It was a wild and wooly Saturday morning.
We talked about crocheting, Euclid and Eratosthenes. Then came the non-Euclidians: Bolyai, Lobachevsky and Gauss. You think the sum of the angles in a triangle is 180°. On a flat plane, sure, but on a sphere the sum is greater than 180 and in hyperbolic space, it approaches zero. How could this not be exciting!?
Coral grows like a crocheted hyperbolic plane. As does kale and other curly leafed plants.
Then we picked up some cultural threads. The role of the opposable thumb in the making of civilization. Is this hyperbolic plane we’re crocheting an example of art or is it artifact? Looks like a sculpture. Is it?
Crocheting is repetitive, you have to count all the time. Valuable as meditation? Yes.
Would high school kids find this interesting?
In a year or so, we’ll have an exhibit of our crocheted hyperbolic planes. Stay tuned.
I offered this workshop last Saturday. Ten people showed up!
Here are a couple of emails, responding to the workshop:
1) “It is addictive, that’s for sure. And are you kidding? This is the perfect match for you: An endeavor that combines the artistic and intellectual…it’s fascinating. I am having trouble grasping the formulas and details of the math, even though I was quite into math and esp geometry back in the day. So much has fallen out of my brain, but that is another story. I am just going on faith though, not getting hung up on having to comprehend everything all at once. This definitely feels good for the brain though.Seems like there are so many options for this with students.”
2) “Thanks for the workshop, the follow-up information and your enthusiasm for the project! Yes, I can hardly stop doing the crochet. It is growing and evolving—”
Addictive! Good for the brain! Growing and evolving!
Who could ask for anything more!?
To pursue this yarn further:
Taimina, Daina. “Crocheting Adventures with Hyperbolic Planes.” 2009
http://www.amazon.com/Crocheting-Adventures-Hyperbolic-Planes-Taimina/dp/1568814526
http://www.ovguide.com/crocheting-adventures-with-hyperbolic-planes-9202a8c04000641f80000000154ab61f
Euclid http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
http://en.wikipedia.org/wiki/Euclidean_geometry
Efi Efrati lecture at University of Chicago, “Frustrating Geometry” http://jfi.uchicago.edu/~efrati/compton/index.html
All contents copyright (C) 2010 Katherine Hilden. All rights reserved.
www.khilden.com
http://facefame.wordpress.com
http://katherinehilden.wordpress.com
www.katherinehilden.com
Read Full Post »
When you forget the yarn about angles in a triangle and exponential progressions (see previous post), the hyperbolic plane looks like a sculpture. I positioned mine in my dining room, in relation to a plant on one side and a painting on the other. The red curly hyperbolic plane relates to both. Perhaps it functions as a mediator, like a thermostat, hmmm. A discussion of when we think of an object as art and when we don’t can get heated because of strong opinions on either side. The question, “what’s the difference between art and artifact,” is really what the workshop was about. But you already suspected that.
artamaze by Katherine Hilden 