Sunday, September 4, 2011

The Most Magical of Magic Squares

If you’ll pardon some personal history, it’s time to explain why I have included what is known as an order 4 magic square on this blog. The generic term magic square usually refers to a square grid filled with consecutive numbers beginning with 1, and having the property that the sum of the numbers in each row, each column and each of the two diagonals is the same. The total is called the magic constant for the magic square. In the magic square I have included the magic constant is 34 as can easily be verified. Magic squares of any size from order 3 upward can be formed and all of them have the above mentioned property, but some are even more special. Yet, none is as special as the order 4. For example the four numbers in the corners sum to 34, as do the four numbers in the center, and several other symmetrically located sets of four numbers.

When I was in high school my mathematics teacher would give us students one problem each week for which we could earn extra credit. One week he drew a blank 4 x 4 grid on the blackboard and challenged us to go home and fill such a grid with the first 16 numbers in such a way that the sum of the numbers in each row, column and in the two diagonals was the same. At home I struggled and struggled for hours on end until I finally got it. Although that moment was marked with elation, even more significantly in terms of my future, it represented a birth. I was hooked. Numbers were not just numbers anymore. They had personalities. They were pure magic.

Years later I began to claim “ownership” of this square and the number 16. The fact that I was born on the 16th of the month was no longer simply random. I counted the number of letters in my full name and found it was also 16. Through the years this number has appeared in special ways at special times. For example when I was awarded my last teaching position, I found that the mathematics department was housed in a 16-sided building. Now how many buildings with 16 sides are there!

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