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	Carrés magiques
Débutants Carrés magiques	Carré magique 4 x 4				Glossaire Carrés magiques
INDEX Carrés magiques Ordres Constructions Magie Jeux de grilles Jeux et énigmes	Carré 4 x 4	Décompte		Formules	Propriétés
	Dürer – Mélancolie		Subirach – Sagrada Familia		Autres
			Romain LV
		Sommaire de cette page >>> Caractéristiques du carré pseudo-magique >>> Le carré magique >>> Configurations basiques et autres >>> 101 configurations magiques

Sagrada Familia – BARCELONE

Carré pseudo-magique 4 x 4

La façade de la basilique de Barcelone – La Sagrada Familia d'Antoni Gaudi – a été décorée par Josep Maria Subirachs (1987).

Elle présente douze groupes de sculptures dont le baiser de Judas (ou la trahison de Judas) flanqué d'un carré magique.

Subirachs avait demandé qu'il puisse utiliser son style personnel, afin de ne pas créer de confusion avec l'œuvre originale de Gaudí.

Caractéristiques du carré pseudo-magique
Contrairement à un carré magique conventionnel, les nombres utilisés ne sont pas les nombres de 1 à 16, mais les nombres 10 et 14 sont doublés et les nombres 12 et 16 sont absents. Ce carré est cependant très intéressant: il contient 101 combinaisons de somme magique.	La somme (lignes, colonnes et diagonales) est 33 et non 34. Ce nombre représente l'âge du Christ à sa mort (fait non-scientifiquement confirmé). Il est formé de "3", symbole de la trinité divine dans le Christianisme.

Le carré magique
Ce carré est bien magique de par ses sommes: 33 Il n'est pas orthodoxe quant aux nombres utilisés: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 13, 14, 14, 15} Il existe 1 680 manières de choisir quatre nombres parmi cette liste; il y en a 88 avec la somme 33 dont 53 sans redondance.

Configurations
Huit carrés réguliers Quelques carrés présentant des configurations remarquables: H et V pour sommes horizontales et verticales; CS: Carrés des sommets D: Diagonales; CC: Avec carré au centre; D2: Diagonales espacées de 2; C2: Carrés avec espace de 2; et B2: Bandes de deux. Sommes 33 Les 30 sommes utilisées sont présentées dans le tableau du dessous à gauche avec repère du type de configuration. Les autres sommes égales à 33 sont listées dans le tableau de droite.
Liste des 88 sommes avec les redondances (du fait des double 10 et double 14) [1, 3, 14, 15], [1, 3, 14, 15], [1, 4, 13, 15], [1, 4, 14, 14], [1, 5, 13, 14], [1, 5, 13, 14], [1, 6, 11, 15], [1, 7, 10, 15], [1, 7, 10, 15], [1, 7, 11, 14], [1, 7, 11, 14], [1, 8, 9, 15], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 11, 13], [1, 9, 10, 13], [1, 9, 10, 13], [2, 3, 13, 15], [2, 3, 14, 14], [2, 4, 13, 14], [2, 4, 13, 14], [2, 5, 11, 15], [2, 6, 10, 15], [2, 6, 10, 15], [2, 6, 11, 14], [2, 6, 11, 14], [2, 7, 9, 15], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 11, 13], [2, 8, 9, 14], [2, 8, 9, 14], [2, 8, 10, 13], [2, 8, 10, 13], [2, 10, 10, 11], [3, 4, 11, 15], [3, 5, 10, 15], [3, 5, 10, 15], [3, 5, 11, 14], [3, 5, 11, 14], [3, 6, 9, 15], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 11, 13], [3, 7, 8, 15], [3, 7, 9, 14], [3, 7, 9, 14], [3, 7, 10, 13], [3, 7, 10, 13], [3, 8, 9, 13], [3, 9, 10, 11], [3, 9, 10, 11], [4, 5, 9, 15], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 11, 13], [4, 6, 8, 15], [4, 6, 9, 14], [4, 6, 9, 14], [4, 6, 10, 13], [4, 6, 10, 13], [4, 7, 8, 14], [4, 7, 8, 14], [4, 7, 9, 13], [4, 8, 10, 11], [4, 8, 10, 11], [4, 9, 10, 10], [5, 6, 7, 15], [5, 6, 8, 14], [5, 6, 8, 14], [5, 6, 9, 13], [5, 7, 8, 13], [5, 7, 10, 11], [5, 7, 10, 11], [5, 8, 9, 11], [5, 8, 10, 10], [6, 7, 9, 11], [6, 7, 10, 10], [6, 8, 9, 10], [6, 8, 9, 10]

101 configurations magiques
Il existe 101 configurations magiques comme les huit exposées ci-dessus. La liste complète est donnée ci-dessous. Les 18 premiers (bleu sur la liste) sont illustrés en carré colorés. Les 18 configurations avec [1, 3, 14, 15] en jaune
Liste des 101 configurations magiques [1, 3, 14, 15], [2, 4, 13, 14], [5, 7, 10, 11], [6, 8, 9, 10] [1, 3, 14, 15], [2, 4, 13, 14], [5, 8, 9, 11], [6, 7, 10, 10] [1, 3, 14, 15], [2, 4, 13, 14], [5, 8, 10, 10], [6, 7, 9, 11] [1, 3, 14, 15], [2, 6, 11, 14], [4, 7, 9, 13], [5, 8, 10, 10] [1, 3, 14, 15], [2, 6, 11, 14], [4, 9, 10, 10], [5, 7, 8, 13] [1, 3, 14, 15], [2, 7, 10, 14], [4, 5, 11, 13], [6, 8, 9, 10] [1, 3, 14, 15], [2, 7, 10, 14], [4, 6, 10, 13], [5, 8, 9, 11] [1, 3, 14, 15], [2, 7, 10, 14], [4, 8, 10, 11], [5, 6, 9, 13] [1, 3, 14, 15], [2, 7, 11, 13], [4, 5, 10, 14], [6, 8, 9, 10] [1, 3, 14, 15], [2, 7, 11, 13], [4, 6, 9, 14], [5, 8, 10, 10] [1, 3, 14, 15], [2, 7, 11, 13], [4, 9, 10, 10], [5, 6, 8, 14] [1, 3, 14, 15], [2, 8, 9, 14], [4, 5, 11, 13], [6, 7, 10, 10] [1, 3, 14, 15], [2, 8, 9, 14], [4, 6, 10, 13], [5, 7, 10, 11] [1, 3, 14, 15], [2, 8, 10, 13], [4, 5, 10, 14], [6, 7, 9, 11] [1, 3, 14, 15], [2, 8, 10, 13], [4, 6, 9, 14], [5, 7, 10, 11] [1, 3, 14, 15], [2, 10, 10, 11], [4, 6, 9, 14], [5, 7, 8, 13] [1, 3, 14, 15], [2, 10, 10, 11], [4, 7, 8, 14], [5, 6, 9, 13] [1, 3, 14, 15], [2, 10, 10, 11], [4, 7, 9, 13], [5, 6, 8, 14] [1, 4, 13, 15], [2, 3, 14, 14], [5, 7, 10, 11], [6, 8, 9, 10] [1, 4, 13, 15], [2, 3, 14, 14], [5, 8, 9, 11], [6, 7, 10, 10] [1, 4, 13, 15], [2, 3, 14, 14], [5, 8, 10, 10], [6, 7, 9, 11] [1, 4, 13, 15], [2, 6, 11, 14], [3, 7, 9, 14], [5, 8, 10, 10] [1, 4, 13, 15], [2, 7, 10, 14], [3, 5, 11, 14], [6, 8, 9, 10] [1, 4, 13, 15], [2, 7, 10, 14], [3, 6, 10, 14], [5, 8, 9, 11] [1, 4, 13, 15], [2, 7, 10, 14], [3, 9, 10, 11], [5, 6, 8, 14] [1, 4, 13, 15], [2, 8, 9, 14], [3, 5, 11, 14], [6, 7, 10, 10] [1, 4, 13, 15], [2, 8, 9, 14], [3, 6, 10, 14], [5, 7, 10, 11] [1, 4, 13, 15], [2, 10, 10, 11], [3, 7, 9, 14], [5, 6, 8, 14] [1, 4, 14, 14], [2, 3, 13, 15], [5, 7, 10, 11], [6, 8, 9, 10] [1, 4, 14, 14], [2, 3, 13, 15], [5, 8, 9, 11], [6, 7, 10, 10] [1, 4, 14, 14], [2, 3, 13, 15], [5, 8, 10, 10], [6, 7, 9, 11] [1, 4, 14, 14], [2, 5, 11, 15], [3, 7, 10, 13], [6, 8, 9, 10] [1, 4, 14, 14], [2, 5, 11, 15], [3, 8, 9, 13], [6, 7, 10, 10] [1, 4, 14, 14], [2, 6, 10, 15], [3, 7, 10, 13], [5, 8, 9, 11] [1, 4, 14, 14], [2, 6, 10, 15], [3, 8, 9, 13], [5, 7, 10, 11] [1, 4, 14, 14], [2, 6, 10, 15], [3, 9, 10, 11], [5, 7, 8, 13] [1, 4, 14, 14], [2, 7, 9, 15], [3, 6, 11, 13], [5, 8, 10, 10] [1, 4, 14, 14], [2, 7, 11, 13], [3, 5, 10, 15], [6, 8, 9, 10] [1, 4, 14, 14], [2, 7, 11, 13], [3, 6, 9, 15], [5, 8, 10, 10] [1, 4, 14, 14], [2, 8, 10, 13], [3, 5, 10, 15], [6, 7, 9, 11] [1, 4, 14, 14], [2, 8, 10, 13], [3, 6, 9, 15], [5, 7, 10, 11] [1, 4, 14, 14], [2, 8, 10, 13], [3, 9, 10, 11], [5, 6, 7, 15] [1, 4, 14, 14], [2, 10, 10, 11], [3, 6, 9, 15], [5, 7, 8, 13] [1, 4, 14, 14], [2, 10, 10, 11], [3, 7, 8, 15], [5, 6, 9, 13] [1, 4, 14, 14], [2, 10, 10, 11], [3, 8, 9, 13], [5, 6, 7, 15] [1, 5, 13, 14], [2, 6, 10, 15], [3, 7, 9, 14], [4, 8, 10, 11] [1, 5, 13, 14], [2, 6, 10, 15], [3, 9, 10, 11], [4, 7, 8, 14] [1, 5, 13, 14], [2, 6, 11, 14], [3, 7, 8, 15], [4, 9, 10, 10] [1, 5, 13, 14], [2, 7, 9, 15], [3, 6, 10, 14], [4, 8, 10, 11]	[1, 5, 13, 14], [2, 7, 10, 14], [3, 4, 11, 15], [6, 8, 9, 10] [1, 5, 13, 14], [2, 7, 10, 14], [3, 6, 9, 15], [4, 8, 10, 11] [1, 5, 13, 14], [2, 7, 10, 14], [3, 9, 10, 11], [4, 6, 8, 15] [1, 5, 13, 14], [2, 8, 9, 14], [3, 4, 11, 15], [6, 7, 10, 10] [1, 5, 13, 14], [2, 10, 10, 11], [3, 6, 9, 15], [4, 7, 8, 14] [1, 5, 13, 14], [2, 10, 10, 11], [3, 7, 8, 15], [4, 6, 9, 14] [1, 5, 13, 14], [2, 10, 10, 11], [3, 7, 9, 14], [4, 6, 8, 15] [1, 6, 11, 15], [2, 3, 14, 14], [4, 7, 9, 13], [5, 8, 10, 10] [1, 6, 11, 15], [2, 3, 14, 14], [4, 9, 10, 10], [5, 7, 8, 13] [1, 6, 11, 15], [2, 4, 13, 14], [3, 7, 9, 14], [5, 8, 10, 10] [1, 6, 11, 15], [2, 7, 10, 14], [3, 8, 9, 13], [4, 5, 10, 14] [1, 6, 11, 15], [2, 8, 9, 14], [3, 7, 10, 13], [4, 5, 10, 14] [1, 6, 11, 15], [2, 8, 10, 13], [3, 7, 9, 14], [4, 5, 10, 14] [1, 7, 10, 15], [2, 3, 14, 14], [4, 5, 11, 13], [6, 8, 9, 10] [1, 7, 10, 15], [2, 3, 14, 14], [4, 6, 10, 13], [5, 8, 9, 11] [1, 7, 10, 15], [2, 3, 14, 14], [4, 8, 10, 11], [5, 6, 9, 13] [1, 7, 10, 15], [2, 4, 13, 14], [3, 5, 11, 14], [6, 8, 9, 10] [1, 7, 10, 15], [2, 4, 13, 14], [3, 6, 10, 14], [5, 8, 9, 11] [1, 7, 10, 15], [2, 4, 13, 14], [3, 9, 10, 11], [5, 6, 8, 14] [1, 7, 10, 15], [2, 6, 11, 14], [3, 8, 9, 13], [4, 5, 10, 14] [1, 7, 10, 15], [2, 8, 9, 14], [3, 5, 11, 14], [4, 6, 10, 13] [1, 7, 10, 15], [2, 8, 9, 14], [3, 6, 10, 14], [4, 5, 11, 13] [1, 7, 10, 15], [2, 8, 9, 14], [3, 6, 11, 13], [4, 5, 10, 14] [1, 7, 10, 15], [2, 8, 10, 13], [3, 5, 11, 14], [4, 6, 9, 14] [1, 7, 11, 14], [2, 3, 13, 15], [4, 5, 10, 14], [6, 8, 9, 10] [1, 7, 11, 14], [2, 3, 13, 15], [4, 6, 9, 14], [5, 8, 10, 10] [1, 7, 11, 14], [2, 3, 13, 15], [4, 9, 10, 10], [5, 6, 8, 14] [1, 7, 11, 14], [2, 4, 13, 14], [3, 5, 10, 15], [6, 8, 9, 10] [1, 7, 11, 14], [2, 4, 13, 14], [3, 6, 9, 15], [5, 8, 10, 10] [1, 7, 11, 14], [2, 6, 10, 15], [3, 8, 9, 13], [4, 5, 10, 14] [1, 7, 11, 14], [2, 8, 9, 14], [3, 5, 10, 15], [4, 6, 10, 13] [1, 7, 11, 14], [2, 8, 10, 13], [3, 5, 10, 15], [4, 6, 9, 14] [1, 7, 11, 14], [2, 8, 10, 13], [3, 6, 9, 15], [4, 5, 10, 14] [1, 7, 11, 14], [2, 8, 10, 13], [3, 6, 10, 14], [4, 5, 9, 15] [1, 8, 9, 15], [2, 3, 14, 14], [4, 5, 11, 13], [6, 7, 10, 10] [1, 8, 9, 15], [2, 3, 14, 14], [4, 6, 10, 13], [5, 7, 10, 11] [1, 8, 9, 15], [2, 4, 13, 14], [3, 5, 11, 14], [6, 7, 10, 10] [1, 8, 9, 15], [2, 4, 13, 14], [3, 6, 10, 14], [5, 7, 10, 11] [1, 8, 9, 15], [2, 6, 11, 14], [3, 7, 10, 13], [4, 5, 10, 14] [1, 8, 9, 15], [2, 7, 10, 14], [3, 5, 11, 14], [4, 6, 10, 13] [1, 8, 9, 15], [2, 7, 10, 14], [3, 6, 10, 14], [4, 5, 11, 13] [1, 8, 9, 15], [2, 7, 10, 14], [3, 6, 11, 13], [4, 5, 10, 14] [1, 8, 9, 15], [2, 7, 11, 13], [3, 6, 10, 14], [4, 5, 10, 14] [1, 8, 10, 14], [2, 3, 13, 15], [4, 5, 10, 14], [6, 7, 9, 11] [1, 8, 10, 14], [2, 3, 13, 15], [4, 6, 9, 14], [5, 7, 10, 11] [1, 8, 10, 14], [2, 4, 13, 14], [3, 5, 10, 15], [6, 7, 9, 11] [1, 8, 10, 14], [2, 4, 13, 14], [3, 6, 9, 15], [5, 7, 10, 11] [1, 8, 10, 14], [2, 4, 13, 14], [3, 9, 10, 11], [5, 6, 7, 15] [1, 8, 10, 14], [2, 5, 11, 15], [3, 6, 10, 14], [4, 7, 9, 13] [1, 8, 10, 14], [2, 5, 11, 15], [3, 7, 9, 14], [4, 6, 10, 13] [1, 8, 10, 14], [2, 5, 11, 15], [3, 7, 10, 13], [4, 6, 9, 14] [1, 8, 10, 14], [2, 6, 10, 15], [3, 5, 11, 14], [4, 7, 9, 13]

Les deux dernières configurations

Suite	Carré diabolique de Dürer Carré de la Sainte Famille Exemple de calcul sur un carré 4 x 4 Carré 4 x 4 en cercles Carré 5 x 5 Carrés magiques – Index
Voir	Carrés – les nombres Carrés en géométrie Carrés mystérieux Dominos magiques Géométrie Humour Jeux	Jeux de chiffres Nombres consécutifs Nombres magiques - Index Pannumérique Rubriques débutants Sudoku Propriétés du carré magique
Diconombre	Nombre 3 / Nombre 15 / Nombre 34
Sites	Liens vers les sites carrés magiques Order 4 Magic Squares – Harvey Heinz – Plus que complet, y compris la liste des 880 carrés magiques.
Cette page	http://villemin.gerard.free.fr/Wwwgvmm/CarreMag/Sagrada.htm