During the 2002 winter holidays, mathematician Hinke Osinga was relaxing with some lace crochet work when her partner and mathematical collaborator Bernd Krauskopf asked, “Why don’t you crochet something useful?” Some crocheters might bridle at the suggestion that lace is useless, but for Osinga, Krauskopf’s question sparked an exciting idea. “I looked at him, and we thought the same thing at the same moment,” Osinga recalls. “We realized that you could crochet the Lorenz manifold.”

For years, Osinga and Krauskopf, both of the University of Bristol in England, had been studying the Lorenz manifold, a complicated surface that emerges from a model of chaotic weather systems. The pair had created an algorithm to generate 2-dimensional computer visualizations of the surface, but Osinga found the flat images unsatisfying. When Krauskopf asked his question, she suddenly realized that the computer algorithm could be interpreted as crochet instructions. “I had to try it,” she says. Eighty-five hours and 25,511 crochet stitches later, Osinga had a Lorenz manifold almost a meter tall and about 25 centimeters in diameter, which now hangs in the pair’s house as a decoration.

Mathematics has long been an essential tool for the fiber arts. Knitters and crocheters use mathematical principles-often without recognizing them as such-to map the pattern of a cable sweater, for instance, or figure out how to space the stitches when adding a sleeve onto a jacket.

Now, the two crafts are returning the favor. In recent years, mathematicians such as Osinga have started knitting and crocheting concrete physical models of hard-to-visualize mathematical objects. One mathematician’s crocheted models of a counterintuitive shape called a hyperbolic plane are enabling her students and fellow mathematicians to gain new insight into startling properties. Other mathematicians have knitted or crocheted fractal objects, surfaces that have no inside or outside, and shapes whose patterns display mathematical theorems.

“Knitting and crocheting are helping us think about math we already know in a different light,” says Carolyn Yackel, a mathematician at Mercer University in Macon, Ga.

Klarreich, Erica. “CRAFTY GEOMETRY.” Science News 170.26/27 (23 Dec. 2006): 411-413. MasterFILE Premier. EBSCO. [Library name], [City], [State abbreviation]. 8 Apr. 2009 <http://0-search.ebscohost.com.millennium.mohave.edu/login.aspx?direct=true&db=f5h&AN=23560436&site=ehost-live>.