“Until the 19th century, mathematicians knew about only two kinds of geometry: the Euclidean plane and the sphere. It was therefore a deep shock to their community to find that there existed in principle a completely other spatial structure whose existence was discerned only by overturning a 2000-year-old prejudice about “parallel” lines. The discovery of hyperbolic space in the 1820s and 1830s by the Hungarian mathematician Janos Bolyai and the Russian mathematician Nicholay Lobatchevsky marked a turning point in mathematics and initiated the formal field of non-Euclidean geometry. For more than a century, mathematicians searched in vain for a physical surface with hyperbolic geometry. 
Starting in the 1950s, they began to suggest possibilities for constructing such surfaces. Eventually, in 1997, Daina Taimina, a mathematician at Cornell University, made the first useable physical model of the hyperbolic — a feat many mathematicians had believed was impossible — using, of all things, crochet. Taimina and her husband, David Henderson, a geometer at Cornell, are the co-authors of Experiencing Geometry, a widely used textbook on both Euclidean and non-Euclidean spaces. Margaret Wertheim, founder of the Institute for Figuring and a new regular contributor to Cabinet, spoke to them about crocheting and non-Euclidean geometry.”
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