'Fair' Partitions of Polygons - an Introduction

TL;DR

This paper investigates the possibility of partitioning convex polygons into equal-area, equal-perimeter convex pieces for various numbers of partitions, proving it for N=2 and N=4, and exploring higher powers of 2.

Contribution

It provides a proof for equal-area, equal-perimeter partitions for N=2 and N=4, and discusses extensions to higher powers of 2, advancing understanding of polygon partitioning.

Findings

Partitioning into 2 equal parts is always possible.

Partitioning into 4 equal parts is always possible.

Discussion on partitioning for higher powers of 2.

Abstract

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