Curves with increasing chords
Mathematical Proceedings of the Cambridge Philosophical Society 115
(1994), 1-12, (Zbl 802.51023).
A curve has increasing chords if AD ≥ BC for any four pointsA,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 2*pi/3 in two dimensions, which is
the optimal bound, and less that 30 in three dimensions.
A related problem concerns the length of generalized
Last update: March 26, 2001.