The project is the brainchild of two sisters, Christine Wertheim and Margaret Wertheim. Daina Taimina of the University of Cornell figured out that using crochet, one can easily create a three-dimensional model of a hyperbolic plane by crocheting in the round and incorporating increases. Thought to be completely theoretical by mathematicians, hyperbolic planes are actually fairly abundant in nature, particularly underwater. It is no coincidence that the Wertheims were inspired by Taimina's work to create crocheted coral reefs to raise awareness of the plight of the earth's oceans.
Here are some that I've made:
The Crochet Coral Reef Project is much like the AIDS quilt, in which many people can contribute and parts of it can be displayed throughout the world. The Community Reef will actually be made up of three separate reefs. The first will be a healthy reef in which many colors and fibers are used; the second will be a bleached reef consisting of only white, gray, and off-white colors; the last is a trash reef made of recycled, found, or trash objects. I'm planning a coral for the trash reef with a trim of soda pop-tabs.
If you're interested in hyperbolic crochet, here's a short article from Interweave Crochet.
If you're more interested in the mathy bits, here's a more substantive article co-authored by Dr. Taimina.
The Smithsonian Community Reef will open October 16, 2010 and run through April 24, 2011 in the Sant Ocean Hall of the Natural History Museum. If you are interested in contributing to the reef, please visit the ravelry group for specifics.