# Math Monday: The Squared Square

By George Hart for the Museum of Mathematics

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.

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### 5 Responses to Math Monday: The Squared Square

1. Anonymous on said:

That is an impressive bit of furniture making, no question.

However, I do not understand the decision to go with birch plywood for drawer faces and doors. Cost is a factor, sure, but given all the other resources committed to this (time!), a more refined hardwood would seem justified (maple, even alder).

2. Anonymous on said:

That is an impressive bit of furniture making, no question.

However, I do not understand the decision to go with birch plywood for drawer faces and doors. Cost is a factor, sure, but given all the other resources committed to this (time!), a more refined hardwood would seem justified (maple, even alder).

3. Anonymous on said:

That is an impressive bit of furniture making, no question.

However, I do not understand the decision to go with birch plywood for drawer faces and doors. Cost is a factor, sure, but given all the other resources committed to this (time!), a more refined hardwood would seem justified (maple, even alder).

• James B on said:

Model62, I agree.  I’ve built a good bit of furniture, some with that type plywood.  I definitely would have put some edge banding or thin strips of hardwood on the edges of a piece like this.  Besides looking good, it would help prevent the top veneer on the plywood from catching and splintering off.

4. Anonymous on said:

That is an impressive bit of furniture making, no question.

However, I do not understand the decision to go with birch plywood for drawer faces and doors. Cost is a factor, sure, but given all the other resources committed to this (time!), a more refined hardwood would seem justified (maple, even alder).