Saturday, May 2, 2009

Hyperbolic geometry that links crochet and coral

This fascinating TED talk video describes the connections between coral reefs, crochet, and hyperbolic geometry.

If you don't know about hyperbolic geometry, you're not alone (and you're in for a treat.) The TED video gives a nice introduction to the basic idea of hyperbolic geometry, contrasting it to the more familiar Euclidian geometry taught in high school as well as the somewhat less familiar spherical geometry.

For more information about hyperbolic space, check out Williams College math professor Colin Adams' fast-talking alter ego "Mel Slugbate" and his pitch selling real estate in hyperbolic space. You can see a video of Mel's sales pitch as well as his overhead slides on this MSRI webpage.

It turns out that it's remarkably difficult to create 3-d physical models of hyperbolic space using the usual rigid materials (e.g., paper) traditionally employed by geometers. Moreover, such materials are fragile and difficult to manipulate for exploration. However, Cornell mathematician Daina Taimina has discovered that crochet is an ideal medium for constructing sturdy and beautiful models of hyperbolic space, such the hyperbolic plane shown above.

You can see some of her beautiful models and some simple directions here. She has also recently published a book Crocheting Adventures with Hyperbolic Planes with more information.

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