A Direct Proof of the 2nd Atiyah-Sutcliffe Conjecture for Convex Quadrilaterals

TL;DR

This paper provides a direct, computer-free proof of the second Atiyah-Sutcliffe conjecture specifically for convex quadrilaterals, utilizing a recently established geometric inequality.

Contribution

It offers the first direct proof for convex quadrilaterals without computational assistance, advancing understanding of the Atiyah-Sutcliffe conjecture.

Findings

Proof confirms the conjecture for convex quadrilaterals

Introduces a new geometric inequality used in the proof

Eliminates need for computer-aided calculations in this case

Abstract

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof relies on a new geometric inequality proved recently by the author.