Magic hypercube (original) (raw)
En mathématiques, un hypercube magique de dimension d est la généralisation d'un carré magique (d = 2), d'un cube magique (d = 3) et d'un tesseract magique (d = 4), c'est-à-dire un ensemble d'entiers strictement positifs arrangés dans un motif de taille n × n × n × ... × n tel que la somme des nombres de chaque pile (le long de chaque axe) ainsi que des (en) principales est égale à un nombre unique, qu'on appelle alors la constante magique de l'hypercube. Le nombre n est appelé l'ordre de l'hypercube.
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| dbo:abstract | In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted Mk(n). If a magic hypercube consists of the numbers 1, 2, ..., nk, then it has magic number . For k = 4, a magic hypercube may be called a magic tesseract, with sequence of magic numbers given by OEIS: . The side-length n of the magic hypercube is called its order. Four-, five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks. Marian Trenkler proved the following theorem:A p-dimensional magic hypercube of order n exists if and only ifp > 1 and n is different from 2 or p = 1. A construction of a magic hypercube follows from the proof. The R programming language includes a module, library(magic), that will create magic hypercubes of any dimension with n a multiple of 4. (en) En mathématiques, un hypercube magique de dimension d est la généralisation d'un carré magique (d = 2), d'un cube magique (d = 3) et d'un tesseract magique (d = 4), c'est-à-dire un ensemble d'entiers strictement positifs arrangés dans un motif de taille n × n × n × ... × n tel que la somme des nombres de chaque pile (le long de chaque axe) ainsi que des (en) principales est égale à un nombre unique, qu'on appelle alors la constante magique de l'hypercube. Le nombre n est appelé l'ordre de l'hypercube. (fr) Een magische hyperkubus is een uitbreiding van een magisch vierkant en de magische kubus. Een magische hyperkubus heeft meer dan drie dimensies, hoewel het magische vierkant en de magische kubus ook als vormen van een magische hyperkubus beschouwd kunnen worden. (nl) Na matemática, um hipercubo mágico é uma extensão do quadrado mágico para diversas dimensões. Isto demonstra que o número de inteiros arranjado da forma padrão n × n × n × ... × n possui uma soma linear padrão para qualquer linha desejada, através de um objeto Mk(n), possuindo assim o número mágico (pt) |
| dbo:wikiPageExternalLink | http://math.ku.sk/~trenkler/Cube-Ref.html http://multimagie.com/indexengl.htm http://www.magichypercubes.com/Encyclopedia http://www.magichypercubes.com/Encyclopedia/d/DynamicNumbering.html http://www.magichypercubes.com/Encyclopedia/index.html http://www.magichypercubes.com/Encyclopedia/k/PathNasiks.zip http://www.multimagie.com/ http://math.ku.sk/~trenkler/05-MagicCube.pdf http://www.magichypercube.com http://homepage2.nifty.com/googol/magcube/en/ http://homepage2.nifty.com/googol/magcube/en/rectangles.htm http://members.shaw.ca/hdhcubes/cube_perfect.htm http://members.shaw.ca/hdhcubes/index.htm%236%20Classes%20of%20Cubes http://www.trump.de/magic-squares/magic-cubes/cubes-1.html http://members.shaw.ca/johnhendricksmath/ |
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| rdfs:comment | En mathématiques, un hypercube magique de dimension d est la généralisation d'un carré magique (d = 2), d'un cube magique (d = 3) et d'un tesseract magique (d = 4), c'est-à-dire un ensemble d'entiers strictement positifs arrangés dans un motif de taille n × n × n × ... × n tel que la somme des nombres de chaque pile (le long de chaque axe) ainsi que des (en) principales est égale à un nombre unique, qu'on appelle alors la constante magique de l'hypercube. Le nombre n est appelé l'ordre de l'hypercube. (fr) Een magische hyperkubus is een uitbreiding van een magisch vierkant en de magische kubus. Een magische hyperkubus heeft meer dan drie dimensies, hoewel het magische vierkant en de magische kubus ook als vormen van een magische hyperkubus beschouwd kunnen worden. (nl) Na matemática, um hipercubo mágico é uma extensão do quadrado mágico para diversas dimensões. Isto demonstra que o número de inteiros arranjado da forma padrão n × n × n × ... × n possui uma soma linear padrão para qualquer linha desejada, através de um objeto Mk(n), possuindo assim o número mágico (pt) In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted Mk(n). If a magic hypercube consists of the numbers 1, 2, ..., nk, then it has magic number . For k = 4, a magic hypercube may be called a magic tesseract, with sequence of magic numbers given by OEIS: . (en) |
| rdfs:label | Hypercube magique (fr) Magic hypercube (en) Magische hyperkubus (nl) Hipercubo mágico (pt) |
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