Description

In recreational mathematics, a magic square isan arrangement of distinct numbers (i.e., each number is usedonce), usually integers, in a square grid, where the numbers ineach row, and in each column, and the numbers in the main andsecondary diagonals, all add up to the same number, called the"magic constant."

A magic square has the same number of rows as it has columns,and in conventional math notation, "n" stands for the number ofrows (and columns) it has. Thus, a magic square always contains n2numbers, and its size (the number of rows [and columns] it has) isdescribed as being "of order n." A magic square that contains theintegers from 1 to n2 is called a normal magic square.

Magic squares were known to Chinese mathematicians as early as650 BC, and explicitly given since 570 AD, and to Islamicmathematicians possibly as early as the seventh century AD. Thefirst magic squares of order 5 and 6 appear in an encyclopedia fromBaghdad circa 983, the Encyclopedia of the Brethren of Purity(Rasa'il Ihkwan al-Safa); simpler magic squares were known toseveral earlier Arab mathematicians. Some of these squares werelater used in conjunction with magic letters, as in ShamsAl-ma'arif, to assist Arab illusionists and magicians.

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