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Hyperbolic Space

The Crochet Reef Project was inspired by the technique of hyperbolic crochet originally developed by Dr Daina Taimina, a mathematician at Cornell. In 1997 Dr Taimina discovered how to make models of the geometry known as "hyperbolic space" using the art of crochet. Until that time many mathematicians believed it was impossible to construct physical models of hyperbolic forms; yet nature had been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry in their anatomies - among them kelps, corals, sponges, sea slugs and nudibranchs. Thus the Crochet Reef not only looks like a coral reef, it draws on the same underlying geometry endemic in the oceanic realm.

A mathematically precise model of a hyperbolic pane by Dr. Diana Taimina.

There are very good reasons why marine organisms take on hyperbolic forms: this geometry is a marveous way to maximize surface area in a imited volume, thereby providing greater opportunity for filter feeding by stationary organisms.

A crochet model that resembles various species of kelp.

Throughout the organic realm, nature has found ways to utiize hyperbolic forms. Such structures are realized not only in the marine word, but also in cactuses, succulents, and fungi. The double-sided hyperbolic plane seen here is specifcally found in certain kinds of seed pods - the large surface area enables the seed to float on the wind and carry for long distances. Many green leafy vegetables such as lettuces and kales also embody hyperbolic geometry, so you often eat hyperbolic froms for lunch.

As a sister project to the Crochet Reef, the Institute For Figuring has been making a cactus garden. Images of the Crochet Cactus Garden may be seen here.