An Elementary Proof of the 3 Dimensional Simplex Mean Width Conjecture

TL;DR

This paper provides a straightforward proof of the 3D simplex mean width conjecture using classical methods and extends some results to higher dimensions.

Contribution

It offers an elementary proof of the 3D conjecture and generalizes parts of the approach to arbitrary dimensions.

Findings

Confirmed the 3D simplex mean width conjecture.

Extended some proof components to higher dimensions.

Abstract

After a Hessian computation, we quickly prove the 3D simplex mean width conjecture using classical methods. Then, we generalize some components to $d$ dimensions.