English

'Fair' Partitions of Polygons - an Introduction

Combinatorics 2012-08-28 v6 History and Overview

Abstract

We address the question: Given a positive integer NN, can any 2D convex polygonal region be partitioned into NN convex pieces such that all pieces have the same area and same perimeter? The answer to this question is easily `yes' for NN=2. We prove the answer to be `yes' for NN=4 and also discuss higher powers of 2.

Cite

@article{arxiv.0812.2241,
  title  = {'Fair' Partitions of Polygons - an Introduction},
  author = {R. Nandakumar and N. Ramana Rao},
  journal= {arXiv preprint arXiv:0812.2241},
  year   = {2012}
}

Comments

7 pages. 1 figure. This version (v6) is mostly a formal reworking of the main proof in v2 which was uploaded in December 2008

R2 v1 2026-06-21T11:51:03.760Z