The Hyperbolic Crochet Coral Reef & other non Euclidean Miscellany


The Institute for Figuring currently have an exhibition in London of their hyperbolic Crochet Coral Reef. A celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world. It literally allows us to think outside of the box! You can check out the Bleached Reef, the Ladies Silurian Reef, the Branched Anemone Garden and the ever-growing Toxic Reef. You’ll also find new environments, the Exploding Plastic Inevitable Reef, the Bearded Reef and the Bottle Tree Grove. What’s more you can add to the exhibition with your own creations if you wish – it’s not too late, there are two more Crochet Nights left to go.

Hyperbolic geometry was developed independently by Nikolai Lobachevski and Farkas Bolyai in the 19th century. It differs from both Euclidean geometry and spherical geometry in that the sum of the angles of a triangle is always less than 180°. Henri Poincare devised a way to visualise infinite two-dimensional hyperbolic space as the interior of a disc Poincare’s tessellation pattern representing an infinitely large hyperbolic plane will be familiar to most through MC Eschers work, notably his Circle Limit series of etchings. Escher came across Poincare’s visualisation via the Geometer Donald Coxeter.

The IFF has published a Field Guide to Hyperbolic Geometry. It’s a highly readable, and at times poetic, exposition of the fantastic world of the Hyperbolas. In it we read of all those names mentioned above and but more importantly the work of mathematician Daina Taimina who worked out a way of making actual physical models of hyperbolic space using a cunning technique – crochet.

‘If, as the Moors believed, repeated patterns connote the divine, we might conclude that Heaven itself would be a hyperbolic space’ – A Field Guide to Hyperbolic Geometry.

‘In the next few years, the WMAP satellite currently taking pictures of the early universe may provide evidence one way or another if its shape and formation is in fact hyperbolic’ – A Field Guide to Hyperbolic Geometry.

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