Hooking Up Manifolds

lorenz manifold

I love crochet. I spent a huge number of hours doing it when I was young, and only in later years did I realize that the same things that attracted it to me then are the same things that drive and motivate a lot of my research interests. (I many have mentioned this before, but it’s worth saying again).

It’s the love of patterns, plain and simple. If your child -of whetever gender- gets interested in any form of needlework, please don’t be shortsighted about it and to try to direct them away from the interest to other more “appropriate” things. You never know where it might lead to, and what they might discover on the way1.

So as you can imagine, I was delighted to see a Science News article about various mathematicians using crochet (hurrah!) and knitting (hiss!2) to construct models of various kinds of mathematical shapes (manifolds) in order to aid visualisation and benefit further research. The image above is a representation of a Lorenz manifold, for example, and this is an illustration (and such a cuddly one!) of hyperbolic geometry:

hyperbolic crochet

The artlcle goes a great deal into the story of how mathematician Hinke Osinga and her partner mathematician Bernd Krauskopf got into this, and why they find it useful. You’ll also hear from mathematicians Carolyn Yackel, Daina Taimina, and Sarah-Marie Belcastro. This has been going on for a while, and there are even published scientific papers with crocheting instructions for various manifolds! How did I miss out on this?! This is great!

Sarah-Marie Belcastro has a website about some of these matters here, although it is mostly about knitting, not crochet, but there are links to other pages and other “crafty” mathematics.

See Daina Taimina’s crocheting page too!

Now, somehow I think I missed picking up on this properly when I blogged about the excellent Insititute for Figuring (based here in Los Angeles) earlier in the year. In the comments, Bee actually pointed to some of the hyperbolic crochet figures there, and I looked, but I did not delve deeply enough. Now, from reading Diana Taimina’s site, I think the Iff’s interest in it stemmed from an earlier visit from her to talk about it. Have a look at their gallery.

I think I’m going to make some of these to decorate the house and the office!



1(Note to self – insert rant about them thanking their stars that it was not video games here? Probably not… someone will try to make the case that hours spent playing video games can lead to great things too. Can’t decide whether I’d agree or not. Best not to open distracting can of worms… end note to self.)

2 Just kidding. Childhood games and rivalries coming back to me.

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