Crocheting Hyperbolic Geometry

Crocheting Hyperbolic Geometry

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Let’s talk about math, shall we? Specifically, here’s a question for you: If I draw a straight line, and then draw a point next to that line, how many lines can you draw through that point that will be parallel to my original line?

If you answered one, then congratulations! You remember as much of high school geometry as I do. But what if I told you that the answer is infinitely many, and that to really understand why that is, you should take up crocheting?

It turns out that the geometry I learned in high school is Euclidean geometry, but there are other kinds of geometry, too. One of those kinds of geometry is hyperbolic geometry–and in hyperbolic geometry, the answer to my earlier question about parallel lines is “infinitely many.”

The really cool part of this is: For years and years and years, mathematicians thought you couldn’t model hyperbolic geometry in the real world. Then Daina Taimina realized in the late 1990s that you can knit or crochet perfect models of this. She has a book called Crocheting Adventures with Hyperbolic Planes, and it looks fabulous.

Also fabulous: This TED talk from 2009, in which Margaret Wertheim talks about crocheting coral reefs, hyperbolic geometry, and the importance of making and modeling things so that all learning doesn’t have to be abstract. Here’s the link to Wertheim’s TED talk again, because seriously, she will make hyperbolic geometry make sense in about 30 seconds by showing off a crocheted model:

As Wertheim says around the 13:10 mark of the TED talk:

We live in a society that completely tends to valorize symbolic forms of representation. Algebraic representations, equations, codes. We live in a society that’s obsessed with presenting information in this way, teaching information in this way. But through… crochet, [and] other plastic forms of play, people can be engaged with the most abstract, high powered, theoretical ideas, the kind of ideas that normally you have to go to university departments to study in higher mathematics, which is where I first learned about hyperbolic space. But you can do it through playing with material objects.

Have you tried any hyperbolic crocheting? I haven’t done it yet, but I want to! Maybe I can use some of my upcoming time off to give it a whirl.


Image Credit: “Crocheted hyperbolic pseudosphere, completed — my favorite side” by Flickr user Cheryl

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