Of torus and Turk’s-Head knots: a polar trigonometric modeling. (English) Zbl 1064.57503

Summary: This article concerns graphical solutions from an artist’s/ craftsperson’s/ knot tyer’s perspective.
The knots depicted may actually be tied utilizing the diagrams contained herein, although a good many of the knots may also be tied “in the hand”, as a sailor/boater would say, because these knots are kept relatively simple for illustrating purposes. Nonetheless, for knots that are more complex, some form of a graphical solution is very often resorted to.
You are very likely to know more about mathematics than I will ever know. I apologize, taking into account your knowledge. In all probability this work has been done before my attempts. It is simply that I do not know of these other attempts, and have never seen these graphs before, elsewhere.
The mathematics presented herein, I should say, consists of many anecdotal cases, for, not being a true mathematician, I do not know how to generalize them into a formal proof.


57M25 Knots and links in the \(3\)-sphere (MSC2010)