Thickness of knots

Classical knot theory studies one-dimensional filaments; in this paper we model knots as more physically real , e.g., made of some rope with nonzero thickness. A motivating question is: How much length of unit radius rope is needed to tie a nontrivial knot? For a smooth knot K, the injectivity radius R(K) is the supremum of radii of embedded tubular neighborhoods. The thickness of K, a new measure of knot complexity, is the ratio of R(K) to arc-length. We relate thickness to curvature, self-distance, distortion, and (for knot types) edge-number. © 1999 Elsevier Science B.V. All rights reserved