MathDB

Problem 3

Part of 1974 Yugoslav Team Selection Test

Problems(1)

combinatorial geometry

Source: Yugoslav TST 1974 P3

5/29/2021
Let SS be a set of nn points P1,P2,…,PnP_1,P_2,\ldots,P_n in a plane such that no three of the points are collinear. Let α\alpha be the smallest of the angles ∠PiPjPk\angle P_iP_jP_k (i≠j≠k≠i,i,j,k∈{1,2,…,n}i\ne j\ne k\ne i,i,j,k\in\{1,2,\ldots,n\}). Find max⁡Sα\max_S\alpha and determine those sets SS for which this maximal value is attained.
combinatorial geometrycombinatoricsgeometry