Math professors express complex concepts through crochet

Math professor Spencer Hamblen flattens the first crochet project he ever completed, a representation of hyperbolic space, to demonstrate how the model’s size increases away from the center.
September 03, 2013

Two math faculty are participants in a new mathematical craze – fiber arts.

While knitting and crocheting and even their connection to math are nothing new, increasing numbers of mathematicians are becoming fiber artists, including associate professor Spencer Hamblen and assistant professor Benjamin Steinhurst of the Mathematics and Computer Science department.

Both professors have noticed colleagues crafting with needles and yarn at conferences, and Hamblen himself admits to crocheting during faculty meetings.

He credits a recent Smithsonian exhibit, the Hyperbolic Crochet Coral Reef, with his own interest in the fiber-art world. This exhibit, created by the nonprofit Institute for Figuring, is a life-sized coral reef made entirely of crochet. Meant to raise awareness of environmental issues, it has inspired communities around the world to create their own reefs. Hamblen said that this project might have something to do with the increased visibility of math-inspired fiber-arts projects.

Math professors express complex concepts through crochet Hamblen is currently crocheting a seedpod (right) based on a pattern from this exhibit, which he obtained at a workshop about hyperbolic geometry and crochet during a conference.

He explained that coral has a hyperbolic structure, and crochet happens to be one of the only ways to create a three-dimensional model of hyperbolic geometry. While traditional, or Euclidean, geometry, is relatively simple to model in two-dimensions on paper, and elliptic geometry can be modeled in three-dimensions on spheres, hyperbolic geometry is more complicated.

“It’s really hard because by its very nature, it can’t fit where we want it to,” he said.

Hamblen demonstrated on his own hyperbolic crochet project that it cannot be completely flattened, a property that is created by increasing the number of stitches each time you go around. Put another way by Steinhurst, “There is too much perimeter for the area.” This results in ruffled edges similar to those of lettuce, flatworms or coral.

In many cases, mathematical crochet is no different than what fiber artists have been doing for years, according to Steinhurst.

“It’s applying a new language to what they’re already doing,” he said.

However, some mathematical fiber artists are taking this a step further and using their crochet or knitting skills to illustrate complicated mathematical concepts by creating one-sided Mobius scarves or Klein bottle hats with no inside or outside. Hamblen plans to attempt projects like those at some point, but for now, he is taking his new hobby one step at a time.

“Historically, I had been terrible at things like this,” he explained.

Steinhurst prefers more traditional crochet projects, but just because he is making blankets and coasters does not mean they are devoid of complex math concepts.

Math professors express complex concepts through crochet For example, his desk features a crocheted fractal geometry coaster that he made. Specifically, it is a Sierpinski carpet (right), a fractal pattern created by repeatedly dividing squares into nine equal parts and removing the center.

His current project is a blanket made of at least 100 hexagonal pieces that will take him about three months to complete. Steinhurst’s fascination with crochet comes from the patterns he is able to create.

“A lot of the patterns are like a scripting language,” he said, joking that crocheting could be considered an introduction to computer programming. For him, planning a geometric blanket pattern usually takes no more than half an hour.

Steinhurst has been crocheting since he was in middle school, a skill he learned from his mother. On the other hand, Hamblen describes himself as a “beginner-novice” and says his pace is much slower than that of his colleague.

They find crocheting to be a good conversation starter, and in fact, part of what first got them talking was that Hamblen was crocheting throughout Steinhurst’s job talk during his interview process.

Steinhurst doesn’t have plans to begin fiber arts projects at faculty meetings like Hamblen does, but he will be making more blankets in the future.

“Some days, you just need to make something,” he said.