Fields Medal-winning mathematician Bill Thurston's mathematical influence can be seen in a number of places: Textbooks, journal articles, in university classrooms, and in one rather unusual place: On the runway.

Top image: Issey Miyake (2010 Winter collection)

Commenter xyzzy12345 popped into this post on a geometric principle that you could understand with a little help from a clementine to describe how Thurston taught them a mathematical principle using one of his favorite examples: the tangerine peel trick.

I was hoping for more on curvature.

If you peel a tangerine very carefully in single peel... the helix stating at the stem end and going to the opposite pole and flatten it out on a sheet of paper, you will get an S shape. You will always get the same degree of spiral regardless of the length of the peel / number of times you go around the sphere peeling that tangerine.

Bill Thurston taught me that... and sadly the only sites I can find on this, are on sites for Bill...


The example (illustrated with this picture provided by xyzzy12345) was one of Thurston's favorite to share with students and eventually, it came to the attention of Issey Miyake Creative Director Dai Fujiwara.

An article in Math Horizons describes how the designer then wrote a letter to the mathematician explaining how he had been using a similar demonstration to illustrate design principles to the fashion designers working for him. That geometric principle eventually became the basis for a collaboration that resulted in the Winter collection Issey Miyake was working on at the time, particularly the badass knitwear you see the models sporting above.


Here's Thurston and Fujiwara talking about their collaboration:

And you can check out the full collection right here: