Abstract
Convexity may imply points of vanishing torsion as the spatial 4-vertex theorem shows. We state here that for a simple closed curve to have nowhere vanishing torsion, it must violate convexity hiding at least twice inside its convex hull. Both the ‘4-vertex’ and Lsquo;hiding-twice’ results are generalized by obtaining a relation between the number of vanishing torsion points (vertices) of a closed space curve and the number of its components inside its convex hull. We also comment on elastic curves.
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