In 1996 two British maths teachers active on an internet knitting forum were asked by a US yarn firm to design it an afghan.
“We were sent into a panic! We had no idea what an afghan was!” remembers Pat Ashforth, who with partner Steve Plummer were known in the crafts community for their maths-inspired knits.
The couple soon discovered that an afghan was a knitted or crocheted blanket or throw. They produced four designs for the US firm, and it began a journey that has defined the rest of their lives.
Ashforth and Plummer decided that the afghan was the perfect canvas for expressing mathematical ideas - and since then they have devoted much of their time to producing as many as they could.
Together they have knitted and crocheted about 90 mathematical afghans. (Math-ghans?) Since each afghan takes about 100 hours to complete, this means the total time spent they have spent making them is about 9,000 hours (which adds up to 375 days - more than a year). And they have also made many other mathematical objects in wool (scroll below to see).
Ashforth and Plummer go under the name of Woolly Thoughts, and they have become celebrities in the world of the mathematical crafts. Some of their afghans have even been bought by the Science Museum in London.
The couple met while teaching at a school in Luton. By 1999 were both working at a school in Nelson, Lancashire, where they married in 2005. Originally the afghans were hung in their classrooms. “They were invaluable as a vehicle for talking about maths, says Ashforth. “Large, touchable, unbreakable items were perfect for encouraging group discussion. It is much easier for everyone to be looking at the same thing than for each individual to have their own separate book.”
Then the time came when there were not enough walls in their classrooms. “We bought a four storey Victorian house just for the size of its walls so we could hang things on them. Several live on a trolley that rolls out from under the bed, after Steve added pieces to make it higher.”
As their profile grew in the maths community, Ashforth and Plummer have travelled widely to give demonstrations at events such as science festivals, schools and craft exhibitions.
“We always tried to make sure that knitting was not seen as a female activity and Steve always knits at any event to emphasise the point,” says Ashforth. “We find more reluctance from women who say they cant do maths than from men who say they can’t knit.”
I first got to know Ashforth when out of the blue she sent me the image above of a crocheted afghan based on a page in Snowflake Seashell Star, the maths colouring book I did with Edmund Harriss. (Called Patterns of the Universe in the US).The image is of a 9x9 grid of three superimposed sudokus, where each of the digits represents a different colour. I had always felt that this image would make a great quilt - so it was nice to see it made into one! They also made a similar knitted version, below:
Not only are the images in the afghans mathematical, but the way they are made also involves mathematical thinking.
“We enjoy the challenge of seeing an idea then working out how it can be made into an afghan in a way that would be easy enough for anyone else to recreate. It is like trying to solve a puzzle and refining it to give the best possible solution.”
On their website if you click on any of the afghans you will be led to a page on the kniting and crochet site ravelry where the patterns can be bought for a small fee.
Ashforth says that another part of the enjoyment of making the afghans is seeing “the effect we have had on children, either directly by them seeing our big colourful blankets and suddenly understanding something they had previously struggled with, or because other teachers have used our ideas (not always in knitted form) to help teach maths in an unconventional way.
“And influencing the lives of so many (most often women) maths-phobics who would not dream of becoming involved with anything mathematical in other circumstances.”
Some more math-ghans before we move on to other soft furnishings...
Speaking of Pythogoras, the next image is surely the most tactile of all proofs of his theorem. Since the triangles are identical, and the areas of both sides are identical, the cushion shows that the square on the hypotenuse (one side) is equal to the square on the other two sides (the other side). Ashforth guarantees that the number of blue stitches on either side are equal!
The Tower of Hanoi is a well-known mathematical game. And now soft to touch.
The next one is the same thing as those wooden cubes you may have played with as a child. But quieter. “This is very tactile, and impossible to put down,” says Ashforth.
Napier’s bones - a device to facilitate calculation invented by John Napier in the seventeenth century - are now unbreakable.
The flat shapes made using five cubes joined together are the polyominoes. And they fit nicely together themselves!
A hexaflexagon is a strip of paper (or knitted/crocheted yarn) folded into triangles so it makes a hexagon.
And finally - the mathekniticians!
All images © Pat Ashforth & Steve Plummer
Don’t forget to check out woollythoughts.com where there is much more information about all these designs. And follow them on Twitter: Pat Ashforth is @matheknitician and Steve Plummer @IllusiveSteve
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I’m the author of several books on maths, as well as the children’s book Football School: Where Football Explains the World. Martyn Heather, Head of Education and Welfare at the Premier League said: “This book will spark a love of learning in any child who reads it. It is intelligent, inspiring, funny, and deserves a large audience!”
You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian puzzle blog.