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The Mathematics of Knitting

For a long time, knitting has been considered an elegant art that has many beneficial outcomes. Though it continued to evolve throughout the years, the origin of knitting still hides many mysteries. Moreover, even though everyone agrees that knitting is based on mathematical patterns, very few tried to understand the science behind them. Thus, physicist Elisabetta Matsumoto is taking the first steps toward understanding the mathematics of knitting.

The origin of knitting

Historians tend to believe that knitting originated from the middle east in the 5th century. It then traveled to Europe through merchants and traders in the 13th century AD. Furthermore, the oldest evidence of knitting is found in Egypt but the pattern wasn’t made out of wool. It was made of cotton fibers. Furthermore, the fabric was knitted in the shape of socks in the  11th century CE. 

Moreover, many of these patterns contained Arabic blessings and symbols. Knitting was also mainly used in creating fishnets. 

The inspiration for this study

Physicist Elisabetta Matsumoto started knitting when she was a child. However, it was only when she noticed an unusual stitch while knitting a Japanese red dragon, did she start wondering about the math behind the patterns. “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.

Imparting new unique properties

According to Matsumoto, the mere basics of knitting involves almost a hundred kinds of stitches. However, switching between the stitches and different variations gives the knitter the ability to alter the elasticity. It also allows the knitter to mechanically strengthen and 3-D  alter the structure of the final outcome. Normally, yarn is not an elastic material. However, once knitted, the fabric can stretch almost twice its initial length. On the other hand, the yarn’s structure itself doesn’t change. Therefore, knitting ends up imparting the final fabric with unique properties that has nothing to do with the materials.

Matsumoto is now working at the Georgia Institute of Technology in Atlanta to figure out all the mathematical rules related to knitting. Furthermore, she is aiming to create a catalog that includes all the different stitch types, as well as their combinations and the resulting fabric properties. She hopes that this dictionary creates a common ground for Knitters, scientists, and manufacturers to benefit from. 

The knot theory

In her research, Matsumoto is using the knot theory as a foundation. The knot theory has succeeded in setting up the mathematical principles that define the science behind knots formation. Later on, these principles played a significant role in explaining the DNA’s ability to both fold and unfold relatively. The principles also laid the basis for the molecule’s makeup theory, along with an explanation behind the physical and chemical characteristics of distribution in space. 

Thus, Matsumoto is using the established theory to better understand the way 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] properties,” she says.

For example, while knitting, if a knitter only used one type of stitch, the fabric would curl at the edges. On the other hand, if a knitter combines two stitch types together while alternating rows or columns, the fabric will have flat edges. Moreover, despite the visual similarity, each one of the final patterns will have its own level of elasticity. Thus, even the smallest alteration will have a  huge impact on the mechanics of the textile. 

Training computers and creating knitting programs

To achieve better results, the team is now teaching a computer to think like a smart knitter. However, they are also imparting it with the knowledge of said knot dictionary as means of solving other unrelated problems. Therefore, with the aid of the multiple yarn properties, mathematical stitch details, and final knitted structures as inputs, the computer will predict the outcome of the pattern. Furthermore, predicting the mechanical properties of fabrics will tailor materials for specific futuristic applications, such as scaffolds for growing human tissue and wearable smart clothing. The program can also aid in everyday knot related problems.


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