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Build your own magic square

A magic square is a grid of numbers in which any row, column, or diagonal adds up to the same total. They look complex, but it’s actually easy to design your own using the Siamese method.

Magic Square

Adapted from Cantons-de-l’Est [CC BY-SA 4.0], via Wikimedia Commons

First, get an arithmetic progression. That’s any sequence of numbers that increase or decrease by a fixed amount: 1, 2, 3… or 12, 17, 23… or 56, 54, 52…

Make a grid with an odd number of sides. Put the first number in the middle of the top row. Then move up and right (wrapping around to the other side of the grid if necessary) and put the next number. Keep going like this; if the space up and right is full go down a row instead. Once the grid is full, you have your own magic square.

Or, to make it even easier, use the magic square pictured above. Fill in your sequence following the same placement order (i.e. put your first number in place of the 1, the second number in place of the 2, and so forth).

This surprisingly simple technique was brought to France by the 17th century mathematician Simon de la Loubère, who had just returned from Siam (modern day Thailand) – hence the name Siamese method. But he actually learned it from a fellow traveller, who picked it up in turn from an unknown mathematician in the Indian city of Surat.


Categories: Asia Early modern history History Mathematics & statistics Places Sciences

The Generalist

I live in Auckland, New Zealand, and am curious about most things.

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