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April 30, 2010

Geek Out!: Crochet sculptures teach higher math

Posted: 09:09 AM ET

Editor's note: Geek Out! posts feature the latest and most interesting in nerd-culture news. From scifi and fantasy to gadgets and science, if you can geek out over it, you can find it on Geek Out! Look for Geek Out! posts on CNN's SciTech blog.

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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Filed under: Geek Out! • Mathematics

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e.b   April 30th, 2010 2:14 pm ET

some great artist have said that they felt closer to mathmeticians than they did to artists.

eilis_artis   April 30th, 2010 5:29 pm ET

Great idea! I was a math major in college and am an avid crocheter.

MissKat – how about putting that scrap yarn to better use – plenty of hospitals and organizations need lapghans and afghans for patients and clients. Your local VA hospital could surely use some.

Franko   April 30th, 2010 10:42 pm ET

Looks like a poisonous sea creature.

carolen   May 1st, 2010 2:35 am ET

An excellent way to replace my now defunct reef tank. These look alot like coral . I plan to build a reef using these creations. Exciting just thinking about it!!!!

Franko   May 1st, 2010 8:13 am ET

Would be an amusing Java script, various mathematical creatures fighting and eating each other - maybe replace my aquarium screen saver ?

Ellipses, parabolas, hyperbolas, cycloids, fractals, in an all you can eat or be eaten survival smörgåsbord. - Put ketchup on the last one.

janet   May 1st, 2010 10:31 pm ET

I think Taimina's book Crocheting Adventures with the Hyperbolic Planes gives a better explanation of this than TED talk

Sency   May 3rd, 2010 3:33 am ET

Very interesting use of sculptures

Jen   May 3rd, 2010 9:39 am ET

Like the lovely lichens....different colors than I have ever seen. Is that a basket? Could you do them in reeds?

Franko   May 4th, 2010 8:44 am ET

Complexity from simple sequences
Interact the sequences and model something alive.

Weaving + Fundamental Theorem of Arithmetic « The way I see it, Barry.   May 10th, 2010 8:13 am ET

[...] anyone is interested in other Art+Math stuff, here's an interesting article from CNN about the intersect of Crocheting and Hyperbolic Geometry. [...]

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