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How one physicist is deciphering knitting’s mathematics

Understanding how knots affect the properties of textiles may contribute to the creation of bespoke materials.

Physicist Elisabetta Matsumoto has been knitting since she was a teenager. Matsumoto discovered an oddly knotty stitch when knitting a pattern for a Japanese red dragon during graduate school at the University of Pennsylvania in 2009.

“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.

Matsumoto claims that there are about a hundred simple stitches. A knitter can change the elasticity, mechanical strength, and 3-D structure of a fabric by changing stitch combinations. Yarn isn’t very elastic on its own. When knitted, however, the yarn produces fabric that can extend more than twice its original length, despite the yarn itself barely stretching.
Matsumoto, who is now at the Georgia Institute of Technology in Atlanta, is trying to figure out the mathematical rules that govern how stitches give fabrics their distinct properties.
She wants to create a catalog of stitch styles, their variations, and the fabric properties that result.

Knitters, scientists, and manufacturers, she claims, may all benefit from a knit dictionary. Matsumoto’s work is based on knot theory, which is a collection of mathematical principles that describes how knots shape. These concepts have been used to describe how DNA folds and unfolds, as well as how a molecule’s composition and spatial distribution confer physical and chemical characteristics.
Matsumoto is using knot theory to figure out how each stitch interacts with its surrounding stitches.

“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 minor adjustments, such as changing a couple of crossings in a knot, can have a significant effect on the textile’s mechanics. A fabric made of just one stitch form, such as knit or purl, for example, has a tendency to curl at the edges. However, if you alternate the two stitch forms in alternating rows or columns, the fabric will lie flat. Despite their similar appearances, the fabrics have different degrees of stretchiness, according to Matsumoto and graduate student Shashank Markande.

Matsumoto’s team is currently teaching a robot to knit. A software can predict mechanical properties of fabrics using yarn properties, mathematical stitch descriptions, and final knitted structures as inputs. These forecasts could one day help customize materials for specific applications, ranging from scaffolds for increasing human tissue to wearable smart clothing, and possibly solve thorny problems in everyday life.

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