A friend on my blog feed recently posted a link to MAKER Saturday Webcasts, which has been running webcasts focusing on creative makers from the SF Bay area every Saturday this summer. Among other very cool things, there's a great discussion of hyperbolic space:

This really isn't news to geeky fiber artists or mathematicians, but several years ago, Cornell mathematician Daina Taimina came up with something that mathematicians had been trying to figure out for years: a way to model hyperbolic space -- using knitting or crochet.

If you follow the link to the MAKER webcasts and scroll down to "Making Hyperbolic Crochet with Margaret Wertheim", you can see a fun interview and discussion about this topic and its convoluted history with Margaret Wertheim of The Institute for Figuring.

This page at The Institute for Figuring's site includes a review and discussion of hyperbolic space and Dr. Taimina's breakthrough in representing this kind of space through crochet (and, if I might say so, quite visually appealing creations).

Favorite quote from the webcast: "Mathematicians spent 2000 years trying to prove that hyperbolic structure was impossible, but sea slugs and nudibranchs didn't know that."

This is very cool stuff, and I really love the interaction of crafts and mathematics as a way to demonstrate how not only do you need math to do crafts (if I have 6 stitches per inch and I want a six inch swatch of fabric, all I need is a simple algebraic equation to figure out how many stitches I need) but you can also make a major breakthrough in mathematics by seeing the world... craftily.