{"id":996,"date":"2023-10-17T11:25:41","date_gmt":"2023-10-17T09:25:41","guid":{"rendered":"https:\/\/eva.louis-le-grand.net\/maths\/?p=996"},"modified":"2023-11-01T11:27:39","modified_gmt":"2023-11-01T10:27:39","slug":"un-gateau-categoriquement-attirant","status":"publish","type":"post","link":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/2023\/10\/17\/un-gateau-categoriquement-attirant\/","title":{"rendered":"Un g\u00e2teau cat\u00e9gorique"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Si vous n\u2019avez jamais entendu parler de la th\u00e9orie des cat\u00e9gories en maths, c\u2019est pourtant un des 50 domaines math\u00e9matiques list\u00e9s par la Maison Poincar\u00e9 \u00e0 Paris.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

C\u2019est l\u2019art de mod\u00e9liser de la meme mani\u00e8re des objets tr\u00e8s diff\u00e9rents.
Regardez ce tableau .<\/p>\n\n\n\n

\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
C\u2019est la r\u00e8gle d\u2018additionon  en binaire .<\/p>\n\n\n\n
0+0=0
1+0=1
0+1=0
1+1=0 et il y a une retenue de 1<\/p>\n\n\n\n
ce qui donne sous forme de tableau:<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
C\u2019est aussi la table pour la r\u00e8gle de signe quand on multiplie deux nombres ensemble et qu\u2019un veut conna\u00eetre le signe du r\u00e9sultat. 
+ x + = +
+ x – = –
– x + = –
– x – =  +
et que l\u2019on peut repr\u00e9senter par un m\u00eame tableau.<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
Ou encore la r\u00e8gle complexe::<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
Ou encore le tableau de multiplication:<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
Ou encore le tableau de composition de rotations:<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Voici maintenant un tableau plus grand:<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
Cela peut repr\u00e9senter \u00e0 la fois la multiplication modulo 8 des nombres impairs:<\/p>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
Ou encore la table de composition des isom\u00e9tries du rectangle:<\/p>\n\n\n\n
Les isom\u00e9tries du rectangle, sont les transformations qui laissent inchang\u00e9es le rectangle.<\/p>\n\n\n\n
%Rectangle\n
\"Rendered<\/p><\/code><\/pre>\n\n\n\n
Ce sont les rotations d’angle 0\u00b0 (identit\u00e9) ou d’angle 180\u00b0, et les sym\u00e9tries horizontales ou verticales. Puis on \u00e9tablit la table de composition de ces transformations.<\/p>\n\n\n\n
%R0: rotation 0\u00b0\n
\"Rendered<\/p>\n%R180: rotation 180\u00b0\n
\"Rendered<\/p>\n%SV: sym\u00e9trie verticale\n
\"Rendered<\/p>\n%SH: sym\u00e9trie horizontale\n
\"Rendered<\/p><\/code><\/pre>\n\n\n\n
\"\renewcommand{\arraystretch}<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Ou encore ce g\u00e2teau:<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\" Conseil cuisine<\/b>
Cuire quatre quatre quarts s\u00e9par\u00e9ment. Etaler de la confiture entre les morceaux. Etaler de la p\u00e2te d’amande entre 2 feuilles de papier sulfuris\u00e9.<\/div>\n\n\n\n
\"\" Lecture<\/b>
Ce lien entre la th\u00e9orie des cat\u00e9gories en math\u00e9matiques et le g\u00e2teau de Battenberg it\u00e9ratif est inspir\u00e9 du livre d’Eugenia Cheng: Comment cuire un neuf<\/i>.<\/td>\"\"<\/td><\/tr><\/table><\/div>\n\n\n\n
\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
Un g\u00e2teau ? non ! la table de multiplication des nombres impairs de 1 \u00e0 7 modulo 8.<\/p>\n","protected":false},"author":1,"featured_media":1105,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-996","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\/996","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=996"}],"version-history":[{"count":152,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/996\/revisions"}],"predecessor-version":[{"id":1682,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/posts\/996\/revisions\/1682"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media\/1105"}],"wp:attachment":[{"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/media?parent=996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/categories?post=996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eva.louis-le-grand.net\/maths\/index.php\/wp-json\/wp\/v2\/tags?post=996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}