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

Received: 6 May 2017     Accepted: 14 June 2017     Published: 18 July 2017
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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), 2017. 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.
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[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
  • 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

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    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

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    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

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  • @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}
    }
    

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

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

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

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

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