$n$-gon centers and central lines

TL;DR

This paper reviews and generalizes the concepts of centers and central lines from triangles to n-gons, establishing their basic properties.

Contribution

It introduces a generalized framework for centers and central lines in n-gons, extending Kimberling's triangle concepts to polygons with n ≥ 3.

Findings

Generalization of triangle centers to n-gons

Introduction of central lines for n-gons

Basic properties of these generalized concepts

Abstract

In this paper we provide a review of the concept of center of a $n$-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for $n$-gons for $n\geq 3$ and establish its basic properties.