Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 2, April 2017, Pages: 54-57
Received: Oct. 25, 2016;
Accepted: Jan. 12, 2017;
Published: Feb. 9, 2017
Views 3552 Downloads 111
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
Follow on us
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.
Napoleon’s Triangle, Napoleon’s Theorem on Quadrilateral, Inside Directions and Congruence
To cite this article
Development of Napoleon’s Theorem on the Rectangles in Case of Inside Direction, International Journal of Theoretical and Applied Mathematics.
Vol. 3, No. 2,
2017, pp. 54-57.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
B. Grunbaum, Is Napoleon′s theorem really Napoleon′s theorem?, The American Mathematical Monthly, 119 (2012), 495–501.
G. Stols, Geogebra in 10 Lessons, http://www.geogebra.org/.../GerritStols Geogebrain10Lesson.
G. A. Venema, Exploring advanced euclidean geometry with Geometer′s Sketchpad, http://www.math.buffalostate.edu/giambrtm/MAT521/eeg.pdf.
J. A. Abed, A proof of Napoleon′s theorem, The General Science Journal, (2009), 1–4.
J. E. Wetzel, Converses of Napoleon′s theorem, The American Mathematical Monthly, 99 (1992), 339–351.
Mashadi, Buku Ajar Geometri, Pusbangdik Universitas Riau, Pekanbaru, 2012.
Mashadi, Geometri Lanjut, Pusbangdik Universitas Riau, Pekanbaru, 2015.
Mashadi, S. Gemawati, Hasriati and H. Herlinawati, Semi excircle of quadrilateral, JP Journal. Math. Sci. 15 (1 & 2) (2015), 1-13.
Mashadi, S. Gemawati, Hasriati and P. Januarti, Some result on excircle of quadrilateral, JP Journal Math. Sci. 14 (1 & 2) (2015), 41-56.
M. Corral, Trigonometry, http://www.biomech.uottawa.ca/fran09/enseignement/notes/ trgbook.pdf.
P. Bredehoft, Special Cases of Napoleon Triangles, Disertasi Master of Science, University of Central Missouri, 2014.
V. Georgiev and O. Mushkarov, Around Napoleon′s theorem, http://www.dynamat.v3d.sk/ uploadpdf/2012‘0221528150.pdf.
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.