##### Have you ever wondered if you could combine arts and crafts with maths and science?

In my day job I am an Engineer. I like understanding how stuff works. So it should be no surprise that I like learning new stitches and coming up with ways to combine patterns and toy features. It should be even less of a surprise to understand that recently knitting has been argued as a form of programming. Additionally knitting and crochet can manipulate an inelastic material (wool) into a range of materials with varying elasticises (think about sweaters and scarves).

Dr. Matsumoto argues that “knitting is coding” and that yarn is a programmable material. The potential dividends of her research range from wearable electronics to tissue scaffolding.

https://www.nytimes.com/2019/05/17/science/math-physics-knitting-matsumoto.html

Additionally knitting and crochet in their simplest forms are a series of knots one after another, making it simple to compare them with knot theory. rows and columns of garter stitch in knitting can be likened to crystalline structures. The links between crochet, knitting and science intrigue me.

So after stumbling on the New York times article I did some more digging… It turns out that theres a whole range of applications where mathematical and scientiffic princiles can be explained by knitting and crochet. These include:

The Lorenz Manifold, If you would like to try to crochet or knit your own. The Lorenz manifold is the surface resulting from the Lorenz equations. The Lorenz equations that describe the nature of chaotic systems like chemical reactions, biological networks even down to homeware appliances like beaters. One way to illustrate these equations is the crochet surface shown above. I won’t go into great detail, you can read more about it here or here.

The Hyperbolic Plane, if you would like to crochet or knit your own although I am informaed that knitting this surface has its challenges. The hyperbolic plane is a surface which always has a negative curvature. Examples from everyday life include lettuce leaves. The hyperbolic plane is part of hyperbolic geometry discovered more than 170 years ago by C.F. Gauss.

Cyclic groups, this is the easiest to picture. The simplest knitting cyclic group is the Knitting Nancy you may have used as a child. A cyclic group is a system of movement that’s generated by one element, then follows a prescribed path back to the starting point and repeats .

Numerical progression, which you can find the knitting pattern for here, is an exploration of expanding a pixel, or squire beyond its 1×1 starting point. for example you can expand it to 1×2.

“What if a pixel could be 1×2, or 5×3?” he asks. “A 9×9 pixel grid could become a 40×40 metapixel grid, if the pixels had varying widths and heights.”

https://www.mentalfloss.com/article/86016/6-math-concepts-explained-knitting-and-crochet

When these pixels are in a grid restraints come into play. If you increase the x measurement the y measurement must match this. In a row, if one pixel increases it forces another pixel to decrease. This creates patterns such as the one seen above. Computer technician Alasdair Post-Quinn the process of writing a computer program that will help him plot these patterns out.

Möbius loop, which you can find crochet and knitting patterns for. Really a Möbius loop can be integrated into many crochet projects including baskets, scarves and bags. What is a Möbius loop is a loop? A Möbius loop is a surface only one side and only one boundary when embedded in three-dimensional Euclidean space. The Möbius loop it has the mathematical property of being unorientable. In non mathematical terms, this means that if its full length were crawled by an ant, the ant would return to its starting point having traversed both sides of the paper without ever crossing an edge.

Basic Maths. Yes, even mathematical basics like multiplication can be demonstrated by knitting and crochet. The afghans knit by now-retired British math teachers Pat Ashforth and Steve Plummer, and the curricula [PDF] they developed around them over several decades, are a significant exception. Even for the “simple” function of multiplication, they found that making a large, knitted chart using colors rather than numerals could help certain students instantaneously visualize ideas that had previously eluded them.

So, who knew knitting and crochet had such a rich intersection with science and mathematical concepts? Don’t forget this is all before you delve into crochet and knitting biology… but that’s a discussion for another day.

If after reading this you are still interested, have a look at these articles: https://2020science.org/2010/07/25/knitting-science/ https://www.nytimes.com/2019/05/17/science/math-physics-knitting-matsumoto.html http://www.lionbrand.com/blog/5-ways-knit-and-crochet-explains-math-and-science/