Equipartitioning triangles

Abstract

An intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for any positive integer n, K can be expressed as the union of n convex sets with disjoint interiors and each having the same area and perimeter. The first difficult case- n = 3- was settled by Bárány, Blagojevi¢, and Szucs using powerful tools from algebra and equivariant topology. Here we give an elementary proof of this result in case K is a triangle, and show how to extend the approach to prove that the conjecture is true for triangles.