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Mathematics holds the secret to ‘ladder-proof’ knitting
Vishal P. Patil is in the Department of Mathematics, University of California, San Diego, La Jolla 92093, California, USA.
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Unlike in a woven fabric, pulling on a single loose thread in a piece of knitting or crochet can cause it to unravel completely. This is because a swatch of knitting or crochet is typically made from a single yarn, and its construction does not involve any knots. Writing in Physical Review X, Shimamoto et al.1 report that knot theory — a branch of mathematics — can be used to classify whether a given textile pattern can be created through knitting or crochet, and whether the fabric will be unravelled by a defect. They show that this can be used to design knitted fabrics that are resistant to ‘laddering’.
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Shimamoto, D. S., Shimamoto, K., Mahmoudi, S. & Poincloux, S. Phys. Rev. X 16, 031006 (2026).
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