Hyperbolic crocheting
Daima Taimina, a Latvian mathematician, crochets objects in two-dimensional hyperbolic space. Such objects have “extra” area. An ordinary pot-holder, 12 inches on a side, has one square foot of area. A hyperbolic pot-holder 12 inches on a side has more than one square foot of area, maybe a lot more, so it has crinkly edges like some kinds of lettuce. In a two-dimensional spherical space, the pot-holder would have less than one square foot of area (in other words, if you draped the pot-holder over a soccer ball, it would have to have less area in order to lie flat). Daima provides the extra area by systematically adding extra stitches as she crochets.
Hyperbolic crochet is also helping more women to explore maths. It is part of a new field called “mathematics and the fibre arts” which includes knitting, quilting and weaving as well as crochet.
The Institute for Figuring has a “crocheted coral reef” exhibit at the Southbank Centre in London.