Mathematics of textiles

October 14, 2019 — August 20, 2020

algebra
topology

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Figure 1: Smith and Skinner Loom for Moquette Carpets.

A side-on divergence into braid theory, jacquard weaving, and lace. Connections with computer science via jacquard looms, algebra, and topology via braid theory.

I’m less interested in crocheting hyperbolic surfaces, although I acknowledge that this is probably the most prominent thing that these keywords call to mind these days. Basically, I’d like to know just a little more about what kind of fishnet stockings I can code up on an industrial weaving machine and what I can know about their properties.

Elisabetta Matsumoto and others at the APS Meeting on fabrics.

Veronika Irvine’s model of bobbin lace.

The Flexible Structure Laboratory.

Also, basic but handy, digital embroidery via EmbroidePy and PEmbroider.

1 Shoelace specialization

2 References

Berger, Ricca, and Centro internazionale matematico estivo, eds. 2009. “Braids and Knots.” In Lectures on Topological Fluid Mechanics: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, July 2-10, 2001. Lecture Notes in Mathematics 1973.
Gailiunas. 2017. “Mad Weave.” Journal of Mathematics and the Arts.
Irvine, and Ruskey. 2014. “Developing a Mathematical Model for Bobbin Lace.” Journal of Mathematics and the Arts.
Jawed, Dieleman, Audoly, et al. 2015. “Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots.” Physical Review Letters.
Kovačević, and Schwarz. 2015. “Weaving Complex Patterns — From Weaving Looms to Weaving Machines.” Cutting Edge Research in Technologies.
Lipschütz, Reitebuch, Skrodzki, et al. 2022. “Weaving Patterns Inspired by the Pentagon Snub Subdivision Scheme.” Journal of Mathematics and the Arts.
McLean, Harlizius-Klück, and Jefferies. 2017. “Introduction: Weaving Codes, Coding Weaves.” TEXTILE.
Roberts. 2019. “‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab.” The New York Times.