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SOME CONTRIBUTIONS TO REGULAR POLYGONS

Year 2017, Volume: 5 Issue: 2, 70 - 77, 15.10.2017
https://izlik.org/JA57YP84UA

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.

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.

Year 2017, Volume: 5 Issue: 2, 70 - 77, 15.10.2017
https://izlik.org/JA57YP84UA

Abstract

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.
There are 7 citations in total.

Details

Subjects Engineering
Journal Section Research Article
Authors

Deniz Öncel This is me

Murat Kirişçi This is me

Submission Date October 13, 2017
Acceptance Date June 7, 2017
Publication Date October 15, 2017
IZ https://izlik.org/JA57YP84UA
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Öncel, D., & Kirişçi, M. (2017). SOME CONTRIBUTIONS TO REGULAR POLYGONS. Konuralp Journal of Mathematics, 5(2), 70-77. https://izlik.org/JA57YP84UA
AMA 1.Öncel D, Kirişçi M. SOME CONTRIBUTIONS TO REGULAR POLYGONS. Konuralp J. Math. 2017;5(2):70-77. https://izlik.org/JA57YP84UA
Chicago Öncel, Deniz, and Murat Kirişçi. 2017. “SOME CONTRIBUTIONS TO REGULAR POLYGONS”. Konuralp Journal of Mathematics 5 (2): 70-77. https://izlik.org/JA57YP84UA.
EndNote Öncel D, Kirişçi M (October 1, 2017) SOME CONTRIBUTIONS TO REGULAR POLYGONS. Konuralp Journal of Mathematics 5 2 70–77.
IEEE [1]D. Öncel and M. Kirişçi, “SOME CONTRIBUTIONS TO REGULAR POLYGONS”, Konuralp J. Math., vol. 5, no. 2, pp. 70–77, Oct. 2017, [Online]. Available: https://izlik.org/JA57YP84UA
ISNAD Öncel, Deniz - Kirişçi, Murat. “SOME CONTRIBUTIONS TO REGULAR POLYGONS”. Konuralp Journal of Mathematics 5/2 (October 1, 2017): 70-77. https://izlik.org/JA57YP84UA.
JAMA 1.Öncel D, Kirişçi M. SOME CONTRIBUTIONS TO REGULAR POLYGONS. Konuralp J. Math. 2017;5:70–77.
MLA Öncel, Deniz, and Murat Kirişçi. “SOME CONTRIBUTIONS TO REGULAR POLYGONS”. Konuralp Journal of Mathematics, vol. 5, no. 2, Oct. 2017, pp. 70-77, https://izlik.org/JA57YP84UA.
Vancouver 1.Deniz Öncel, Murat Kirişçi. SOME CONTRIBUTIONS TO REGULAR POLYGONS. Konuralp J. Math. [Internet]. 2017 Oct. 1;5(2):70-7. Available from: https://izlik.org/JA57YP84UA
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