Math Monday: The Squared Square

Furniture & Lighting Science Woodworking
Math Monday: The Squared Square

By George Hart for the Museum of Mathematics

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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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See all of George Hart’s Math Monday columns

10 thoughts on “Math Monday: The Squared Square

  1. Anonymous says:

    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 says:

    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 says:

    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). 

    1. James B says:

      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 says:

    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). 

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Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy man’s memoir,” called Borg Like Me.

View more articles by Gareth Branwyn
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