en>BethNaught: clean up, typo(s) fixed: parrallelepiped → parallelepiped (2) using AWB

2015-01-11T15:37:06Z

clean up, typo(s) fixed: parrallelepiped → parallelepiped (2) using AWB

← Older revision		Revision as of 17:37, 11 January 2015
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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],

	~~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}}~~

	~~[[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]].]]~~

	~~:<math>M_3(n) = \frac{n(n^3+1)}{2}.</math>~~

	~~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]].~~

	~~==Alternate definition==~~
	~~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.~~

	~~==[[Multimagic cube]]s==~~
	~~{{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}}~~
	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.~~

	~~==Magic cubes based on Dürer~~'~~s and Gaudi Magic squares==~~
	~~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]

	~~==See also~~==
	~~<div class="references-small" style="-moz-column-count:3; column-count:3;">~~
	* [[Perfect magic cube]]
	* [[Semiperfect magic cube]]
	* [[Multimagic cube]]
	* [[Magic tesseract]]
	* [[Magic hypercube]]
	* [[Magic cube class]]
	* [[Magic series]]
	* [[Asymptotic magic hyper-tesseract]]
	* [[Nasik magic hypercube]]
	* [[John R. ~~Hendricks]]~~
	~~</div>~~

	~~==External links==~~
	* {{MathWorld \|urltitle=MagicCube \|title=Magic Cube}}
	* Harvey Heinz, [http://~~members~~.~~shaw~~.ca/~~hdhcubes/index.htm All about Magic Cubes~~]
	* Marian Trenkler, [http:~~//math.ku.sk/~trenkler/aa-cub-01.pdf Magic p-dimensional cubes]~~
	* Marian Trenkler, [http://~~math~~.~~ku.sk/~trenkler/05-MagicCube.pdf An algorithm for making magic cubes]~~
	* arian Trenkler, [http:~~//www.imi.ajd.czest.pl/zeszyty/zeszyt13/Trenkler.pdf On additive and multiplicative magic cubes]~~
	* [http://~~sites.google~~.~~com/site/aliskalligvaen/home-page Ali Skalli's magic squares and magic cubes]~~

	~~[[Category:Magic squares]~~]

76.111.113.152 at 15:10, 25 January 2014

2014-01-25T15:10:00Z

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69.254.131.117: /* Derivation */ DOS

2012-08-07T05:18:46Z

Derivation: DOS

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Debye model - Revision history

en>BethNaught: clean up, typo(s) fixed: parrallelepiped → parallelepiped (2) using AWB

76.111.113.152 at 15:10, 25 January 2014

69.254.131.117: /* Derivation */ DOS