Math Monday: The Squared Square

by George Hart

If you’re a cabinet maker, geometry is essential to all of the lengths and angles that you calculate. The cabinet shown here goes further and presents the solution to a rather difficult dissection problem. This is the simplest perfect squared square. The entire area is a square and it is divided into squares of distinct integer sizes.There are twenty one different squares, with the sizes indicated below, covering a 112 by 112 area. Of course, a square can be divided into fewer squares, e.g. four quarters, but then sizes repeat. It has been proven that a square can not be tiled with fewer than twenty one distinct squares.Taking this solution and turning it into a beautiful piece of furniture was the work of Bob Mackay. I love how the compartments open in many different whimsical ways.

This article first appeared on Make: Online, June 13, 2011.

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