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Math Trek

Magic Square Physics

3:57pm, June 30, 2006

The study of magic squares has a long, long history. In ancient Babylonian times, these array of numbers were held to have magical powers. Over the years, they have also served as protective charms and religious symbols.

At the recreational level, they're fun for all ages, says Peter Loly of the University of Manitoba.

Loly himself has investigated the "physical" properties of magic squares—treating the numbers of each such square as physical quantities.

A magic square is a square matrix drawn as a grid filled with numbers. It consists of a set of integers arranged in the form of square so that the numbers in each row, column, and diagonal all add up to the same total. If the integers are consecutive numbers from 1 to n2, the square is said to be of nth order. The magic sum itself is given by n(n2 + 1)/2.

Suppose, for example, you interpret the numbers as masses. You can then determine a magic square's moment of iner

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