sum of squares of lengths of different segments of regular n-gon
Source: 1984 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2
November 21, 2022
geometrycombinatorial geometryregular polygon
Problem Statement
Given is a regular -gon with circumradius . is the set of (different) lengths of all connecting segments of its endpoints. What is the sum of the squares of the elements of ?