Crocheting mathematician brings principle into reach

note: this Newsday article appeared on p. A5 of the Wilmington News Journal on March 6, 2005, under the headline
Crocheting mathematician brings principle into reach

the Newsday article is at
http://www.nynewsday.com/entertainment/ny-cool2-knit,0,3420694.story
for more information on this topic, with a gallery of crocheted and other illustrations, see
http://www.theiff.org/lectures/05a.html

The science of knitting

March 2, 2005

A 200-year-old hole in the fabric of mathematics has finally been mended.

In a recent lecture at The Kitchen theater in Chelsea, a brainy -- and dexterous -- Cornell mathematician described how she made a real-life model of a principle that has mystified scientists for centuries. She crocheted it.

Since the early 1800s, mathematicians have known about something called "hyperbolic space," but they couldn't figure out a way to illustrate it. Enter Daina Taimina. After watching her husband, fellow mathematician David Henderson, make a rather flimsy version out of paper, she decided to use her knowledge of handicrafts to create a more durable one. When her knitted model proved too droopy, she tried crocheting it with coarse synthetic yarn and the rendering turned out exactly as she had hoped.

One of the models is now on display at the Smithsonian, and the scientific community is abuzz with requests for her handicrafts.

So what is hyperbolic space? "The easiest way of understanding it is that it's the geometric opposite of a sphere," Taimina says. "On a sphere, the surface curves in on itself and is closed. But on a hyperbolic plane, the surface is space that curves away from itself at every point."

Still confused? That's where her models come in. Verbal descriptions are so hard to understand that, until recently, only a small group of mathematicians really knew what it all meant. And even they overlooked naturally occurring examples, like some kinds of lettuce and seaweed.

Now, using the crocheted models, fifth graders are learning about hyperbolic planes. Neurosurgeons also find the models useful because the planes' surface is similar to that of the brain. Henderson says scientists speculate that this kind of folding allows the brain to store information and retrieve it more quickly than if the surface were stretched out flat. Even cartoons can benefit from the models. Pixar animators use this kind of geometry to make certain surfaces, like fabric and skin, appear three-dimensional on screen.