A Simple Proof of Thue's Theorem on Circle Packing

TL;DR

This paper presents a straightforward proof of Thue's circle packing theorem using density analysis of Delaunay triangulation, simplifying the understanding of optimal circle arrangements.

Contribution

It introduces a simplified proof method for Thue's theorem based solely on Delaunay triangulation density analysis.

Findings

Proof is more accessible and easier to understand.

Validates Thue's theorem through a new geometric approach.

Potentially facilitates further research in circle packing problems.

Abstract

A simple proof of Thue theorem on Circle Packing is given. The proof is only based on density analysis of Delaunay triangulation for the set of points that are centers of circles in a saturated circle configuration.