Crochet and the Gentle Art of Hyperbolic Geometry

[daidoji_gisei]

I first encountered the crocheted hyperbolic plane in an article from the 2005 Special Crochet Issue of Interweave Knits, "Taking Crochet to a Higher Plane", which told of the work of a mathematics researcher at Cornell, Dr. Dania Taimina. An avid crocheter, Dr. Taimina realized that not only could you generate a hyperbolic plane by means of making the appropriate number of increases as you worked, but that if you used cheap acrylic yarn and a hook several sizes too small you could make it sturdy enough to be picked up and fondled by entranced geometry students.


I was smitten with the idea of creating an abstract mathematical object out of yarn and patience, so I dug out some red yarn and went to work. It proved to be a challenge--the pattern itself is disarmingly easy to understand, but working with worsted-weight yarn and a C hook results in a gauge so tight it's sometimes hard to figure out when your last increase was, and getting the increases right is the heart of the hyperbolic plane. I ripped out and redid so many rows I almost think I crocheted it twice over. But when it was all over, I had my very own crocheted hyperbolic plane. Mere words cannot convey the geeky rapture that this acrylic abstract inspired.


I've made two so far, both of which I intend to send off to some of my equally-geeky but non-crocheting friends. I need to make more, because I have more than two EGBNCF and I think they all need their own hyperbolic friendsplanes. But now I have to think about what kind of hyperbolic plane to make for who, because I've discovered the Institute of Figuring's Gallery of Crocheted Hyperbolic Models. My first two planes were like the red one that starts the series. I could just go on and make more like it--it's a perfectly respectable hyperbolic plane--but the kelpie-looking on the end of the second row beckons. It would be a heartbreaker to make, but oh, the pretty! The lettucy one that starts the third row is also attractive. Very few of the models come with directions, but this is crochet, not rocket science. (Err...)


The 2005 Crochet issue also had a pattern for a pillbox hat decorated with flowers and leaves that I also decided I wanted one of. It's most-of-the-way done, and it will be wonderful when it's finshed, but I'm now wondering if maybe I should make a second one and decorate it with small hyperbolic planes. Or maybe I should just lie down and see if the feeling passes.

Comments

[helen-keeble.livejournal.com]

For a true geek fashion statement, I think you should decorate a scarf with little hyperbolic planes, and accessorise it with a Klein Bottle Hat ("perfect for the zero-volume head!").

[daidoji-gisei.livejournal.com]

Wow! *examines diagram* I'm not sure how to crochet a Klein bottle--it might be an object in which knitting is the correct medium. Hmm...do you suppose one could get a research grant for this?

[jackbishop.livejournal.com]

(I found you by way of yhlee, to pre-emptively answer the question "who's this guy?")

Daina Taimina's hyperbolic crochet work is absolutely ingenious -- crochet is actually an amazing medium for exhibiting local and global curvature, and it's absolutely the cleverest way to create and actually understand surfaces of negative curvature.

Incidentally, there's a whole lot of work on mathematical fiber arts out there: sarah-marie belcastro has collected a lot of resources (http://www.toroidalsnark.net/mathknit.html) on the subject, and together with Carolyn Yackel she runs a knitting circle at the annual math-society meetings, and in 2005 organized a contributed address session on mathematics and mathematics education in fiber arts (http://www.toroidalsnark.net/mkss.html).

Lastly, returning to local and global curvature, instructions for constructing a Lorenz manifold (http://www.enm.bris.ac.uk/staff/hinke/crochet/). Not quite as easy as the hyperbolic manifold, unfortunately. But very pretty.