en>Frietjes: cleanup (wikitables, html markup, layout, etc.)

2014-07-02T23:37:39Z

cleanup (wikitables, html markup, layout, etc.)

en>Knecht03: reference

2013-07-19T22:59:57Z

reference

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			{{Merge to\|Magic hypercube\|discuss=Talk:Magic hypercube#Merge from 4\|date=November 2010}}
			In [[mathematics]], a '''magic tesseract''' is the [[Four-dimensional space\|4-dimensional]] counterpart of a [[magic square]] and [[magic cube]], that is, a number of [[integers]] arranged in an ''n'' × ''n'' × ''n'' × ''n'' pattern such that the sum of the numbers on each pillar (along any axis) as well as the main [[space diagonal]]s is equal to a single number, the so-called [[magic constant]] of the [[tesseract]], denoted ''M''<sub>4</sub>(''n''). It can be shown that if a magic tesseract consists of the numbers 1, 2, ..., ''n''<sup>4</sup>, then it has magic constant {{OEIS\|id=A021003}}

			:<math>M_4(n) = \frac{n(n^4+1)}{2}.\,</math>

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			== Perfect magic tesseract ==
			If, in addition, the numbers on every [[cross section (geometry)\|cross section]] diagonal also sum up to the tesseract's magic constant, the tesseract is called a '''perfect magic tesseract'''; otherwise, it is called a '''semiperfect magic tesseract'''.

			==Alternative Definition==
			The above assumes that one of the older definitions for perfect magic cubes is used. See [[Magic Cube Classes]].
			The '''''Universal Classification System for Hypercubes''''' (John R. Hendricks) requires that for any dimension hypercube, ''all'' possible lines sum correctly for the hypercube to be considered ''perfect'' magic. Because of the confusion with the term ''perfect'', '''''nasik''''' is now the preferred term for ''any'' magic hypercube where '''''all''''' possible lines sum to ''S''. Nasik was defined in this manner by C. Planck in 1905. A nasik magic tesseract has 40 lines of ''m'' numbers passing through each of the m<sup>4</sup> cells.

			The smallest possible ''nasik'' magic tesseract is of order 16; its magic constant is 524296. The first one was discovered by retired [[meteorologist]] [[John R. Hendricks]] from [[British Columbia]] in 1999 with the help of [[Cliff Pickover]] at the [[IBM Thomas J. Watson Research Center]] in [[Yorktown Heights]], [[New York]] after about ten hours of computing time on an [[IBM]] [[IntelliStation]] computer system.

			== See also ==

			* [[Magic hypercube]]
			* [[Magic hypercubes]]
			* [[Nasik magic hypercube]]
			* [[John R. Hendricks]]

			== References ==
			* Andrews, W.S., ''Magic Squares and Cubes'', Dover, Publ., 1960, this is a facsimile of an Open Court 1917 edition. Two essays on 'octahedrons' (pages 351 - 375 written by Kingsley and Planck.

			* Hendricks, John R., ''Magic Squares to Tesseract by Computer'', Self-published, 1998, 0-9684700-0-9

			* Hendricks, John R., ''All Third-Order Magic Tesseracts'', Self-published, 1999, 0-9684700-2-5

			* Hendricks, John R., ''Perfect n-Dimensional Magic Hypercubes of Order 2<sup>''n''</sup>'', Self-published, 1999, 0-9684700-4-1.

			* Heinz, H.D., & Hendricks, J.R., ''Magic Square Lexicon: Illustrated'', HDH, 2000, 0-9687985-0-0

			* Unfortunately, all of Hendricks books (except the Lexicon) are now out-of-print. Some are available for download in PDF from his web site. All are available at the Strens Recreational Mathematics Collection (Univ. of C.)

			==External links==
			* [http://members.shaw.ca/johnhendricksmath/ John Hendricks Math]
			* [http://www.ucalgary.ca/lib-old/sfgate/strens/index.html University of Calgary, Strens Rec. Math * [http://math.ku.sk/~trenkler/06-MagicTesseract.pdf Marian Trenkler: An algorithm for magic tesseract] Collections]
			* [http://members.shaw.ca/tesseracts/ 11 pages about magic tesseracts]

			{{DEFAULTSORT:Magic Tesseract}}
			[[Category:Magic squares]]

en>Hmainsbot1: AWB general fixes and, delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)

2012-07-21T16:18:22Z

AWB general fixes and, delink dates per WP:DATELINK, WP:YEARLINK and MOS:UNLINKYEARS using AWB (8097)

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Perfect magic cube - Revision history

en>Frietjes: cleanup (wikitables, html markup, layout, etc.)

en>Knecht03: reference

en>Hmainsbot1: AWB general fixes and, delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)