{"id":3321,"date":"2024-01-16T00:07:02","date_gmt":"2024-01-15T23:07:02","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=3321"},"modified":"2024-01-18T17:46:15","modified_gmt":"2024-01-18T16:46:15","slug":"toasts-pour-binomes","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2024\/01\/16\/toasts-pour-binomes\/","title":{"rendered":"Toasts pour binomes"},"content":{"rendered":"\n

Voici des toasts, \u0153uf, jambon, fromage, parfaits pour un brunch, mais il en aurait fallu le double. Comment partager chaque toast en 2 parties superposables ?<\/p>\n\n\n\n

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<\/p>\n\n\n\n

\"\" Inspiration<\/b>
Michel Criton a cr\u00e9\u00e9 de nombreux jeux math\u00e9matiques pour le magazine Tangente<\/a> et le concours de la F\u00e9d\u00e9ration Fran\u00e7aise de Jeux Math\u00e9matiques<\/a>. Voici r\u00e9v\u00e9l\u00e9 une m\u00e9thode d’exercice qui lui est ch\u00e8re.
\nIl y a une technique plus ou moins syst\u00e9matique:
\n\nOn consid\u00e8re l’ensemble S des \u00ab\u00a0sommets\u00a0\u00bb auxquels on adjoint les milieux des \u00ab\u00a0c\u00f4t\u00e9s\u00a0\u00bb (un \u00ab\u00a0c\u00f4t\u00e9\u00a0\u00bb peut \u00e9ventuellement \u00eatre courbe si le \u00ab\u00a0polygone\u00a0\u00bb est curviligne) de la figure \u00e0 d\u00e9couper. On prend deux points de l’ensemble S, on choisit un sens de d\u00e9placement \u00e0 partir de chacun de ces deux points (il y a donc 4 choix possibles), puis on se d\u00e9place simultan\u00e9ment le long du bord de la m\u00eame mani\u00e8re.\n
\nL’algorithme invent\u00e9 par Kimmo Eriksson repose sur le fait que si une figure F est d\u00e9composable en deux parties superposables, alors il existe deux parties du bord de F qui se correspondent. Autrement dit, l’image du bord de F dans la correspondance entre les deux parties ne peut \u00eatre enti\u00e8rement incluse dans l’int\u00e9rieur de F.
\nQuant \u00e0 un nombre de parties stricte- ment plus grand que 2, aucune m\u00e9thode de r\u00e9solution ne semble connue.\n<\/td>		\"\"<\/td><\/tr><\/table><\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Comment partager chaque toast en 2 parties superposables ?<\/p>\n","protected":false},"author":1,"featured_media":3338,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3321","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\/3321","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=3321"}],"version-history":[{"count":11,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/3321\/revisions"}],"predecessor-version":[{"id":3431,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/3321\/revisions\/3431"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/3338"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=3321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=3321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=3321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}