BOOK

a field guide to hyperbolic space

We have built a world of rectilinearity. The rooms we inhabit, the skyscrapers we work in, the grid-like arrangement of our streets speak to us in straight lines. Yet outside our boxes the natural world teems with swooping, curving and crenellated forms, from the fluted surfaces of lettuces and kales to the frilled skirts of corals and the animal undulations of sea slugs. All these organisms are biological manifestations of the hyperbolic geometry, a structure mathematicians spend hundreds of years trying to prove impossible. In this short elegant text, Margaret Wertheim offers a poetic introduction to the history of hyperbolic geometry, a radical alternative to the Euclidean variety we learn about in school. The discovery of hyperbolic space in the early nineteenth century ushered in a mathematical revolution that led to the geometry underlying general relativity, which describes the structure of spacetime itself. Wertheim spins an eloquent yarn weaving together the story of hyperbolic mathematics and its relevance to physics and biology. In addition, the book introduces the technique of hyperbolic crochet discovered by Dr. Daina Taimina, and offers a how-to ‘field guide’ to the forms that underlie the celebrated Crochet Coral Reef project created by Margaret and Christine Wertheim.

The book was inspired by a lecture given at the Institute For Figuring by Dr. Daina Taimina and Dr. David Henderson in 2004 as part of the IFF’s “figuring series” curated by Margaret Wertheim