Woolly Math

One of the many things we love about knitting and crochet - and all the fiber arts - is how it satisfies on many levels: It's fun, it's great to look at, it keeps us warm, no creature needs to suffer in order for us to obtain the materials and it's soothing to the spirit. As many of us know, it's also an excellent way to practice our math skills. Some schools use it to teach the basics and beyond. So, when we discovered this website, we were smitten:

Click here to be transported in the best way.

Click here to be transported in the best way.

Pat Ashforth and Steve Plummer are self-descirbed "mathekniticians". It's the perfect description for two educators who use textile art as one of the vehicles for making mathematics easier to comprehend. Now retired from formal teaching, their knitting and crochet work has expanded well beyond their beginnings and brought them a new kind of notice and a career in design. It's a great story and here's a brief rendition. You can read a more complete version by visiting their website which is filled with fascinating facts and great pictures.

A married British couple, both math teachers were active on an online knitting forum when they were asked to produce an afghan pattern based upon a mathematical  formula. They wound up producing 4 designs and it began a journey that  led them on a new and exciting path. Recognizing that the afghan was the perfect template for expressing math formulas, they employed it as as a canvas and, simultaneously  created some visually exciting works of art.  At last count, that was 90 afghans ago. Take a look at some stunning examples:

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

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

Counting Pane: a grid of the numbers from 1 to 100. Each number cell contains the colors 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

Counting Pane: a grid of the numbers from 1 to 100. Each number cell contains the colors 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

This one is one of my favorites. It also makes me want to crochet.

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

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

Like the math they taught (how I wish one of them had taught me), the patterns are easy to understand and require basic skills. If one wishes to understand theory, it's explained on their website, but a person can undertake it for the sheer enjoyment of sailing along on a work of art, secure in the knowledge that science is in accord. 

Ashforth and Plummer have become celebrities in the world of mathematical crafts. Some of their afghans have been bought by the Science Museum in London. That said, they don't sell their finished products, but they do sell the patterns via their website, which is also filled with information about the mathematical truths behind the  "proof" afghans.  There are also other product patterns offered for sale, including "toys" which demonstrate theory in a playful way. 

This is a knit version of a  popular toy. It is made up from eight cubes, joined in a special way. you can fold and unfold the large cube continuously to reveal several different faces. There is also a crochet version available. 

This is a knit version of a  popular toy. It is made up from eight cubes, joined in a special way. you can fold and unfold the large cube continuously to reveal several different faces. There is also a crochet version available. 

When traversing their website, it quickly becomes apparent that each of the couple have strong right and left brain capabilities. On one hand, they have the ability to visualize a creative way to showcase a mathematical fact, while, on the other, each possesses the ability  to explain how to produce it. Here's a quote from Pat, which says it well:

“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.”  

Both Ashforth and Plummer  are accomplished knitters and, when conducting workshops, they are equal partners in knitting and/or crochet skills.  A recent article in "The Guardian", a British publication, quotes Pat: “We always try to make sure that knitting is not seen as a female activity and Steve always knits at any event to emphasize the point,” says Ashforth. “We find more reluctance from women who say they can’t do math than from men who say they can’t knit.”

Here are a few more "afghan-a-matics" (my word).   

Pythagoras tree: an image based on Pythagoras’s theorem. For each black triangle you see the square on the hypotenuse and the squares on the other two sides. The Science Museum have the original. Photograph: Pat Ashforth.;My comment: Given the colors used, this  one is evocative of african tribal art.  

Pythagoras tree: an image based on Pythagoras’s theorem. For each black triangle you see the square on the hypotenuse and the squares on the other two sides. The Science Museum have the original. Photograph: Pat Ashforth.;My comment: Given the colors used, this  one is evocative of african tribal art.  

 Pseudoku Photograph: Pat Ashforth

 Pseudoku Photograph: Pat Ashforth

Amazement: a knitted maze. Photograph: Pat Ashforth; PERSONAL THOUGHT: THAT CENTER FORMATION MAKES ME THINK OF A KEITH Haring figure.

Amazement: a knitted maze. Photograph: Pat Ashforth; PERSONAL THOUGHT: THAT CENTER FORMATION MAKES ME THINK OF A KEITH Haring figure.

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 colorful 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 math 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.”

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

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

in the next post, we will follow up with a look at their newest fascination: Illusion Knitting. In the meantime, should you wish to visit their site, which contains lots more pictures and information, just click on the header on top. Pat can  be found on Ravelry here. Steve can be found here, and their  group on Ravelry is here. In addition, you will find them on twitter: Pat Ashforth is@matheknitician and Steve Plummer @IllusiveSteve

Steve Plummer & Pat Ashforth: The mathekniticcians themselves

Steve Plummer & Pat Ashforth: The mathekniticcians themselves