Hyperbolic space is a non-Euclidean geometic form, and it's a hard thing to get one's head around. Mathematicians describe it as a shape with a constant negative curvature--the opposite of a ball, which has a constant positive curve. For years, researchers thought it was impossible to create a physical model of hyperbolic space, but Daina Taimina and her crochet hook proved them wrong. Taimina has since become something of a celebrity for the crafty-geeky set, with her work featured in videos and art shows.
For more, check out Taimina's new book, Crocheting Adventures With Hyperbolic Planes.