查看“魔術正方體”的源代码

{{about|數學上的魔術立方體|益智玩具|魔術方塊}}
[[File:Simple Magic Cube.svg|thumb|right|一個3&nbsp;&times;&nbsp;3&nbsp;&times;&nbsp;3[[简易魔术正方体]]的例子]]
在[[数学]]中，'''魔術正方體'''指[[維度|三維]]的[[幻方]]，也就是排列成''n''&nbsp;&times;&nbsp;''n''&nbsp;&times;&nbsp;''n''正方體的一組不重複[[整數]]，其中每行、每列、每個柱及四條{{tsl|en|Space diagonals||空間對角線}}上數字的和均相同，等於立方體的[[幻方常數]]，記為''M''<sub>3</sub>(''n'')。<ref name=":0">{{Cite web|url=http://mathworld.wolfram.com/MagicCube.html|title=Magic Cube|last=W.|first=Weisstein, Eric|website=mathworld.wolfram.com|language=en|access-date=2016-12-04}}</ref>若魔術立方體由數列1, 2, ..., ''n''<sup>3</sup>構成，則可以證明其幻方常數為{{OEIS|id=A027441}}
:<math>M_3(n) = \frac{n(n^3+1)}{2}</math>
另外，如果每個[[截面 (幾何)|截面]]對角線上的數字之和亦等於幻方常數，則稱此立方體為{{tsl|en|perfect magic cube||完美魔方}}；否則，稱其為{{tsl|en|semiperfect magic cube||半完美魔方}}。數字''n''稱為魔方的階。如果幻方{{tsl|en|broken space diagonal||破碎空間對角線}}上的數字和也等於幻方常數，則稱其為[[泛對角線立方體]]。

==參見==
{{colbegin||20em}}
* {{tsl|en|Magic hypercube||魔術超立方體}}
* {{tsl|en|Magic series||魔術系列}}
* {{tsl|en|Nasik magic hypercube||Nasik魔術超立方體}}
* {{tsl|en|John R. Hendricks||John R. Hendricks}}
{{colend}}

== 注釋 ==
{{reflist}}

==外部連結==
* {{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]
* Marian Trenkler, [https://web.archive.org/web/20120321091253/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:魔術正方體]]
[[Category:趣味數學]]
[[Category:幻方]]