The Mathematics Of Crochet

The other day, I “liked” the status of a friend on Facebook. She was talking about applying the principle of positivity to life and how someone else remarked that he had never been able to apply the quadratic principle in his own life. I thought it was pretty funny.

How this woman applies hyperbolic geometry to crocheting is nothing short of amazing, though; and no, it is not funny. It is jaw-dropping amazing.


Daina Taimina is an adjunct professor at Cornell University, and she has been creating these crocheted marvels since 1997. She says that she got the idea of creating crocheted models of the hyperbolic plane from the work of William Thurston, who made paper models without using any formulas. The idea was simple (to them, I guess) – to glue anuli together. Daina says that it occurred to her that if it were possible to make such models on paper, then it should be possible to crochet them as well. And boy, was she right!

More details from her:

I thought if something can be made out of paper, it can also be crocheted, so I made my first crocheted hyperbolic planes in June 1997 by increasing stitches in constant ratio – after every two stitches I did an increase by one stitch. The number of stitches in each row grew exponentially, so after finishing my first small, very ruffled one I realized that to explore the hyperbolic plane I have to change the ratio of increase. For classroom use the best is to use the ratio 12:13 – it means to increase one stitch after every 12 single crochet stitches.

I barely understand the math. I don’t know how to crochet. But, I sure appreciate the beauty of these mathematical models!