2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152202What length of rope (of given diameter) is required to tie a particular knot? To answer this question, we define some new notions of thickness for a space curve, one based on Gromov's distortion, and another generalizing the thickness of Litherland, Simon et al. We prove a basic inequality between these thickness measures, and show that the distortion thickness is upper semi-continuous in the C^0 topology, suggesting that shortest curves of thickness 1 should exist in each knot class.13 pages, LaTeX2eDifferential Geometrytext