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.
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