Bisections of centrally symmetric planar convex bodies minimizing the maximum relative diameter

TL;DR

This paper investigates how to divide centrally symmetric convex shapes in a plane to minimize the largest diameter of the resulting parts, providing conditions for optimal bisections and analyzing a standard division method.

Contribution

It introduces necessary and sufficient conditions for minimal maximum diameter bisections and examines the properties of the standard bisection method.

Findings

Characterization of minimal maximum diameter bisections

Conditions for optimality of bisections

Analysis of the standard bisection behavior

Abstract

In this paper we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give necessary and sufficient conditions for being a minimizing bisection, as well as analyzing the behavior of the so-called standard bisection.