Diagonal magic cube
Encyclopedia
A Diagonal Magic Cube is an improvement over the simple magic cube
. It is the second of six magic cube classes
when ranked by the number of lines summing correctly.
In a diagonal magic cube of order m, all 6m of the diagonals in the m planes parallel to the top, front, and sides of the cube must sum correctly. This means that the cube contains 3m simple magic squares of order m.
Because the cube contains so many magic squares, it was considered for many years to be perfect (although other types of cubes were also sometimes called a perfect magic cube
.
It is now known that there are three higher classes of cubes.
The (proper) diagonal magic cube has a total of 3m2 + 6m + 4 correctly summing lines and 3m + 6 simple magic squares.
The new definition perfect magic cube has a total of 13m2 correct lines and 9m pandiagonal magic squares.
NOTE: Traditionally, n has been used to indicate the order of the magic hypercube. However, in recent years, due to the increasing emphasis on higher dimension hypercubes, there is a trend to use m to indicate order and n to indicate dimension.
Magic cube
In 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...
. It is the second of six magic cube classes
Magic cube classes
Every magic cube may be assigned to one of six magic cube classes, based on the cube characteristics.This new system is more precise in defining magic cubes...
when ranked by the number of lines summing correctly.
In a diagonal magic cube of order m, all 6m of the diagonals in the m planes parallel to the top, front, and sides of the cube must sum correctly. This means that the cube contains 3m simple magic squares of order m.
Because the cube contains so many magic squares, it was considered for many years to be perfect (although other types of cubes were also sometimes called a perfect magic cube
Perfect magic cube
In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant....
.
It is now known that there are three higher classes of cubes.
The (proper) diagonal magic cube has a total of 3m2 + 6m + 4 correctly summing lines and 3m + 6 simple magic squares.
The new definition perfect magic cube has a total of 13m2 correct lines and 9m pandiagonal magic squares.
NOTE: Traditionally, n has been used to indicate the order of the magic hypercube. However, in recent years, due to the increasing emphasis on higher dimension hypercubes, there is a trend to use m to indicate order and n to indicate dimension.
External links
- New definition: