Art as Math that Meets Crochet
Gabriele Meyer is a Senior Lecturer Emerita in the Department of Mathematics, at the University of Wisconsin. She creates beautiful art by crocheting mathematical shapes.
In a recent article on a crocheting website, quoting an earlier statement, Gabi explained the connection this way:
“In math, if you want to prove something really beautiful, you have to understand the structure. And the structure means you understand the beauty of an object and with that knowledge you oftentimes can make a very important and deep proof. That’s why beauty matters tremendously in mathematics.”
Today I want to share some of Gabi’s work of crocheting shapes that follow hyperbolic geometry. This includes crocheted algae, flowers, sea anemones, and other organic shapes.
Some of Her Art
The crocheting article relates that Gabi is “happy to give a new spin to a traditional European women’s craft while also connecting it to mathematics.” Besides the sea anemones, flower blossoms, and algae, she draws inspiration from abstract forms in topology. One could say she bridges between what is structurally ideal and what is biologically real, as well as from mathematics to art and culture more generally.
Gabi’s work was featured in the Bridges 2013 conference on mathematical connections in art, music, architecture, and culture. This began a streak of nine consecutive appearances at Bridges conferences, and in 2022 at the Joint Mathematics Meetings. Some more of her hyperbolic art is on her own site.
Her pieces are made by creating hyperbolic crochet around an original shaping line, giving it structure in three dimensions. One principle noted in her talk slides for Bridges 2019 is that neighborhoods of any point in hyperbolic geometry have more stuff than in flat Euclidean geometry or spherical geometry, forcing a local saddle structure having negative curvature. Crochet enables embodying this locality more robustly than weaving or knitting would. The effect of increasing the local stitch count is explained in greater detail in a nice 2016 article by Anna Lambert. That crocheting is friendlier than William Thurston’s paper models for hyperbolic surfaces was discovered in 1997 by Cornell’s Daina Taimina, who has also exhibited at Bridges and elsewhere.
Open Problems
My dear wife, Kathryn Farley and I, have had one of her artworks in our house for years. We knew her first through her husband, Jin-Yi Cai, and Ken has also known both as colleagues in Buffalo. We have also just purchased some more of her art work for our new condo. Gabi also has a separate line of linoleum prints.
John Conway famously kept myriad models of polyhedra and networks in his office for inspiration. The polyhedra illustrate positive curvature. What kind of mathematical creativity is best inspired by surfaces of negative curvature?
