A Field Guide to Hyperbolic Space: An Exploration of the Intersection of Higher Geometry and Feminine Handicraft
Margaret Wertheim

For two thousand years mathematicians knew about only two kinds of geometry – the plane and the sphere. But in the early nineteenth century they became aware of another space in which lines cavorted in aberrant formations. Offending reason and common sense, this new space came to be known as the hyperbolic plane, in homage to its abundant excess of parallel lines. Though the formalities of this space were known for 200 years, it was only in 1997 that mathematician Daina Taimina finally worked out how to make a physical model of the hyperbolic plane. The method she used was crochet. Here, IFF director Margaret Wertheim presents a brief history of hyperbolic space and a field guide to its crocheted manifestations.

This olive green seedpod-like model is a double spiral. It was made by beginning with a line of chain stitch and then crocheting around the line on both sides. The resulting form is akin to two hyperbolic planes joined at the baseline.
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An Institute for Figuring publication, 2005, paperback, 99 pages