# Mathematics of textiles


A side on divergence into braid theory and 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.

Berger, Mitchell Anthony, Renzo L. 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. Berlin: Springer. http://www.algorithmica-technologies.com/pdfs/cases/Braids_and_Knots.pdf.

Gailiunas, Paul. 2017. “Mad Weave.” Journal of Mathematics and the Arts 11 (1): 40–58. https://doi.org/10.1080/17513472.2016.1273037.

Irvine, Veronika, and Frank Ruskey. 2014. “Developing a Mathematical Model for Bobbin Lace.” Journal of Mathematics and the Arts 8 (3-4): 95–110. https://doi.org/10.1080/17513472.2014.982938.

Jawed, M. K., P. Dieleman, B. Audoly, and P. M. Reis. 2015. “Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots.” Physical Review Letters 115 (11): 118302. https://doi.org/10.1103/PhysRevLett.115.118302.

Kovačević, Stana, and Ivana Schwarz. 2015. “Weaving Complex Patterns — from Weaving Looms to Weaving Machines.” Cutting Edge Research in Technologies, October. https://doi.org/10.5772/61091.

Roberts, Siobhan. 2019. “‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab.” The New York Times: Science, May 17, 2019. https://www.nytimes.com/2019/05/17/science/math-physics-knitting-matsumoto.html.