Find all your DIY electronics in the MakerShed. 3D Printing, Kits, Arduino, Raspberry Pi, Books & more!

By George Hart for the Museum of Mathematics

Math_Monday_banner02_600px.jpg

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.

squared square closed 482x600 Math Monday: The Squared Square

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.

squared square Math Monday: The Squared Square

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.

squared square open Math Monday: The Squared Square

More:
See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.


Related
blog comments powered by Disqus

Related Supplies at Maker Shed

Follow

Get every new post delivered to your Inbox.

Join 26,133 other followers