The science of knitting - the mathematics of knot theory

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Long-time readers of my blog know that I have a passion for the way knitting and crochet intersects with science and mathematics.

Knitting and crochet are so much more than 'just' a hobby - they can be incredibly powerful tools for science and mathematics.

Crochet and Mathematics

In an earlier blog post I wrote about the intriguing work of Dr. Daina Taimina, who used crochet as a way to bring complex geometry to life and aid our understanding of the hyperbolic geometry. Margareth Wertheim then used Taimina's work in her Crochet Reef project, which is absolutely amazing.

Here is Margareth Wertheim on why she started the project and where it has taken her:

If you are keen to create your own coral reef, there are plenty of YouTube videos with instructions, just google "hyperbolic crochet" and you will be surprised what you can find.

More recently, knitting has found its way into a new physics research project to understand the mathematical rules underlying knitting:

Knitting and Physics

What looks to a seasoned knitter as a fairly simple technique of using knitting needles and yarn to create a knitted fabric is actually the application of highly complex mathematical rules known as knot theory, or as the New York Times put it "Knit theory is knot theory".

Untangling the mathematical and physical properties of knitting is the focus of a new project by Elisabetta Matsumoto of the Georgia Institute of Technology in Atlanta which she presented at the March 2019 meeting of the American Physical Society in Boston, Massachusetts.

Why would a physicist be interested in knitting? Firstly, there is complex engineering involved in knitting. You are creating a three dimensional object that will fit a particular shape and have a set of desired properties. You achieve this by using one-dimensional yarn and a complex series of interlocking knots. And all you use  are the most simplest of tools, namely two sticks. That in itself is actually quite amazing.

But it gets even more exciting from there. While a single strand of yarn tends to be relatively rigid and not too stretchy, the knitted fabric displays completely different properties depending on the stitches used. Despite using only a small handful of different stitches (knit, purl, yarn-overs and various combinations of those), the same yarn can be used to create something super-stretchy (such as fisherman's rib), create a more dense fabric (for example using pearl stitch) or something light and airy such as lace knitting.

These are amazing properties that are produced by the types of loops and knots used in knitting rather than the material itself. The mathematics behind knitting is highly complex, and mathematicians and physicists are only just beginning to unravel the mystery of knitting. But the future applications of this research are wide-reaching from aerospace engineering to medicine.

So, next time you pick up your knitting needles, remember that knitting is essentially applied mathematics. Think of yourself as part of this amazing human endeavor of creating and understanding the world.

Further reading:

The Home of Mathematical Knitting: http://www.toroidalsnark.n/mathknit.html

The science of knitting:

The science of knitting, unpicked:

New York Times: ‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab':


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