 2 ce qu'on a \u00e0 d\u00e9couper.\nOn garde un des 2 morceaux.\nOn coupe en 2 le reste. \nOn garde un des 2 morceaux.\nOn donne l'autre \u00e0 la premi\u00e8re personne.\nOn regroupe tous les morceaux qu' on a gard\u00e9, et avec on recommence tant qu'il reste quelque chose de pas trop petit \u00e0 d\u00e9couper.\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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-f023f5c5d5e9e2d36636eed4e0fcece8_l3.png\" height=\"629\" width=\"554\" 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-d74035b2e0be6e2102b417ca25b642ad_l3.png\" height=\"629\" width=\"554\" 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-bc26b1ed6dab43224d9fe5e7c92de7a0_l3.png\" height=\"627\" width=\"554\" 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-6f1af71927a85e48cad4ef500da99099_l3.png\" height=\"654\" width=\"554\" 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-789c07818e25151ba7444f5e9a968898_l3.png\" height=\"682\" width=\"554\" 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-537d8fddfccd12fd994ebe2f4caf942a_l3.png\" height=\"737\" width=\"600\" 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-e6e2df9cef42bd35ad15d8813dcf7ed0_l3.png\" height=\"767\" width=\"601\" 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<p class=\"wp-block-paragraph\">Mais cette technique fait beaucoup de miettes de cookie. Ne pourrait-on pas utiliser le fait que les cookies sont carr\u00e9s ?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3) rep\u00e9rer 1\/7e de la longueur du  cot\u00e9 d&rsquo;un <em>carr\u00e9<\/em> ?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Construction pour&nbsp;<\/strong><strong>SEPT<\/strong><strong>&nbsp;bandes<\/strong><strong><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Plus grande puissance de 2 inf\u00e9rieure \u00e0 7 :&nbsp;4<br>Fraction: (7 \u2013&nbsp;4) \/&nbsp;4&nbsp;= 3 \/ 4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Milieu de BC, puis milieu de CE: point F.<br>Le point F est au trois-quarts de BC.<br>Tracer AF et BD: point G.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Parall\u00e8le \u00e0 BC en G.<br>Le point G se trouve \u00e0 la fraction (7 \u2013&nbsp;4) \/ 7 = 3\/7 de HI. Alors: HG = 3\/7 HI et GI&nbsp;&nbsp;= 4\/7 HI.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Milieu J de GI, puis milieux de IJ et de JG.<br>Report de IK sur GH (ouverture d&rsquo;un compas) en GM, MN et NH.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Le segment IH est divis\u00e9 en sept.<br>Tracer les six parall\u00e8les \u00e0 AB pour obtenir les sept bandes.<\/strong><\/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-3cb7ad162d5e4ea78f4bf7974e9c6ec9_l3.png\" height=\"188\" width=\"296\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"991\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-1024x991.jpg\" alt=\"\" class=\"wp-image-2508\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-1024x991.jpg 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-300x290.jpg 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-768x743.jpg 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-1536x1486.jpg 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/cookie-7e-2-2048x1981.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">4) Mais certains auront tout le bord !<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">D&rsquo;autres que le milieu, ce n&rsquo;est pas juste. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Voici un autre partage possible. On fait 7 parts de 51,4\u00b0<\/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-5164cc014ffdc405b7b7cd141ceb6e56_l3.png\" height=\"540\" width=\"527\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Les parts ont toutes du bord \u00e0 peu pr\u00e8s \u00e9galement, mais il y a des parts plus grandes, celles dans les coins.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">5) 7 parts de m\u00eame aire, avec autant de bord:<\/h2>\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-b73a4ab92cc1e25e6ed2f0a5b73d3c47_l3.png\" height=\"279\" width=\"279\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Pourquoi \u00e7a marche ? <\/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-9e2149e6b72a2e4e11321261670971cb_l3.png\" height=\"388\" width=\"388\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">L&rsquo;aire d&rsquo;un triangle est <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/ql-cache\/quicklatex.com-139e3b03e027467d8cac939eec7cd74d_l3.png\" class=\"ql-img-inline-formula \" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#105;&#114;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#97;&#115;&#101;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#97;&#117;&#116;&#101;&#117;&#114;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"143\" style=\"vertical-align: -6px;\"\/> Chaque part est un triangle ou la somme de 2 triangles qui ont tous les m\u00eame longueur de hauteur, et la m\u00eame longueur de base.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">6) Mais peut \u00eatre que seuls certains pr\u00e9f\u00e8rent le bord<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">On va utiliser la m\u00e9thode du couteau qui bouge.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>On commence avec le couteau au bord et on le d\u00e9place progressivement de part en part. D\u00e8s qu'une des 7 personne est satisfait de la part en train d'\u00eatre d\u00e9coup\u00e9e, il dit stop, on tranche et il r\u00e9cup\u00e8re sa part.\nOn recommence ensuite avec les 6 autres personnes qui restent et le reste de gateau.\nEt ainsi de suite.\n\nPar exemple, si tous pr\u00e9f\u00e8rent le bord sauf une personne, on pourrait obtenir le d\u00e9coupage suivant qui est meilleur pour tous que les pr\u00e9c\u00e9dentes m\u00e9thodes.\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-e248354ebbfa796a254ce2db30363f7d_l3.png\" height=\"278\" width=\"278\" class=\"ql-img-picture \" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Mais il peut y avoir des jaloux. Ou m\u00eame des personnes qui souhaiteraient au final s&rsquo;\u00e9changer des parts. Mais \u00e7a, c&rsquo;st une autre histoire, on a plus de cookie \u00e0 partager.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"975\" src=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-1024x975.png\" alt=\"\" class=\"wp-image-2506\" srcset=\"https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-1024x975.png 1024w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-300x285.png 300w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-768x731.png 768w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-1536x1462.png 1536w, https:\/\/eva.louis-le-grand.net\/maths\/wp-content\/uploads\/2023\/12\/Gouter-Maths-Cookie-2048x1949.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Comment partager un g\u00e2teau carr\u00e9 en 7 ?<\/p>\n","protected":false},"author":1,"featured_media":2502,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2388","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\/2388","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=2388"}],"version-history":[{"count":80,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/2388\/revisions"}],"predecessor-version":[{"id":4362,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/2388\/revisions\/4362"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/2502"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=2388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=2388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=2388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}