Minimum of a function
Source: Iran TST 2008
May 25, 2008
functioninequalitiesvectorgeometry3D geometrytetrahedrongeometry proposed
Problem Statement
Let be points on the unit sphere. Prove that \sum_{i\neq j}\frac1{|P_i\minus{}P_j|} takes its minimum value if and only if these four points are vertices of a regular pyramid.