How one physicist is unraveling the mathematics of knitting

Physicist Elisabetta Matsumoto is an avid knitter and has been since taking up the hobby as a child. During graduate school at the University of Pennsylvania in 2009, Matsumoto came across an unusually knotty stitch while knitting a pattern for a Japanese red dragon. “I have books with thousands of different stitch patterns, but the one in the red dragon wall hanging was one I had never seen,” she says. That got her thinking about the geometry of stitches and, eventually, led her to study the mathematics of knitting.

There are a hundred or so basic stitches, Matsumoto says. By varying stitch combinations, a knitter can alter the elasticity, mechanical strength and 3-D structure of the resulting fabric. Yarn on its own isn’t very elastic. But when knitted, the yarn gives rise to fabric that can stretch by more than twice its length while the yarn itself barely stretches.

Matsumoto, now at the Georgia Institute of Technology in Atlanta, is teasing out the mathematical rules that dictate how stitches impart such unique properties to fabrics. She hopes to develop a catalog of stitch types, their combinations and the resulting fabric properties. Knitters, scientists and manufacturers could all benefit from a dictionary of knits, she says.

Matsumoto’s research builds on knot theory (SN: 10/31/08), a set of mathematical principles that define how knots form. These principles have helped explain how DNA folds and unfolds and how a molecule’s makeup and distribution in space impart it with physical and chemical characteristics (SN: 5/23/08; SN: 8/27/18). Matsumoto is using knot theory to understand how each stitch entangles with its neighbors. “The types of stitches, the differences in their geometries as well as the order in which you put those stitches together into a textile may determine [the fabric’s] properties,” she says.

Making tiny changes, such as altering a couple of crossings in a knot, could have a huge impact on the mechanics of the textile. For instance, a fabric made of just one stitch type, such as a knit or purl, tends to curl at the edges. But combine the two stitch types together in alternating rows or columns, and the fabric lays flat. And despite looking nearly identical, the fabrics have varying degrees of stretchiness, Matsumoto and grad student Shashank Markande reported in July in the Bridges 2020 Conference Proceedings.

Matsumoto’s team is now training a computer to think like a knitter. Using yarn properties, mathematical stitch details and final knitted structures as inputs, a program can predict mechanical properties of fabrics. These predictions could someday help tailor materials for specific applications — from scaffolds for growing human tissue to wearable smart clothing (SN: 6/1/18) — and perhaps solve knotty problems of everyday life.