Thanks for sharing this! I've gotten into knot tying in the new year, and keep finding applications and things to do with knots.<p>Here are some other resources I've used: Ashley Book of Knots [0], Grog's animated knots [1], and youtube.<p>A lot of useful knots build on basic knots and variations of basic knots. More complex knots used to be daunting to me (trying to memorize how to tie the whole thing). But they become easier when you can recognize the basic knots used in the complex ones. Learning the use cases for the knots also helped.<p>[0]: <a href="https://archive.org/details/TheAshleyBookOfKnots/mode/2up" rel="nofollow">https://archive.org/details/TheAshleyBookOfKnots/mode/2up</a><p>[1]: <a href="https://www.animatedknots.com/" rel="nofollow">https://www.animatedknots.com/</a>
One of my favourite applications of knot theory is to classify all aesthetic tie knots, using topology to uncover unknown sartorial gems. It is a great piece of research from Cambridge, a short and accessible paper called “Tie knots, random walks and topology” by Thomas M.A. Fink and Yong Mao published in Physica A 276 (2000) 109–121.<p>It is available on the authors’ home page:<p><a href="http://www.tcm.phy.cam.ac.uk/~tmf20/" rel="nofollow">http://www.tcm.phy.cam.ac.uk/~tmf20/</a>