The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction

Mashadi; Chitra Valentika; Sri Gemawati; Hasriati

doi:doi:10.11648/j.pamj.20170604.11

| Peer-Reviewed

The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction

Mashadi, Chitra Valentika, Sri Gemawati, Hasriati

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 4)

Received: 6 May 2017 Accepted: 14 June 2017 Published: 18 July 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 4)
DOI	10.11648/j.pamj.20170604.11
Page(s)	108-113
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Napoleon’s Theorem, Napoleon’s Theorem on Rectangles, Outside Direction, Congruence

References

[1]	Ainul Wardiyah, Mashadi and Sri Gemawati, Relationship of Lemoine circle with a symmedian point, JP Journal Math. Sci., 17 (2) (2016), 23–33.
[2]	B. J. McCartin, Mysteries of the Equilateral Triangle, Hikari Ruse, 2010.
[3]	B. Grunbaum, Is Napoleon′s theorem really Napoleon′s theorem, The American Mathematical Monthly, 119 (2012), 495–501.
[4]	G. A. Venema, Exploring advanced euclidean geometry with Geometer′s Sketchpad, http://www.math.buffalostate.edu/giambrtm/MAT521/eeg.pdf, accessed 26 july 2016.
[5]	J. A. H. Abed, A proof of Napoleon's theorem, The General Science Journal, (2009), 1-4.
[6]	J. E. Wetzel, Converses of Napoleon′s theorem, The American Mathematical Monthly, 99 (1992), 339–351.
[7]	Mashadi, Buku Ajar Geometri, Pusbangdik Universitas Riau, Pekanbaru, 2012.
[8]	Mashadi, Geometri Lanjut, Pusbangdik Universitas Riau, Pekanbaru, 2015.
[9]	Mashadi, S. Gemawati, Hasriati and H. Herlinawati, Semi excircle of quadrilateral, JP Journal Math. Sci. 15 (1 & 2) (2015), 1-13.
[10]	Mashadi, S. Gemawati, Hasriati and P. Januarti, Some result on excircle of quadrilateral, JP Journal Math. Sci. 14 (1 & 2) (2015), 41-56.
[11]	Mashadi, Chitra Valentika and Sri Gemawati, International Journal of Theoritical and Applied Mathematics, 3 (2), (2017), 54 – 57.
[12]	M. Corral, Trigonometry, http://www.biomech.uottawa.ca/fran09/enseignement/notes/ trgbook.pdf, accessed 26 july 2016.
[13]	N. A. A. Jariah, Pembuktian teorema Napoleon dengan pendekatan trigonometri, http://www.academia.edu/12025134/_Isi_NOVIKA_ANDRIANI_AJ_06121008018, accessed 6 Oktober 2015.
[14]	P. Bredehoft, Special Cases of Napoleon Triangles, Master of Science, University of Central Missouri, 2014.
[15]	P. Lafleur, Napoleon’s Theorem, Expository paper, http://www.Scimath.unl.edu/MIM/files/MATEexamFiles, accessed 24 November 2015.
[16]	V. Georgiev and O. Mushkarov, Around Napoleon′s theorem, http://www.dynamat.v3d.sk/ uploaddf 20120221528150.pdf, accessed 24 july 2016.
[17]	Zukrianto, Mashadi and S Gemawati, A Nonconvex Quadrilateran and Semi-Gergonne Points on it: Some Results and Analysis, Fundamental Journal of Mathematics and Mathematical Sciences, 6 (2), (2016), 111-124.

Cite This Article

Plain Text BibTeX RIS

APA Style

Mashadi, Chitra Valentika, Sri Gemawati, Hasriati. (2017). The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure and Applied Mathematics Journal, 6(4), 108-113. https://doi.org/10.11648/j.pamj.20170604.11

Copy | Download

ACS Style

Mashadi; Chitra Valentika; Sri Gemawati; Hasriati. The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure Appl. Math. J. 2017, 6(4), 108-113. doi: 10.11648/j.pamj.20170604.11

Copy | Download

AMA Style

Mashadi, Chitra Valentika, Sri Gemawati, Hasriati. The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure Appl Math J. 2017;6(4):108-113. doi: 10.11648/j.pamj.20170604.11

Copy | Download

@article{10.11648/j.pamj.20170604.11,
  author = {Mashadi and Chitra Valentika and Sri Gemawati and Hasriati},
  title = {The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {4},
  pages = {108-113},
  doi = {10.11648/j.pamj.20170604.11},
  url = {https://doi.org/10.11648/j.pamj.20170604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170604.11},
  abstract = {In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction
AU  - Mashadi
AU  - Chitra Valentika
AU  - Sri Gemawati
AU  - Hasriati
Y1  - 2017/07/18
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170604.11
DO  - 10.11648/j.pamj.20170604.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 108
EP  - 113
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170604.11
AB  - In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
VL  - 6
IS  - 4
ER  -

Copy | Download

Author Information

Mashadi

Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Chitra Valentika

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Sri Gemawati

Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia
Hasriati

Analysis and Geometry Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Riau, Pekanbaru, Indonesia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Mashadi, Chitra Valentika, Sri Gemawati, Hasriati. (2017). The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure and Applied Mathematics Journal, 6(4), 108-113. https://doi.org/10.11648/j.pamj.20170604.11

Copy | Download

ACS Style

Mashadi; Chitra Valentika; Sri Gemawati; Hasriati. The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure Appl. Math. J. 2017, 6(4), 108-113. doi: 10.11648/j.pamj.20170604.11

Copy | Download

AMA Style

Mashadi, Chitra Valentika, Sri Gemawati, Hasriati. The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction. Pure Appl Math J. 2017;6(4):108-113. doi: 10.11648/j.pamj.20170604.11

Copy | Download

@article{10.11648/j.pamj.20170604.11,
  author = {Mashadi and Chitra Valentika and Sri Gemawati and Hasriati},
  title = {The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {4},
  pages = {108-113},
  doi = {10.11648/j.pamj.20170604.11},
  url = {https://doi.org/10.11648/j.pamj.20170604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170604.11},
  abstract = {In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction
AU  - Mashadi
AU  - Chitra Valentika
AU  - Sri Gemawati
AU  - Hasriati
Y1  - 2017/07/18
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170604.11
DO  - 10.11648/j.pamj.20170604.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 108
EP  - 113
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170604.11
AB  - In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
VL  - 6
IS  - 4
ER  -

Copy | Download