The Mathematics Of Knitting

I am one of those knitters who does it when I have a bit of time or when I'm watching a video and need to keep from phasing out.  I was thrilled when I found an article about a physicist who was working on unraveling the mathematics of knitting.  

If you look, you'll notice there are at about 100 basic knots, which if you vary the combinations, you  alter elasticity, strength, and the three dimensional structure of the finished product.  

One of the first steps in this process was to sit down and list all the possible stitches before figuring out how to classify them. 

Although yarn by itself is not very elastic, the elasticity doubles when it is made into a knitted fabric. Elisabetta Matsumoto is researching this topic.  She hopes to create a dictionary of stitch types, the various combinations of stitches, and the resulting fabric.  She is basing her research on knot theory which says that a knot is a tangled circle, or a circle embedded with crossings that cannot be undone. 

 Knot theory is what explains how knots are formed and is used to explain how DNA folds and unfolds and much more. She uses knot theory to explain how each stitch entangles with each of it's neighbors. She has discovered that when small changes are made such as moving how the yarn crosses in a knot, can influence the mechanics of the finished fabric. 

Knitting is actually a series of slipknots in a row. These slipknots when placed rows and columns form a lattice similar to a crystalline structure. When a knitter uses one stitch such as all knitting or all purls, the edge of the fabric curls where as if these two are combined by alternating rows or columns, the fabric lies much flatter. Although the two fabrics may look the same, the amount of elasticity is different. 

She argues that knitting is a type of coding while the yarn is the programable material. For a presentation, she knitted a swatch that illustrated a type of plastic surgery called Z-plasty.  Z-plasty is a plastic surgery technique which can improve both the functional and cosmetic appearance of scars.  

Matsumoto is working with several programmers to get the computer to think like a knitter by teaching it about the properties of yarn, the mathematics of each stitch, any intentional stitch defects, constraints, the twists and compresses of yarn blends, the number of plies, its thickness, and how floofy it is. Floofy is a term that refers to the location of the fuzzy fibers that stick out. 

Eventually, they hope the program will be able to predict the properties of the finished fabric.  They hope this information can be used for growing human tissue or used in wearable electronics.  Let me know what you think, I'd love to hear.  Have a great day.