{"id":1077,"date":"2019-12-19T09:32:23","date_gmt":"2019-12-19T08:32:23","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=1077"},"modified":"2020-02-18T17:30:29","modified_gmt":"2020-02-18T16:30:29","slug":"le-carre-luoshu","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/12\/19\/le-carre-luoshu\/","title":{"rendered":"Le carr\u00e9 Luoshu"},"content":{"rendered":"

La premi\u00e8re r\u00e9f\u00e9rence \u00e0 un carr\u00e9 magique est une l\u00e9gende chinoise associ\u00e9e \u00e0 la rivi\u00e8re Luohe, un affluent du fleuve Jaune, qui eut son heure de gloire pendant le mill\u00e9naire pr\u00e9c\u00e9dant notre \u00e8re, quand la ville de Luoyang, b\u00e2tie sur ses rives, \u00e9tait capitale de la Chine. Ses multiples versions parlent toutes d\u2019une tortue portant d\u2019\u00e9tranges inscriptions sur son dos.<\/p>\n

Une tortue l\u00e9gendaire<\/h2>\n

Pour calmer le dieu de la rivi\u00e8re, \u00e0 chaque inondation, les habitants d\u2019un village menac\u00e9 d\u2019\u00eatre englouti lui offraient des sacrifices en vain. Cependant, ils remarqu\u00e8rent qu\u2019\u00e0 chaque fois, une tortue venait sur les lieux du sacrifice et repartait. Le dieu du fleuve n\u2019en tenait cure jusqu\u2019\u00e0 ce qu\u2019un jour, un enfant remarqua des formes curieuses sur le dos de l\u2019animal.<\/em><\/p>\n

\"\"
Dos de la tortue selon la l\u00e9gende<\/figcaption><\/figure>\n

Dans chaque ligne, chaque colonne et chaque diagonale, le nombre \u00e9tait le m\u00eame. Ainsi, les villageois comprirent que le dieu du fleuve demandait quinze sacrifices, et purent l\u2019apaiser\u2026<\/em><\/p>\n

Les carr\u00e9s magiques<\/h2>\n

Ce carr\u00e9 est depuis appel\u00e9 \u00ab\u00a0carr\u00e9 Luoshu\u00a0\u00bb du nom de la rivi\u00e8re. Il a vite conquis le Moyen-Orient puis la Gr\u00e8ce o\u00f9 il \u00e9tait connu de Pythagore. Il est toujours utilis\u00e9 comme amulette porte-bonheur et dans des exercices divinatoires. De nos jours, ces carr\u00e9s o\u00f9 les sommes des nombres des lignes, colonnes et diagonales sont identiques sont appel\u00e9s \u00ab\u00a0carr\u00e9s magiques\u00a0\u00bb, preuve de l\u2019antique croyance. On peut de plus ajouter une contrainte, celle de n\u2019utiliser que les premiers nombres donc ceux de 1 \u00e0 9, dans le cas d\u2019un carr\u00e9 d\u2019ordre trois, et ceux de 1 \u00e0 16 pour ceux d\u2019ordre quatre. Avec cette derni\u00e8re contrainte, il n\u2019existe aucun carr\u00e9 d\u2019ordre deux\u00a0: vous pouvez disposer les nombres de 1 \u00e0 4 comme vous le voulez, le carr\u00e9 form\u00e9 ne sera jamais magique. De ce fait, les pythagoriciens en faisaient un symbole du chaos. Aux sym\u00e9tries pr\u00e8s, le carr\u00e9 d\u2019ordre trois est unique, c\u2019est le Luoshu (voir \u00e0 la fin de cet article). De nos jours, les \u00e9sot\u00e9riques pr\u00e9f\u00e8rent l\u2019\u00e9crire de fa\u00e7on \u00e0 faire appara\u00eetre le nombre 618 en premi\u00e8re ligne car ce sont les premi\u00e8res d\u00e9cimales du nombre d\u2019or. Pour eux, il devient ainsi doublement magique.<\/p>\n

Le carr\u00e9 magique d’ordre 3<\/h2>\n
\"\"
Carr\u00e9 magique d’ordre 3 faisant appara\u00eetre les d\u00e9cimales du nombre d’or.<\/figcaption><\/figure>\n

Sch\u00e9ma de preuve<\/h2>\n

Si les cases du carr\u00e9 contiennent tous les nombres de 1 \u00e0 9, la somme de toutes les cases est 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9, c\u2019est-\u00e0-dire 45. Les sommes de toutes les rang\u00e9es et des diagonales sont donc \u00e9gales \u00e0 45 divis\u00e9 par 3, soit 15. Selon leur place, les nombres participent \u00e0 4, 3 ou 2 sommes \u00e9gales \u00e0 15. En partant d\u2019un nombre initial, comme 1, nous examinons le nombre de d\u00e9compositions donnant 15 en tout. Pour 1, il en existe deux : 9 + 5 et 8 + 6. En op\u00e9rant ainsi, nous obtenons le tableau :<\/p>\n

\"\"<\/p>\n

Ce tableau permet de remplir le carr\u00e9.<\/p>\n","protected":false},"excerpt":{"rendered":"

La premi\u00e8re r\u00e9f\u00e9rence \u00e0 un carr\u00e9 magique est une l\u00e9gende chinoise associ\u00e9e \u00e0 la rivi\u00e8re Luohe, un affluent du fleuve Jaune, qui eut son heure de gloire pendant le mill\u00e9naire pr\u00e9c\u00e9dant notre \u00e8re, quand la ville de Luoyang, b\u00e2tie sur ses rives, \u00e9tait capitale de la Chine. Ses multiples versions parlent toutes d\u2019une tortue portant … Continuer la lecture de Le carr\u00e9 Luoshu<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":1078,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[8,63,29],"tags":[401,403,402],"class_list":["post-1077","post","type-post","status-publish","format-aside","has-post-thumbnail","hentry","category-enigmes","category-histoire","category-maths-2","tag-carre-magique","tag-chine","tag-luoshu","post_format-post-format-aside"],"yoast_head":"\nLe carr\u00e9 Luoshu, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/12\/19\/le-carre-luoshu\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le carr\u00e9 Luoshu, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"La premi\u00e8re r\u00e9f\u00e9rence \u00e0 un carr\u00e9 magique est une l\u00e9gende chinoise associ\u00e9e \u00e0 la rivi\u00e8re Luohe, un affluent du fleuve Jaune, qui eut son heure de gloire pendant le mill\u00e9naire pr\u00e9c\u00e9dant notre \u00e8re, quand la ville de Luoyang, b\u00e2tie sur ses rives, \u00e9tait capitale de la Chine. 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