April 30, 2010
Posted: 09:09 AM ET
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This work of art has a logic to its beauty: It was inspired by a branch of mathematics called hyperbolic geometry. Daina Taimina, adjunct professor at Cornell University, has been making these crochet creations since 1997, both for teaching and for aesthetic value.
Taimina remembers that when she was a student of non-Euclidian geometry, her instructor would tell the class to imagine the concepts being studied. “Why should I trust something I can imagine?” Taimina asks. She wanted to be able to construct something that would represent the complex ideas of higher mathematics. When she began teaching non-Euclidian geometry, crochet allowed her to explain concepts not on a blackboard or computer screen but in something tangible.
Most middle school students are taught Euclidian geometry, which puts forth that if you have a line and a point outside of it, there is only one other line you could draw that would could go through the point and also be parallel to it. This is the case for a two-dimensional plane, on a flat piece of paper, for example. But in hyperbolic space, that is no longer true. “This is something you can really can see only after have crocheted it,” Taimina says. This model illustrates the point: In this space, there are three lines going through the point that will not intersect with the fourth line on the bottom.
The models Taimina uses for instructional purposes take about 10 hours to make. Her largest crochet work took eight months to construct. “In some ways I feel like I’m making sculptures with crocheting,” she said. “I’m interested how long you can crochet the same shape over and over.” The image above is an example of a manifold, which can be folded into an infinite number of shapes without distorting the geometry of the surface.
"Hyperbolic geometry" may sound esoteric, but there are plenty of real-world applications. It describes how skin grows on wounds, so plastic surgeons must be aware of it; for example, in reducing the visibility of scarring after surgery, Taimina said. It also plays a role in computer animation. In nature, you can see hyperbolic geometry in nature all the time, from kale to sea kelp to the holly pictured above.
To learn more, visit Taimina's Web site.
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