# Squaring the square, in glass

As of the **23rd May 2022 this website is archived** and will receive **no further updates**.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Here is my latest stained glass effort, seen on a snowy day.

It is a 'square of squares', where all the constituent squares are of different sizes. Here are the dimensions -

It is copied from the logo of the Trinity Mathematical Society, who point out that it is the *unique smallest simple squared square (smallest in that it uses the fewest squares, and simple in that no proper subset of the squares of size at least 2 forms a rectangle).* It was proved to be the smallest such square by Duijvestijn in 1978, but this was by exhaustive computer search, which seems a bit like cheating.

There is a fine Wikipedia site which contains more than you ever wish to know about squaring-the-square.

## Challenge

I wanted to only use 4 colours without any square touching another of the same colour, and of course I knew this is possible due to the 4-colour theorem. But I wanted the four large outer squares to be 'white' (in order to increase the Mondrian appeal). It took some effort and trial-and-error to find a 4-colouring with this property. Are there others?

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## Comments

Perhaps

Fri, 01/02/2013 - 4:31pm

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## More solutions

Perhaps

Fri, 01/02/2013 - 4:36pm

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## 6 more

whuber

Wed, 06/02/2013 - 4:29pm

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## All solutions

david

Wed, 06/02/2013 - 5:19pm

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## wonderful!

A beautiful array. It is tempting to try a vast stained glass window featuring all of these!

Perhaps

Wed, 06/02/2013 - 6:50pm

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## Field 11 and 19 are the same

whuber

Wed, 06/02/2013 - 9:20pm

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## Correction

jhodsdon

Thu, 26/09/2013 - 4:31pm

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## Challenge