Mathematicians Get Crafty with Geometry

Crocheted Hyperbolic Plane i i

A model of the hyperbolic plane crocheted by Daina Taimina. Steve Rowell/The Institute For Figuring hide caption

itoggle caption Steve Rowell/The Institute For Figuring
Crocheted Hyperbolic Plane

A model of the hyperbolic plane crocheted by Daina Taimina.

Steve Rowell/The Institute For Figuring
Circular hyperbolic plane i i

Crocheted from the center and spiraling out, this model simulates a circular region around a point on a hyperbolic plane. Steve Rowell/The Institute For Figuring hide caption

itoggle caption Steve Rowell/The Institute For Figuring
Circular hyperbolic plane

Crocheted from the center and spiraling out, this model simulates a circular region around a point on a hyperbolic plane.

Steve Rowell/The Institute For Figuring
Hyperbolic Pants i i

The hyperbolic plane can wrap into a double cylindrical form resembling a pair of pants. Steve Rowell/The Institute For Figuring hide caption

itoggle caption Steve Rowell/The Institute For Figuring
Hyperbolic Pants

The hyperbolic plane can wrap into a double cylindrical form resembling a pair of pants.

Steve Rowell/The Institute For Figuring

The crinkled edges of a lettuce leaf curve and expand in a shape that has perplexed mathematicians for centuries. Those curves — an example of a high-level geometry concept called the hyperbolic plane — were not even defined by geometry theorists until the 19th century. And in the almost 200 years following, mathematicians struggled to find a way to model the complex shape known as the geometric opposite of the sphere.

Then mathematician Daina Taimina picked up her crochet needles and some synthetic yarn, and the problem was solved. In 1997, Taimina, of Cornell University, found a way to crochet her way into "hyperbolic space." Her woolen creations, which resemble crenulated flowers and hair scrunchies, became the first physical models of the hyperbolic plane.

Taimina and her husband, fellow Cornell mathematician David Henderson, are the co-authors of Experiencing Geometry, a widely used textbook on both Euclidean and non-Euclidean spaces. They talk to NPR's Jacki Lyden about hyperbolic geometry and crochet.

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