SOME CONTRIBUTIONS TO REGULAR POLYGONS

Year 2017, Volume: 5 Issue: 2, 70 - 77, 15.10.2017

Deniz Öncel Murat Kirişçi

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.

Keywords

Napoleon's Theorem, regular polygon

References

• [1] S. Brodie, Napoleon's Theorem, Two simple proofs, http://www.cut-theknot. org/proofs/napoleon.shtml (Accessed on 16 March 2016).
• [2] H. Demir, Solution to Problem E2122, Amer. Math. Monthly, 76, (1969), 833. [3] L. Gerber, Napoleon's theorem and the parallelogram inequality for ane regular polygons, Amer. Math. Monthly, 87, (1980), 644-648.
• [4] J. A. Grzesik, Yet another analytic proof of Napoleon's Theorem, Amer. Math. Monthly, 123(8), (2016), 824.
• [5] B. Grunbaum, Is Napoleon's Theorem Really Napoleon's Theorem?, Amer. Math. Monthly, 119(6), (2012), 495-501.
• [6] M. Hajja, H. Martini, M. Spirova, On Converse of Napoleon's Theorem and a modied shape function, Beitr. Algebra Geom., 47, (2006), 363383.
• [7] H. Martini, On the theorem of Napoleon and related topics, Math. Semesterber., 43, (1996), 47-64, http://dx.doi.org/10.1007/s005910050013
• [8] Wetzel, J.E., Converse of Napoleon's Theorem, Amer. Math. Monthly, 99(4), (1992), 339-351.