Crocheting Adventures with the Hyperbolic Planes

A sphere has a constant positive curvature, a banana has positive and negative curvature. A surface with constant negative curvature, called a hyperbolic plane, has been traditionally difficult to visualize. While attending a geometry workshop in 1997 at Cornell, Daina Taimina saw the fragile paper models of hyperbolic planes used by mathematicians to visual theses complex shapes. She decided to try to make more durable models, and did so by crocheting them. Daina’s curvy creations, made of yarn, are a great example of art influencing mathematics and vice-versa.