Some contributions to Regular Polygons

TL;DR

This paper explores the extension of Napoleon's Theorem beyond triangles to other regular polygons, investigating whether similar properties hold and under what conditions such generalizations are possible.

Contribution

It introduces a novel approach to applying Napoleon's Theorem to various regular polygons, examining its limitations and potential generalizations.

Findings

Napoleon's Theorem can be extended to certain regular polygons.

Conditions under which Napoleon's Theorem applies to polygons with more than three sides.

Potential new geometric properties related to regular polygons and Napoleon's configurations.

Abstract

The aim of this work is to use Napoleon's Theorem in different regular polygons, and decide whether we can prove Napoleon's Theorem is only limited with triangles or it could be done in other regular polygons that can create regular polygons.