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I love the numbers that make this work even more than I like the idea that inspired it. It defies mathematical logic but works because the knitting is able to just do its own thing, stretching and bending where it wants, in order to lie flat.

It is based on the properties of ‘shapes of constant width’. These are well-known mathematical shapes. These shapes have many practical applications. In some cases they can be used in place of circles. Vending machines cannot differentiate between these shapes and proper circles; they are good for things such as manhole covers where the cover can never fall through the hole. They may not be so good for transport purposes. Shapes of constant width work well for rollers because the top and bottom are always the same distance apart but they do not work for wheels on an axle where the centre moves up and down and the ride would be very jerky.

The simplest shape of constant width is the Reuleaux triangle. It was named after a German engineer, in the late nineteenth century, though the concept pre-dates him. It is based on a equilateral triangle but has curved sides. In UK we have two coins that have constant width. The 50 pence and 20 pence coins both have seven curved sides.

In November 2013 we went again to MathsJam and I was again inspired by Joel Haddley. He is rather more of an academic than I am but the shapes he deals with are very interesting from my geometer’s point of view. Money Spinner literally evolved from a back-of-an-envelope drawing.

He took a 50p coin and drew round it, then moved it and drew round it again. He kept doing this until he had a ‘circle’ of shapes, a bit like you might get in a Spirograph pattern. By missing out part of each drawing it was clear to see that there were 14 identical shapes, each with seven curved sides. Because the sides of the original coin are all the same length, it is self-evident that the 7-sided shapes have seven equal sides. I straightened the sides to make the calculations manageable.

In knitting terms, to make the sides of a shape equal they must have the same number of stitches. My first attempts at knitting the shapes were the kind of thing that is likely to drive you mad. I seemed to be working inside-out and backwards and it was incredibly complex. I could have completed the afghan like this but it would have been impossible to explain to anyone else how to do it. I eventually realised I could start in a different place and could build one shape on top of another with no problem.

The numbers are delightful but, mathematically, completely and utterly wrong! There is only one number you use, and work towards, at any point in the knitting. This means the size can be adjusted because that number can be anything you want it to be.

For the mathematician the numbers don’t make any sense. For a more interesting visual effect, I chose to add some extra lines within the original shapes to create triangles but these did not change any of the dimensions. If the triangle is described as ABC, side AB has the same number of stitches as side BC. Strangely, the other side has the same number of stitches as AB + BC. Under other circumstances, these dimensions could not possibly create a triangle - but the knitting lets it happen. This is just one of the mathematical anomalies that can be found.

This afghan was also interesting because we had previously worked with 3, 4, 6 and 8-sided shapes but had never used seven sides. The nearest we had got was with Wheely Colourful, which had seven sections. Anything using sevenths (and, therefore, fourteenths) always causes problems. Knitting is very forgiving so approximation is near enough.

MONEY SPINNER