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.
Famous quotes containing the word magic:
“The middle years of parenthood are characterized by ambiguity. Our kids are no longer helpless, but neither are they independent. We are still active parents but we have more time now to concentrate on our personal needs. Our children’s world has expanded. It is not enclosed within a kind of magic dotted line drawn by us. Although we are still the most important adults in their lives, we are no longer the only significant adults.”
—Ruth Davidson Bell. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)