Knot theory was likely originally motivated by the study of real-world knots such as these:
Indeed, mathematical knot tables to this day look not too dissimilar from the familiar "age of sail"-style knot collections that decorate the walls of countless homes and restaurants around the world:
So, has knot theory as a purely topological discipline taught us anything about knots?
In particular
- have practical knots been developed based on topological results?
- has the discipline of knot tying benefited from results such as knot equivalence (e.g. simpler procedures for tying certain knots due to topological insight)?
- are there any other applications of mathematical knot theory to physical knots?