Some contributions to Regular Polygons
Deniz Oncel, Murat Kirisci

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.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Advanced Theoretical and Applied Studies in Material Sciences and Geometry
