#crocheting mathematical models is apparently a Thing

[math10andme]

Numbers and Patterns: Hyperbolic Crochet

I don’t understand much of what’s going on but whatever it is, it looks cool.

This is a crocheted coral from Crochet Coral Reef’s exhibition being made in Toronto, Canada. This combination of fiber arts and science is reminiscent of M.C. Escher’s fusion of mathematics and illustrations in his Circle Limit series.

The best part about this is that you can actually crochet one of these on your own using instructions from this article by David W. Henderson of Cornell University! :^) . Personally, I love fiber arts, I love knitting and crochet and I might give this a shot. The article has some mathematical models in it which I don’t get you can skip those. This is all worked in single crochet. The following written below is according to Henderson’s paper. 

First you should chose a yarn which will not stretch a lot. Every yarn will stretch a little but you need one which will keep its shape. Now you are ready to start the stitches:

 Make your beginning chain stitches (Figure 2a). (Topologists may recognize that as the stitches in the Fox-Artin wild arc!) About 20 chain stitches for the beginning will be enough.

For the first stitch in each row insert the hook into the 2nd chain from the hook. Take yarn over and pull through chain, leaving 2 loops on hook. Take yarn over and pull through both loops. One single crochet stitch has been completed. (Figure 2b.)

For the next N stitches proceed exactly like the first stitch except insert the hook into the next chain (instead of the 2nd).

For the (N+1)st stitch proceed as before except insert the hook into the same loop as the N-th stitch.

Repeat Steps 3 and 4 until you reach the end of the row.

At the end of the row before going to the next row do one extra chain stitch.

When you have the model as big as you want, you can stop by just pulling the yarn through the last loop.

Be sure to crochet fairly tight and even. That's all you need from crochet basics. Now you can go ahead and make your own hyperbolic plane. You have to increase (by the above procedure) the number of stitches from one row to the next in a constant ratio, N to N+1 the ratio determines the radius (the r in the annular hyperbolic plane) of the hyperbolic plane. You can experiment with different ratios BUT not in the same model. You will get a hyperbolic plane ONLY if you will be increasing the number of stitches in the same ratio all the time.

References:

Crocheting the hyperbolic plane. (n.d.). Retrieved April 15, 2021, from http://pi.math.cornell.edu/~dwh/papers/crochet/crochet.html

Knight, —, & Haraway, —. (n.d.). Crochet coral reef. Retrieved April 15, 2021, from https://crochetcoralreef.org/

Other related links which you should click:

The Beautiful Math of Coral TED talk by Margaret Wertheim on climate change feminism and crocheting 

Hyperbolic Crochet blog by Daina Taimiða, an author, lecturer and fiber art sculpturist who partnered with David Henderson on the article.

their interview by the IFF!