Meet the mathekniticians – and their amazing woolly maths creations

Married couple Pat Ashforth and Steve Plummer have been knitting and crocheting mathematical images and objects fore more than two decades

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 is known in the crafts community for 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.

Counting
Counting Pane: a grid of the numbers from 1 to 100. Each number cell contains the colours of the numbers from 1 to 10 that divide it, with 1 being blue, 2 being yellow, 3 red, and so on. So 12, which is divisible by 1, 2, 3, 4 and 6 has the colours of blue, yellow, red, green and black. A copy of this was sold to the Science Museum. Photograph: Pat Ashforth

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 can.

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.

Square
Square Deal: the smallest possible example of a square divided into smaller squares, where the sides of each of the squares are all whole numbers, and where no two squares are the same size. Photograph: Pat Ashforth

Ashforth and Plummer go under the name of Woolly Thoughts, and have become celebrities in the world of the mathematical crafts. Some of their afghans have even been bought by the Science Museum in London.

Double
Double Base: A representation of binary numbers. Photograph: Pat Ashforth

The couple met while teaching at a school in Luton. By 1999 they 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.

Curve
Curve of Pursuit: Ashforth and Plummers most popular pattern. The edges of the squares represent four points that are each moving towards each other. Each point is closing in on the next point clockwise to it. Photograph: Pat Ashforth

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 cant knit.

Psesudoku:
Psesudoku: A crochet version of three superimposed Sudoku patterns. Photograph: Pat Ashforth

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 (its called Patterns of the Universe in the US). The image is of a 9×9 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:

Pseudoku
Pseudoku Photograph: Pat Ashforth

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.

Amazement:
Amazement: a knitted maze. Photograph: Pat Ashforth

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…

About
About Turn: half-and-half diagonally knitted squares. Photograph: Pat Ashforth

Spacecraft:
Spacecraft: Hilbert open Peano curve. Photograph: Pat Ashforth

Fibo-optic:
Fibo-optic: Fibonacci sequence in two directions on the face of a cube Photograph: Pat Ashforth

Finite
Finite field: crochet representation of a finite field Photograph: Pat Ashforth

Rule
Rule of three: an impossible triangle Photograph: Pat Ashforth

Scaled
Scaled up: dragon curves Photograph: Pat Ashforth

Penrose:
Penrose: This was based on a drawing that Sir Roger Penrose sent to Ashforth and Plummer, involving his own Penrose tiles. Photograph: Pat Ashforth