Magic Squares

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In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary 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 of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n." A magic square that contains the integers from 1 to n2 is called a normal magic square.

Magic squares were known to Chinese mathematicians as early as 650 BC, and explicitly given since 570 AD, and to Islamic mathematicians possibly as early as the seventh century AD. The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983, the Encyclopedia of the Brethren of Purity (Rasa'il Ihkwan al-Safa); simpler magic squares were known to several earlier Arab mathematicians. Some of these squares were later used in conjunction with magic letters, as in Shams Al-ma'arif, to assist Arab illusionists and magicians.

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