Algebraic relations between moments of plane polygons

TL;DR

This paper investigates the algebraic relations governing the harmonic and anti-harmonic moments of planar polygons with fixed vertices, providing insights into their geometric and algebraic properties.

Contribution

It introduces a novel algebraic framework for understanding the moments of non-convex polygons, extending previous work on convex shapes.

Findings

Derived explicit algebraic relations for polygon moments

Extended moment relations to non-convex polygons

Provided a new algebraic perspective on polygon geometry

Abstract

We describe the algebraic relations satisfied by the harmonic and anti-harmonic moments of simply connected, but not necessarily convex planar polygons with a given number of vertices.