Knitting mathematics

The latest issue of Science News profiles the work of several mathematicians who crochet and knit incredibly strange surfaces to illustrate certain complicated mathematical principles. For example, two researchers from the University Bristol used their computer algorithm as crochet instructions to create a Lorenz manifold, a shape that emerges from chaotic systems such as weather. Other crafty scientists crocheted Möbius strips, Klein bottles, and hyperbolic planes (seen here). From the article:
 Articles 20061223 A7996 5548 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.
Link

Previously on BB:
• HOWTO crochet a Lorenz manifold Link
• Chaotic crochet Link
• Fabric brain art Link
• Gigantic Klein bottle Link
• Moebius strip playground equipment Link