What is the exact opposite of a sphere?

The answer lies in a special kind of math called hyperbolic geometry: just as a sphere constantly closes in on itself, a hyperbolic plane constantly spreads away from itself. Discovered in the 1800s, hyperbolic geometry is totally different from the common geometry on a flat surface or a sphere that we're all familiar with (it too has a name: Euclidean geometry).

Mathematicians struggled to find a good way to draw or model hyperbolic space so that others could understand it. A breakthrough came in 1997, when Daina Taimina, a professor at Cornell University, thought of using crochet. She crocheted hyperbolic models by constantly adding stitches to a form as she worked outward; the result was a shape that spread away from itself, making waves and ruffles. Taimina's students could hold and bend these yarn models to learn about the rules of hyperbolic geometry.

Hyperbolic geometry is not just an abstract idea; it exists in nature. Plants like lettuce and kelp, and animals like sea slugs, exhibit this geometry in their ruffled edges. Margaret and Christine Wertheim, sisters from Australia who founded an organization called the Institute for Figuring, saw another potential use for Taimina's models: they could be used to create a model coral reef. Corals and many of the creatures that inhabit them have hyperbolic forms.The Wertheims wanted to use the art of crochet to draw attention to the Great Barrier Reef and other reefs that are in serious danger from pollution and global warming.

The Wertheims were flooded with crochet donations from artists around the world. Just like in real reef, small individual pieces grew into a huge and colorful creation. The Hyperbolic Crochet Coral Reef is more than 40 feet long and still growing. The Wertheims hope that this astonishing hybrid of math and art will alert people to the plight of the world's coral reefs before it's too late.

-E.P.

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