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. 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. 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. 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. 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. 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