Curves with increasing chords
Günter Rote · Mathematical Proceedings of the Cambridge Philosophical Society · 1994
Abstract A curve has increasing chords if AD ≥ BC for any four points A, B, C, D lying on the curve in that order. The length of such a curve that connects two points at distance 1 is at most 2π/Z in two dimensions, which is the optimal bound, and less than 30 in three dimensions.