11 March 2005
Vol. 307 No. 5715
Knot theory is no longer the only branch of mathematics that
appeals to the handicrafts set. A big crowd showed up last
month at the Kitchen, one of Manhattan's hippest performance
spaces, to hear a pair of Cornell mathematicians talk about
hyperbolic space. Their main props: crocheted models of objects
in the hyperbolic plane, a central concept in non-Euclidean
In ordinary Euclidean space, a flat plane stretches out forever
and parallel lines never meet, explained geo-meters Daina
Taimina and David Henderson.
However, as mathematicians discovered in the early 1800s,
that's not true in other kinds of space. In the sphere, for
example, parallel lines meet at the poles. In the hyperbolic
plane, which can be thought of as the opposite of the sphere,
parallel lines shy away from each other.
Hyperbolic space is very hard to picture. For more than a
century, mathematicians struggled without notable success
to make 3D models of it. Then Taimina had the idea of using
her crochet hook. She and Henderson use crocheted models in
their classes at Cornell and hope that when people create
and play with the objects--which look like witches' hats,
flamenco skirts, or curly kale--they'll develop an intuitive
sense of what hyperbolic geometry is all about. "We all
play with balls as children. With a sphere, you have that
memory in your hands. But you don't have that with hyperbolic
geometry," says Taimina.
CREDIT: CROCHETED MODEL OF A HYPERBOLIC "PSEUDOSPHERE"
MADE BY DR. DAINA TAIMINA/IMAGE: THE INSTITUTE FOR FIGURING