Generalization of Kimberling's concept of triangle center for other polygons

Abstract

In this article we introduce a general definition of the concept of center of an $n$-gon, for $n\geq 3$, generalizing the idea of C. Kimberling for triangle. We define centers associated to functions instead of to geometrical properties. We discuss the definition of those functions depending on both, the vertices of the polygons or the lengths of sides and diagonals. We explore the problem of characterization of regular polygons in terms of these $n$-gon center functions and we study the relation between our general definition of center of a polygon and other approaches arising from Applied Mathematics.