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| {{about|the mathematical concept|the flashbulb cartridges|Magicube|the puzzle|Rubik's Cube}}
| | Eusebio is the name persons use to call me and I think it's sounds quite good when you say it. Idaho is our birth room. I used to be unemployed but then now I am a fabulous cashier. My partners say it's not really for me but something I love doing is also to bake but I'm thinking on [http://Search.About.com/?q=starting starting] something new. I'm not good at [http://Www.webdesign.org/ web design] but you might aspire to check my website: http://prometeu.net<br><br>My webpage: hack clash of clans; [http://prometeu.net try what she says], |
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| In [[mathematics]], a '''magic cube''' is the [[dimension|3-dimensional]] equivalent of a [[magic square]], that is, a number of [[integers]] arranged in a ''n'' x ''n'' x ''n'' pattern such that the sum of the numbers on each row, each column, each pillar and the four main [[space diagonal]]s is equal to a single number, the so-called [[magic constant]] of the cube, denoted ''M''<sub>3</sub>(''n''). It can be shown that if a magic cube consists of the numbers 1, 2, ..., ''n''<sup>3</sup>, then it has magic constant {{OEIS|id=A027441}}
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| [[Image:Simple Magic Cube.svg|thumb|right|An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a [[simple magic cube]].]]
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| :<math>M_3(n) = \frac{n(n^3+1)}{2}.</math>
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| If, in addition, the numbers on every [[cross section (geometry)|cross section]] diagonal also sum up to the cube's magic number, the cube is called a [[perfect magic cube]]; otherwise, it is called a [[semiperfect magic cube]]. The number ''n'' is called the order of the magic cube. If the sums of numbers on a magic cube's [[broken space diagonal]]s also equal the cube's magic number, the cube is called a [[pandiagonal cube]].
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| ==Alternate definition==
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| In recent years, an alternate definition for the [[perfect magic cube]] has gradually come into use. It is based on the fact that a pandiagonal magic square has traditionally been called '''perfect''', because all possible lines sum correctly. This is not the case with the above definition for the cube.
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| ==[[Multimagic cube]]s==
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| {{Update|inaccurate=yes|reason = see the main article more information has been picked up from MathWorld and other sources about the known cubes|date=October 2011}}
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| As in the case of magic squares, a [[bimagic cube]] has the additional property of remaining a magic cube when all of the entries are squared, a [[trimagic cube]] remains a magic cube under both the operations of squaring the entries and of cubing the entries. (Only two of these are known, as of 2005.) A [[tetramagic cube]] remains a magic cube when the entries are squared, cubed, or raised to the fourth power.
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| ==Magic cubes based on Dürer's and Gaudi Magic squares==
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| A magic cube can be built with the constraint of a given magic square appearing on one of its faces [http://sites.google.com/site/aliskalligvaen/home-page/-magic-cube-with-duerer-s-square Magic cube with the magic square of Dürer], and [http://sites.google.com/site/aliskalligvaen/home-page/-magic-cube-with-gaudi-s-square Magic cube with the magic square of Gaudi]
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| ==See also==
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| <div class="references-small" style="-moz-column-count:3; column-count:3;">
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| * [[Perfect magic cube]]
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| * [[Semiperfect magic cube]]
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| * [[Multimagic cube]]
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| * [[Magic tesseract]]
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| * [[Magic hypercube]]
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| * [[Magic cube class]]
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| * [[Magic series]]
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| * [[Asymptotic magic hyper-tesseract]]
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| * [[Nasik magic hypercube]]
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| * [[John R. Hendricks]]
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| </div>
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| ==External links==
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| * {{MathWorld |urltitle=MagicCube |title=Magic Cube}}
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| * Harvey Heinz, [http://members.shaw.ca/hdhcubes/index.htm All about Magic Cubes]
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| * Marian Trenkler, [http://math.ku.sk/~trenkler/aa-cub-01.pdf Magic p-dimensional cubes]
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| * Marian Trenkler, [http://math.ku.sk/~trenkler/05-MagicCube.pdf An algorithm for making magic cubes]
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| * arian Trenkler, [http://www.imi.ajd.czest.pl/zeszyty/zeszyt13/Trenkler.pdf On additive and multiplicative magic cubes]
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| * [http://sites.google.com/site/aliskalligvaen/home-page Ali Skalli's magic squares and magic cubes]
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| [[Category:Magic squares]]
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Eusebio is the name persons use to call me and I think it's sounds quite good when you say it. Idaho is our birth room. I used to be unemployed but then now I am a fabulous cashier. My partners say it's not really for me but something I love doing is also to bake but I'm thinking on starting something new. I'm not good at web design but you might aspire to check my website: http://prometeu.net
My webpage: hack clash of clans; try what she says,