魔術正方體：修订间差异
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{{about|the mathematical concept|the flashbulb cartridges|Magicube|the puzzle|Rubik's Cube}} |
{{about|the mathematical concept|the flashbulb cartridges|Magicube|the puzzle|Rubik's Cube}} |
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[[File:Simple Magic Cube.svg|thumb|right|一個3 × 3 × 3簡易魔術正方體的例子。 In this example, no slice is a magic square. In this case, the cube is classed as a [[简易魔术正方体]].]] |
[[File:Simple Magic Cube.svg|thumb|right|一個3 × 3 × 3簡易魔術正方體的例子。 In this example, no slice is a magic square. In this case, the cube is classed as a [[简易魔术正方体]].]] |
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以[[数学]]方面論述，'''魔術正方體''' 在[[維度]]上相當於[[幻方]]，也就是以''n'' × ''n'' × ''n'' 方式排列的方體，在每個線段交點填上任意不重複的[[整数]]，並使得每行、每列及每個柱上數字的和相同。而此立方體的[[幻方常數]]表示為''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> |
以[[数学]]方面論述，'''魔術正方體''' 在[[維度]]上相當於[[幻方]]，也就是以''n'' × ''n'' × ''n'' 方式排列的方體，在每個線段交點填上任意不重複的[[整数]]，並使得每行、每列及每個柱上數字的和相同。而此立方體的[[幻方常數]]表示為''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，則可以證明該數列列為「魔術常數」。{{OEIS|id=A027441}} |
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:<math>M_3(n) = \frac{n(n^3+1)}{2}.</math> |
:<math>M_3(n) = \frac{n(n^3+1)}{2}.</math> |
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2018年3月27日 (二) 03:43的版本
此條目介紹的是the mathematical concept。关于the flashbulb cartridges，请见「Magicube」。关于the puzzle，请见「Rubik's Cube」。
以数学方面論述，魔術正方體 在維度上相當於幻方，也就是以n × n × n 方式排列的方體，在每個線段交點填上任意不重複的整数，並使得每行、每列及每個柱上數字的和相同。而此立方體的幻方常數表示為M3(n).[1]若魔術立方體由數列1, 2, ..., n3構成，則可以證明該數列列為「魔術常數」。（OEIS數列A027441）
If, in addition, the numbers on every 截面 (幾何) 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 diagonals 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.
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如同魔術方塊一般， 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.[1] (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 Magic cube with the magic square of Dürer, and Magic cube with the magic square of Gaudi
See also
References
- ^ 1.0 1.1 W., Weisstein, Eric. Magic Cube. mathworld.wolfram.com. [2016-12-04] （英语）.
External links
- 埃里克·韦斯坦因. Magic Cube. MathWorld.
- Harvey Heinz, All about Magic Cubes
- Marian Trenkler, Magic p-dimensional cubes
- Marian Trenkler, An algorithm for making magic cubes
- Marian Trenkler, On additive and multiplicative magic cubes
- Ali Skalli's magic squares and magic cubes