Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction

Mashadi; Chitra Valentika; Sri Gemawati

doi:doi:10.11648/j.ijtam.20170302.11

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Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction

Mashadi, Chitra Valentika, Sri Gemawati

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)

Received: 25 October 2016 Accepted: 12 January 2017 Published: 9 February 2017

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Abstract

In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ijtam.20170302.11
Page(s)	54-57
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 Triangle, Napoleon’s Theorem on Quadrilateral, Inside Directions and Congruence

References

[1]	B. Grunbaum, Is Napoleon′s theorem really Napoleon′s theorem?, The American Mathematical Monthly, 119 (2012), 495–501.
[2]	G. Stols, Geogebra in 10 Lessons, http://www.geogebra.org/.../GerritStols Geogebrain10Lesson.
[3]	G. A. Venema, Exploring advanced euclidean geometry with Geometer′s Sketchpad, http://www.math.buffalostate.edu/giambrtm/MAT521/eeg.pdf.
[4]	J. A. Abed, A proof of Napoleon′s theorem, The General Science Journal, (2009), 1–4.
[5]	J. E. Wetzel, Converses of Napoleon′s theorem, The American Mathematical Monthly, 99 (1992), 339–351.
[6]	Mashadi, Buku Ajar Geometri, Pusbangdik Universitas Riau, Pekanbaru, 2012.
[7]	Mashadi, Geometri Lanjut, Pusbangdik Universitas Riau, Pekanbaru, 2015.
[8]	Mashadi, S. Gemawati, Hasriati and H. Herlinawati, Semi excircle of quadrilateral, JP Journal. Math. Sci. 15 (1 & 2) (2015), 1-13.
[9]	Mashadi, S. Gemawati, Hasriati and P. Januarti, Some result on excircle of quadrilateral, JP Journal Math. Sci. 14 (1 & 2) (2015), 41-56.
[10]	M. Corral, Trigonometry, http://www.biomech.uottawa.ca/fran09/enseignement/notes/ trgbook.pdf.
[11]	P. Bredehoft, Special Cases of Napoleon Triangles, Disertasi Master of Science, University of Central Missouri, 2014.
[12]	V. Georgiev and O. Mushkarov, Around Napoleon′s theorem, http://www.dynamat.v3d.sk/ uploadpdf/2012‘0221528150.pdf.
[13]	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.

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APA Style

Mashadi, Chitra Valentika, Sri Gemawati. (2017). Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. International Journal of Theoretical and Applied Mathematics, 3(2), 54-57. https://doi.org/10.11648/j.ijtam.20170302.11

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ACS Style

Mashadi; Chitra Valentika; Sri Gemawati. Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. Int. J. Theor. Appl. Math. 2017, 3(2), 54-57. doi: 10.11648/j.ijtam.20170302.11

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AMA Style

Mashadi, Chitra Valentika, Sri Gemawati. Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. Int J Theor Appl Math. 2017;3(2):54-57. doi: 10.11648/j.ijtam.20170302.11

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@article{10.11648/j.ijtam.20170302.11,
  author = {Mashadi and Chitra Valentika and Sri Gemawati},
  title = {Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {54-57},
  doi = {10.11648/j.ijtam.20170302.11},
  url = {https://doi.org/10.11648/j.ijtam.20170302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.11},
  abstract = {In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.},
 year = {2017}
}

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TY  - JOUR
T1  - Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction
AU  - Mashadi
AU  - Chitra Valentika
AU  - Sri Gemawati
Y1  - 2017/02/09
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.11
DO  - 10.11648/j.ijtam.20170302.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 54
EP  - 57
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.11
AB  - In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.
VL  - 3
IS  - 2
ER  -

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Author Information

Mashadi

Analysis and Geometry Group Department of Mathematics, Fakulty of Mathematics and Natural Sciences University of Riau, Bina Widya Campus, Pekanbaru, Indonesia
Chitra Valentika

Fakulty of Mathematics and Natural Sciences, University of Riau Bina Widya Campus, Pekanbaru, Indonesia
Sri Gemawati

Analysis and Geometry Group Department of Mathematics, Fakulty of Mathematics and Natural Sciences University of Riau, Bina Widya Campus, Pekanbaru, Indonesia

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APA Style

Mashadi, Chitra Valentika, Sri Gemawati. (2017). Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. International Journal of Theoretical and Applied Mathematics, 3(2), 54-57. https://doi.org/10.11648/j.ijtam.20170302.11

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ACS Style

Mashadi; Chitra Valentika; Sri Gemawati. Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. Int. J. Theor. Appl. Math. 2017, 3(2), 54-57. doi: 10.11648/j.ijtam.20170302.11

Copy | Download

AMA Style

Mashadi, Chitra Valentika, Sri Gemawati. Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction. Int J Theor Appl Math. 2017;3(2):54-57. doi: 10.11648/j.ijtam.20170302.11

Copy | Download

@article{10.11648/j.ijtam.20170302.11,
  author = {Mashadi and Chitra Valentika and Sri Gemawati},
  title = {Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {54-57},
  doi = {10.11648/j.ijtam.20170302.11},
  url = {https://doi.org/10.11648/j.ijtam.20170302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.11},
  abstract = {In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction
AU  - Mashadi
AU  - Chitra Valentika
AU  - Sri Gemawati
Y1  - 2017/02/09
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.11
DO  - 10.11648/j.ijtam.20170302.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 54
EP  - 57
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.11
AB  - In this paper will be discussed Napoleon’s Theorem on rectangles that has two parallel pair sides of the square case that built inside direction. The theorem will be proven by using congruence approach. At the end of Napoleon's theorem was discussed the development of Geogebra application in case of inside direction.
VL  - 3
IS  - 2
ER  -

Copy | Download