NOTE ON THE NUMBER OF OBTUSE ANGLES IN POINT SETS
Ruy Fabila‐Monroy, Clemens Huemer, Eulàlia Tramuns · International Journal of Computational Geometry & Applications · 2014
In 1979 Conway, Croft, Erdős and Guy proved that every set S of n points in general position in the plane determines at least [Formula: see text] obtuse angles and also presented a special set of n points to show the upper bound [Formula: see text] on the minimum number of obtuse angles among all sets S. We prove that every set S of n points in convex position determines at least [Formula: see text] obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case. Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved.