magic square
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The simplest of all magic squares (figure 1) is formed by the 9 digits, with 5 in the centre and the even numbers at the corners, so that the sum of any row or column is 15. In figure 2 the numbers 1 to 5 are arranged in any order in the first row; the second commences with the fourth number from the first row and proceeds in the same relative order. The third row starts with the fourth number from the second row, and so on. Figure 3 consists of the numbers 0 to 4 multiplied by 5, and each row starts with the third number from the row above. Adding together the corresponding numbers from figures 2 and 3 produces the magic square in figure 4.
In mathematics, a square array of numbers in which the rows, columns, and diagonals add up to the same total. A simple example employing the numbers 1 to 9, with a total of 15, has a first row of 6, 7, 2, a second row of 1, 5, 9, and a third row of 8, 3, 4.
A pandiagonal magic square is one in which all the broken diagonals also add up to the magic constant.
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