Far from the research laboratories and hallowed halls of Academia, across the Atlantic Ocean, a young girl, aged 13, stands mesmerized in front of a knitted afghan displayed at the annual North-East Math Fair, in Lancashire, England. Constructed of one hundred brightly colored squares, the intricately striped fabric is the creation of Pat Ashforth and Steve Plummer, of Woolly Thoughts. Knitters, teachers, mathematicians and partners, Pat and Steve have found that basic mathematical principles make for beautiful knitwear designs, and that knitting is an excellent way of explaining complex theorems to their students.
Vibrating with color, and reminiscent of African Kente cloth, it’s hard to believe that the Counting Panes afghan was created as a teaching tool. Within its one hundred brightly colored squares, in ten columns and ten rows, however, lie lessons in multiplication, division, pattern and numerical relationships. Says Pat, “At its most basic the afghan offers a very graphic way for children to understand the difference between odd and even, and to realize that this is really the same as knowing if a number is divisible by 2.” Even the average person, however, who considers they have a reasonable grasp of the numbers 1-100, may find that the piece raises interesting questions about the relationships between the colors. Why is there a backward sloping line of orange? Why does green always appear with baby blue?
Questions like these were posed to the 13 year old girl at the math fair. Pat spoke with her about the patterns she was seeing, and her responses suggested that she had a very logical train of thought, as well as a thorough understanding of the concepts they were discussing. They were shocked to find that she was in a “useless at math”, low-ability class, and that she hadn’t really wanted to attend the fair at all. Her teacher had made her come. The young girl returned to “Counting Panes” again and again, throughout the day, bringing with her a succession of friends and, finally, her math teacher. When she began to describe the relationships and patterns in the afghan, her teacher was astounded. It is easy to see why Counting Panes remains the perpetual favorite of the teachers from Lancashire who created it.
Pat Ashforth took up knitting seriously in 1986, as a way of regaining mobility in her hands and arms, after a battle with serious illness left her with restricted strength. A mathematician’s fascination with simple geometric shapes led her to explore what she could make out of knitted squares, and a limited palette. She began by using up an inheritance of countless balls of wool that her mother had left her, all in various shades of blue. Pat’s father had been a policeman, and every year Pat’s mother had knit him a sweater. “There was always wool left over,” she says, “But as she never seemed to use the same blue twice, I was left with all this wool in different shades of blue.”
Working in simple garter stitch, which (as fans of Elizabeth Zimmerman know) is one of the few stitch patterns that will create a true square, with the number of rows equal to the number of cast on stitches, Pat constructed diagonally knit squares. She later joined these to make simple sweaters. By dividing each square diagonally, and knitting each half in different shades of blue, the educator in her delighted to discover a design with limitless potential for lessons on rotation, reflection, symmetry and tessellation – a mathematical term used to describe how pieces that fit together form a pattern. When she wore her geometric sweaters to class, she says, “The kids were always coming up and touching me, tracing the shapes with their fingers.”
Steve Plummer, a mathematician with arts training, arrived at the school where Pat was teaching, and also took an interest in Pat’s knitting, realizing the tremendous teaching value inherent in her creations. She soon taught him to knit, and they spent hours together creating mathematical models. Romance blossomed over the knitting needles, and they are now partners in every sense of the word. They spent several years designing sweaters based on mathematical principles, but it wasn’t until Brown Sheep Yarn saw their sweater designs, and suggested that the couple design an afghan based on mathematical principles, that their mathematical models really took off.
The increased size of their new canvas allowed them to represent mathematical models on a much larger scale than ever before. Their first designs for Brown Sheep Yarns – simple mosaics of bi-colored squares – opened their eyes to the possibilities inherent in their new “blanket canvas”. They went on to create Counting Panes, and hundreds of other intricately patterned, and wittily named pieces – Square Deal, Best of Both Whirls, and Take Five — both for their beauty and their worth as mathematical models.
These geometrically based patterns have all been applied to knit wear, although it is their value as teaching tools that forms the basis for most of their work. “[The Brown Sheep commission] was a real breakthrough in our designing careers,” said Steve. “But,” added Pat, “Our main function is still as Mathematics teachers”. The afghan continues to be their favored form, as Pat explains, “They feel nice and look good. They can be touched, and counted. There is just so much math we can get out of them.” It is clear that Pat and Steve have created a model for both design and teaching, which they can use, quite literally, to infinite potential.