Just as Art and Science are thought to be at the opposite ends of the spectrum, crochet and advanced mathematics are thought of as poles apart. Tied up within this notion are assumptions of gender, aspects of embodied versus disembodied, abstract versus concrete, and so on. But within the crocheted hyperbolic plane, the humble, feminine art of crochet can coexist comfortably and elegantly with advanced mathematics, integrating art and science in a beautiful way.

A Gateway to Advanced Mathematics

The hyperbolic plane is a surface of constant negative curvature. It is an object in non-Euclidean geometry and it was thought to be an impossible object until the 19th century. The mathematician William Thurston started making paper models of the hyperbolic plane towards the end of the 20th century, and more recently, Cornell University professor Daina Taimina improved on the paper models by crocheting the planes out of yarn. The crocheted hyperbolic planes are more robust than the paper models and can be manipulated without breaking, which allows them to become props for teaching advanced mathematics.

The planes are not made using a knitting pattern; they are made using an algorithm. So if you teach people to make a crocheted hyperbolic plane, you’re teaching them about algorithms. You're also teaching them about emergence, because the algorithm is dead simple, and yet, as you repeat the algorithm, you get this increasingly complex and curvaceous form. With textiles, you can teach engineering and material sciences and chemistry of dyes and many other topics.  

Mass Appeal

The crocheted hyperbolic planes are enormously effective at starting conversations. When people ask, “Well, what do you do with them?” I tell them I use them to start conversations. They are enormously effective at that. Sometimes I hear stories about people’s relationship to math, including stories about their anxieties. Crocheted hyperbolic planes can be an antidote to math anxiety.

Math can be daunting, but just about everybody is delighted by these interesting, fuzzy and tangible forms. Some people look at them and they see coral or kelp or sea creatures, which is very apt. This sort of hyperbolic curved surface does occur in nature—in the sea as coral reefs, and in lettuce and kale.