Magic Polygons and Their Properties

TL;DR

This paper introduces the concept of magic polygons as a generalization of magic squares, exploring their existence and inherent properties to expand understanding of these mathematical structures.

Contribution

It defines magic polygons, investigates their existence, and analyzes their properties, extending the classical concept of magic squares to polygonal arrangements.

Findings

Existence conditions for magic polygons

Properties inherent to magic polygons

Generalization of magic squares to polygons

Abstract

Magic squares are arrangements of natural numbers into square arrays, where the sum of each row, each column, and both diagonals is the same. In this paper, the concept of a magic square with 3 rows and 3 columns is generalized to define magic polygons. Furthermore, this paper will examine the existence of magic polygons, along with several other properties inherent to magic polygons.