## Writeup – Julia Collins – Knitting Mathematics

Julia Collins is a Knitter with a difference. She is a mathematician, a topologist in fact, and her PhD from Edinburgh University involved Knot Theory. One question she poses is this: would mathematics have developed faster if they’d asked the knitters? Knitters have been utilising concepts which did not make their way into mainstream mathematics until the 19th Century.

Julia reminded us the rules of geometry leaned in high school ‘only work in the flat’. Triangles made by drawing lines on a sphere, such as Earth, don’t add up to 180 degrees. Parallel lines don’t behave as we are told either. Curvature does weird things to geometry; she pointed, for example, to hyperbolic geometry – the geometry of the negative curve. It is common in knitting, but difficult to visualise when talking mathematics. Daina Taimina, Latvian born adjunct professor of mathematics at Cornell, crocheted the hyperbolic plane in the 1990s – she went on to develop this kind of crochet, and wrote a book about it.

Knitting also incorporates patterns and coding. Just like maths. To record instructions knitters use run length encoding technique. The first punch card system was developed for the Jaquard Loom. Julia even demonstrated the use of Excel to generate quasi-random patterns. And we got to handle the samples, the strange Möbius strip creations, the even stranger Klein Bottle… Want a closer look at Knitting Mathematics? Try www.woolythoughts.com or put Julia Collins, or even Daina Taimina, into your search engine.