Hyperbolic Crochet: A Creative Approach to Teaching and Understanding Geometry

In summary, Mathematician Daina Taimina came up with the idea of representing hyperbolic geometric forms as crocheted models after needing to create a sturdier model for a class on hyperbolic geometry. Her work is on display at The Institute for Figuring and has inspired others to create similar objects. While it may be difficult to translate these patterns into knitting, there are other interesting projects, such as a knitted klein bottle, that can be made using knitting techniques.
  • #1
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I was just reading a very cool article called "Knit Theory" in the March issue of Discover magazine. Mathematician Daina Taimina came up with the very clever idea of representing hyperbolic geometric forms as crocheted models.

The idea was born out of necessity when she went to teach a class on hyperbolic geometry at Cornell, and the classroom model for a hyperbolic plane was a very fragile and shopworn creation which had been fashioned by taping together thin paper strips. "So I spent the summer crocheting a classroom set of hyperbolic forms," she said.

Here are some samples of her work on display at The Institute for Figuring:
http://theiff.org/oexhibits/05b.html

These are particularly interesting to me because I have constructed several similar looking objects by "happy accident" when I was learning to crochet!:smile:
 
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  • #2
To be honest, I fell about laughing!
But I had to call my wife in, and she thought it was wonderful. (Like I thought she would :smile: )
It is also a remarkably accurate copy of what the computer simulation provoded.
My wife also felt that your "happy accidents" were no doubt the result of an intensely creative urge within you trying to express itself.
 
  • #3
My mom loves to knit and crochet and I think she saw this in a crocheting magazine a while ago and made me one.. it's pretty cool it still seems pretty fragile though even made of yarn.
 
  • #4
I am definitely going to try out the hyperbolic plane pattern that was on the site. Maybe I'll turn one into a ruffle for a collar or something.
 
  • #5
That's awesome! I might finally find the motivation to pick up crocheting again. Now if I can just figure out how to translate these into knitting patterns I'll be set.
 
  • #6
I remember in the article she said that it would be difficult to knit these rather than crochet. I guess it's because with crochet method you start with a small chain and work outward making concentric rows and increasing the stitches as you go out. I am not sure how to do that with knitting, but then again, I have never been able to knit anything more complex than a scarf!

However, I found a couple of other cool projects for you, Jeff. Here's a knitted http://cerebro.cs.xu.edu/~smbelcas/mkmb.html" !:cool:
 
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  • #7
I'd seen someone working on the klein bottle before. She was making a stocking cap out of one. That's an interesting way of doing the mobius strip. I would've just knitted a narrow strip, twisted it, and kitchnered the ends together. I think I may have found the motivation to pick my needles back up!
 

1. What are crocheted hyperbolic models?

Crocheted hyperbolic models are three-dimensional geometric structures that are made by crocheting yarn or thread in a specific pattern. These models mimic the shape of a hyperbolic plane, which is a mathematical surface with negative curvature.

2. How are crocheted hyperbolic models created?

To create a crocheted hyperbolic model, a series of increases are made in each round of crocheting, causing the rows to become more and more tightly curved. This creates the characteristic ruffled appearance of hyperbolic models.

3. What is the purpose of creating crocheted hyperbolic models?

Crocheted hyperbolic models have been used in mathematical art and science to visualize complex mathematical concepts, particularly in the field of topology. They are also often used in educational settings to teach students about geometry and non-Euclidean geometry.

4. Are there any real-life applications of crocheted hyperbolic models?

Yes, crocheted hyperbolic models have been used in various real-life applications, including architecture, engineering, and biology. In architecture, they have been used to create structures with strong structural integrity, while in biology, they have helped scientists better understand the shapes and structures of coral reefs.

5. Can anyone learn how to make crocheted hyperbolic models?

Yes, anyone can learn how to make crocheted hyperbolic models with some basic crochet skills and a pattern or tutorial. There are also many resources available online for beginners to learn and practice creating these models.

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