Approximating the thickness of a knot
knots, thickness of knots
The thickness of a unit length C2 knot is the radius of the thickest “rope” one can place about a knot at the instant that the “rope” self-intersects. Thickness is difficult to compute for all but a few examples. To use computers, a polygonal version of thickness must be defined. The most natural definition does not correctly approximate thickness so a different polygonal version is necessary. This paper contains a definition of a continuous polygonal thickness which correctly approximates smooth thickness. Results on approximation and continuity are stated and examples given of thickness approximations.
Series on Knots and Everything
Rawdon, E.J. (1998). Approximating the thickness of a knot. In Ideal Knots, volume 19 of Series on Knots and Everything: 143–150. https://doi.org/10.1142/9789812796073_0009.