All of these sums are equal to fifteen. The mysterious number fifteen is known as the magical constant. Muhammad s work in the mathematical arts consisted of developing a system to come up with higher order magical squares. The order of a magic square is found by counting the number of rows and columns. For example, the magic square that appeared on the divine turtle Lo Shu, above is of order three.
All magic squares have an odd order.
The odd order is necessary because an even order square does not comply with every property of a magic square. For example, one can have an even order in which the columns and rows add to the same. However, the diagonals of the square will not sum to the same magical constant. The numbers will repeat themselves, and in a true magical square the numbers are used only once. The numbers used in a magic square can be found by multiplying the number of rows by the number of columns.