91av

Yes, it’s a crocheted coral reef. But don’t laugh. These sumptuous swirls of wool hide some serious geometry.

It all started in the mathematics department at Cornell University in Ithaca, New York, where was studying – a surreal world in which surfaces don’t follow the usual rules. In a flat plane, distance increases linearly as you move away from a point, but a hyperbolic plane expands exponentially. Such geometry works, but is notoriously hard to visualise.

While fragile models of hyperbolic planes had been made by gluing together repeating paper shapes, Taimina realised she could make more durable versions using crochet, by increasing the number of stitches in each row as she crocheted around a point. The crenulated balls that emerged worked perfectly, and even led to some new results, since Taimina could test out her equations by crocheting them (91av, 22 December 2001, p 38).

Sisters Margaret and Christine Wertheim, founders of the , which celebrates aesthetic aspects of maths and science, teamed up with Taimina in 2004 to make more models, and noticed their similarity to coral. Mathematicians through most of history didn’t realise it, but hyperbolic structures appear throughout nature, for example in frilly lettuces. Corals use them to maximise their surface area in contact with nutrient-rich seawater.

The Wertheims stitched a dizzying variety of coral-like shapes, and the was born. A blend of maths and handicrafts, it aims to raise awareness of the damage being done to corals across the world from global warming and pollution. The reef has since been exhibited around the world, and has received contributions from more than 100 women (and two men). Its woolly fans and tentacles will be draped through until 17 August.

Endangered species – Learn more about the conservation battle in our comprehensive special report.