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.