Journal of Knot Theory and Its Ramifications · 2003 · 38 citations · 9 references
Ideal KnotsGeometryKnot TheoryScale Invariant RatioLoop SpaceEnumerative GeometryKnot Type
Ideal knots are curves are that maximize the scale invariant ratio of thickness to length. Here we present a simple argument to establish the existence of ideal knots for each knot type and each isotopy class and show that they are C 1,1 curves.
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Optimal shapes of compact strings
Amos Maritan, Cristian Micheletti, Antonio Trovato et al. · Nature · 2000 · 281 citations
Vsevolod Katritch, Jan Bednář, Didier Michoud et al. · Nature · 1996 · 245 citations