While Taimina’s and Osinga’s models have achieved the most fame, a host of other mathematicians in recent years has started crocheting and knitting mathematical shapes. An exhibit of mathematically inspired fiber arts at the 2005 annual Joint Mathematics Meeting in Atlanta boasted an impressive array of such models. In addition to Taimina’s hyperbolic planes and a Lorenz surface crocheted by Yackel, the exhibit featured Möbius strips, which are twisted rings that have only one side, and Klein bottles, which are closed surfaces that have no inside. There were also crocheted versions of the five Platonic solids-the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron-as well as a bricklike fractal object called Menger’s sponge. Continue reading →

Osinga launched her crochet project in the hopes of finally getting her hands on a Lorenz manifold, a mathematical object that she had been studying theoretically for years. Meteorologist Edward Lorenz, now an emeritus professor at the Massachusetts Institute of Technology, had set down three equations in 1963 as a highly simplified description of weather dynamics. These Lorenz equations have tremendous mathematical and historical significance. While simulating the equations’ dynamics on a computer, Lorenz found that tiny round-off errors result in hugely different outcomes, a discovery that launched the field of chaos theory. Continue reading →

In 1997, as Daina Taimina geared up to teach an undergraduate-geometry class, she faced a challenge. As a visiting mathematician at Cornell University, she planned to cover the basic geometries of three types of surfaces: planar, or Euclidean; spherical; and hyperbolic. She knew that everyone can use intuition to conceive of the first two geometries, which are the realms of, say, sheets of paper and basketballs. The hyperbolic plane, however, lies outside of daily experience of the physical world. Continue reading →

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.”

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