Daina Taimina’s Hyperbolic Planes

Daina Taimina’s Hyperbolic Planes

December 18, 2009, 1:50 AM
Filed under: artists in review | Tags: crochet reef, crocheted reef, daina taimina, fractals, great crochet reef, hyperbolic space, margaret wertheim, non-euclidian, spinhandspun, the quick and the dead

Daina Taimina

Hyperbolic space is a non-Euclidean geometic form described by Mathematicians as a shape with a constant negative curvature. Essentially, it is the opposite of a ball. They occur naturally in the curves of lettuce leaves, Chinese wood, and ear mushrooms.

For years, researchers believed creating a physical model of these spaces was impossible, until 1997 when Daina Taimina’s crochet hook proved them wrong.

Born in Latvia, Taimina had been an avid knitter and crocheter since childhood. She and her husband were on a camping trip when she first constructed a plane.

The concept is simple: the crocheter begins with a circle, and frequently increases stitches at a constant rate — for example, one increase for every four stitches — in order to create the ruffled edges which form as it enlarges.

Previously, Taimina had been using frail paper models to familiarize her Cornell University students with hyperbolic space. By constructing crocheted versions, students were able to pick up and handle their physical forms.

In 2006, Margaret Wertheim and The Institute for Figuring adopted Taimina’s technique, inviting crocheters to model our coral reefs in an effort to celebrate their beauty, their underlying mathematical structures, and to encourage conservation efforts.

Like a reef, which is made up of many various sub-reefs, the quality of yarn, style of stitch, and tightness of the crochet all affect the finished forms so that each becomes its own unique living organism.

Since 2006, the project has exploded. This past February, Wertheim presented their efforts at the 2009 TED Conference. The full video is available below.

I had the opportunity to see one of Taimina’s pieces at The Walker this spring for their conceptual show entitled The Quick and the Dead. Though I had already been warned by a guard in an earlier gallery for standing too close to a painting, it took every effort not to reach out and remove the tiny hyperbolic object from its shelf. I envied Taimina’s students — the medium itself proved familiar and inviting, with its formal elements begging to be turned over by hand and observed.

Perhaps the pattern I’ve listed above will come in handy. Sorry knitting… it’s gonna be me and the hook for a while…

For more on hyperbolic space, check out this interview with Taimina and geometer David Henderson.

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