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344 pages, Spiral-bound
First published January 1, 2009

(quoted from: http://www.msnbc.msn.com/id/25011806/)
The modern interest in math and craft began in 1997 when Taimina devised a plan for crocheting a hyperbolic plane. Hyperbolic planes are spaces of negative curvature (imagine the shape of a riding saddle) where all lines curve away from each other. Hyperbolic planes are fairly common in nature, appearing everywhere from the frills on a sea slug to growth patterns of coral to the way the brain folds.
The craft objects themselves tend to be common shapes, such as discs, spheres and cones. However, just as a triangle that normally only has 180-degrees worth of angles can have three 90-degree angles when drawn on a sphere, the shapes take on novel and surprising forms when projected across hyperbolic space.
Despite being widespread in nature and well understood in theoretical math, no good physical models of a hyperbolic shape existed until Taimina crocheted her first plane. In hyperbolic space, points move away from each other as the shape expands. While it is hard to model this using paper or plastic, it is easily replicated by simply increasing the number of stitches per row as the shape is knit or crocheted.
“What you can do is get a tactile insight. I theoretically understand the concept, but [the model:] allows me to communicate it,” said Taimina.
After Taimina’s crocheted models gained a degree of notoriety, Hinke Osinga realized that if a hyperbolic plane could be modeled with crochet, then a model of the complex shape her research focused on could be made the same way. Osinga was looking at the Lorenz manifold, another shape that had yet to be presented in a physical model. Manifolds are shapes where the curved nature of the larger shape can be treated as a flat plane over short distances, like a 2-D road map sufficiently representing a portion of the 3-D Earth.
The Lorenz manifold models how objects move through a chaotic space such as a flowing river or the atmosphere. Various applications include meteorological prediction and spacecraft navigation. Before Osinga made her crochet Lorenz manifold, there had never been a physical model of this shape for reference.
Around the same time that Osinga was using craft to answer questions about math, Yackel and Belcastro began their attempt to answer questions raised by craft with math.
Belcastro designed a mathematical proof detailing why any topological surface can be knit. While seemingly limited to explaining yarn work, the proof could have ramifications for biology. A range of phenomena from shell growth to bird’s nest-building replicate knitting by building up a structure one line at a time.