Simultaneous packing and covering in the two-dimensional Euclidean plane II

TL;DR

This paper establishes the optimal upper bound for simultaneous packing and covering constants of 2D centrally symmetric convex domains, solving a long-standing open problem in geometric optimization.

Contribution

It provides the first definitive solution to the problem of determining these bounds for 2D centrally symmetric convex shapes after over thirty years.

Findings

Established the optimal upper bound for the constants.

Solved a problem open for more than thirty years.

Advances understanding of packing and covering in convex geometry.

Abstract

This paper determines the optimal upper bound for the simultaneous packing and covering constants of the two-dimensional centrally symmetric convex domains. It solved a problem opening for more than thirty years.