Physicist Elisabetta Matsumoto is an avid knitter and has been considering that taking up the hobby as a kid. Throughout graduate school at the University of Pennsylvania in 2009, Matsumoto encountered an uncommonly knotty stitch while knitting a pattern for a Japanese red dragon. “I have books with thousands of different stitch patterns, however the one in the red dragon wall hanging was one I had actually never seen,” she says. That got her thinking about the geometry of stitches and, ultimately, led her to study the mathematics of knitting.
There are a hundred approximately standard stitches, Matsumoto says. By varying stitch combinations, a knitter can change the elasticity, mechanical strength and 3-D structure of the resulting fabric. Yarn on its own isn’t really elastic. When knitted, the yarn gives rise to fabric that can stretch by more than two times its length while the yarn itself hardly extends.
Matsumoto, now at the Georgia Institute of Innovation in Atlanta, is teasing out the mathematical guidelines that dictate how stitches impart such distinct residential or commercial properties to fabrics. She hopes to establish a brochure of stitch types, their combinations and the resulting material properties.
Matsumoto’s research study builds on knot theory ( SN: 10/31/08), a set of mathematical principles that specify how knots form. These concepts have helped discuss how DNA folds and unfolds and how a particle’s makeup and circulation in space impart it with physical and chemical attributes ( SN: 5/23/08; SN: 8/27/18). Matsumoto is using knot theory to comprehend how each stitch entangles with its neighbors. “The kinds of stitches, the distinctions in their geometries in addition to the order in which you put those stitches together into a fabric might identify [the fabric’s] residential or commercial properties,” she says.
A material made of just one stitch type, such as a knit or purl, tends to curl at the edges. Combine the 2 stitch types together in rotating rows or columns, and the fabric lays flat.
Matsumoto’s team is now training a computer to believe like a knitter. Using yarn homes, mathematical stitch information and final knitted structures as inputs, a program can anticipate mechanical homes of materials.