|
|
|
|
|
Magic CubeIn mathematics, a magic cube is the 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 diagonals is equal to a single number, the so-called magic constant of the cube, denoted M3(n). It can be shown that if a magic cube consists of the numbers 1, 2, ..., n³, then it has magic constant -
An example of a 3 × 3 × 3 magic cube follows: Top slice: 8 24 10 12 7 23 22 11 9 Middle slice: 15 1 26 25 14 3 2 27 13 Bottom slice: 19 17 6 5 21 16 18 4 20 Note that in this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube. If, in addition, the numbers on every 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 diagonals also equal the cube's magic number, the cube is called a pandiagonal cube. An 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. See also External link
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|