Layers of Meaning

Crocheted Math

My own math skills tend to be limited to mathematics that have a visible component. Geometry is wonderful. Trigonometry is fun too. Calculus gets a bit dicey and I remain perennially confused about logarithms. I was delighted when I discovered that a crocheter has used her talents to create previously un-creatable mathematical shapes.

"For thousands of years mathematicians believed there were just 2 types of geometry, the plane and the sphere. But another more aberrant structure lurks beneath the surface of Euclid's laws - one that has been illuminated through the art of crochet." Institute for Figuring

" The crinkled edges of a lettuce leaf curve and expand in a shape that has perplexed mathematicians for centuries. Those curves -- an example of a high-level geometry concept called the hyperbolic plane -- were not even defined by geometry theorists until the 19th century. And in the almost 200 years following, mathematicians struggled to find a way to model the complex shape known as the geometric opposite of the sphere. Then mathematician Daina Taimina picked up her crochet needles and some synthetic yarn, and the problem was solved. In 1997, Taimina, of Cornell University, found a way to crochet her way into 'hyperbolic space.' Her woolen creations, which resemble crenulated flowers and hair scrunchies, became the first physical models of the hyperbolic plane." All Things Considered

When asked how she decided to crochet hyperbolic planes, Taimina explains:

"Many students and mathematicians... wanted to have a more direct experience of hyperbolic geometry - an experience similar to handling a physical sphere. In 1868, the Italian mathematician Eugenio Beltrami ... made a version of his model by taping together long skinny triangles - the same principle behind the flared gored skirts some folk dancers wear. In the 1970s the American geometer William Thurston had described a model of hyperbolic space that could be made by taping together a series of paper annuli, or thin circular strips. All these models were time-consuming to make and hard to handle; they are fragile and they tear easily. I realized that Thurston's construction could be made with knitting or crochet - basically all you'd have to do is increase the number of stitches in each row. I grew up in Latvia doing these handicrafts and I decided to try and make one. At first I tried knitting, but after a while you had so many stitches on the needles it became impossible to handle. I realized that crochet was the best method." Cabinet Magazine