MathDB

Convex polygon and equilateral triangles

Source: ISL 2007, C8, AIMO 2008, TST 7, P3

June 3, 2008

combinatoricscombinatorial geometrypolygonExtremal combinatoricsIMO Shortlist

Problem Statement

Given is a convex polygon

P

with

n

vertices. Triangle whose vertices lie on vertices of

P

is called good if all its sides are unit length. Prove that there are at most

\frac {2n}{3}

good triangles.
Author: Vyacheslav Yasinskiy, Ukraine