Studio54: Hyperbolic Crochet, Sarah McLeod

Crochet model of hyperbolic plane by Daina Taimina

In 1997 Cornell University mathematician Daina Taimina finally worked out how to make a physical model of hyperbolic space that allows us to feel, and to tactilely explore, the properties of this unique geometry. The method she used was crochet.

Dr Taimina’s inspiration was based on a suggestion that had been put forward in the 1970’s by the geometer William Thurston (also now at Cornell). Noting that one of the qualities of hyperbolic space is that as you move away from a point the space around it expands exponentially, Thurston designed a paper model made up of thin cresent-shaped annuli taped together.

But Thurston’s model is difficult to make, hard to handle, and inherently fragile. Taimina intuited that the essence of this construction could be implemented with knitting or crochet simply by increasing the number of stitches in each row. As you increase, the surface naturally begins to ruffle and crenellate. Taimina, who grew up in Latvia with a childhood steeped in feminine handicrafts, immediately set about making a model. At first she tried knitting - and you can indeed knit hyperbolic surfaces - but the large number of stitches on the needles quickly becomes unmanageable and Taimina realized that crochet offered the better approach.

From the Institute of Figuring

Below are some of my hyperbolic textile works