A Napoleon-like Theorem for Quadrilaterals

Abstract

Napoleon’s theorem states that if we place equilateral triangles externally on the sides of an arbitrary triangle, the centers of these equilateral triangles will form an equilateral triangle. In this note, we introduce a Napoleon-like, or simply Napoleonic result for quadrilaterals.

MSC:

• 97G40

Acknowledgments

The author would like to express his profound gratitude to Bonnie Ponce, Managing Editor of the Monthly, who has encouraged him throughout his work on this paper. The author gratefully thanks the Referees for reading the manuscript very carefully and for giving the author very valuable comments. The author sincerely thanks Professor Della Dumbaugh for her enthusiasm throughout this manuscript process.