Erdös-Mordell Inequality
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Published:
Nov 27, 2018
Keywords:
Erdös-Mordell Inequality Hypotenuse Similar Triangle
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Abstract
The article shows the proof of Erdös-Mordell inequality for any triangle, there exist a point inside the triangle which the sum of the orthogonal projection from the point to all three sides is less than or equal to half of the sum of the distance from the point to the three vertices of the triangle. The proof is based on the work of Claudi Alsina and Roger B. Nelson which published in Forum Geometricorum V7(2007) 99-102.
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How to Cite
Chitsakul, P. (2018). Erdös-Mordell Inequality. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 62(692), 19–30. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/157368
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Academic Article
References
[1] Paul Erdős, “American Mathematical Monthly,” Problem 3740, vol. 42, pp. 396, 1935.
[2] Mordell L. J. and Barrow D. F., “American Mathematical Monthly,” Solution to 3740, vol. 44, pp. 252-254, 1937.
[3] Claudi Alsina and Roger B. Nelsen, “Forum Geometricorum,” A Visual Proof of the Erdös-Mordell Inequality, vol. 7, pp. 99-102, 2007.
[4] Michigan Math J., “The Michigan Mathematical Journal,” A Simple Proof of the Erdős-Mordell Inequality for Triangles, vol. 4, pp. 97-98, 1957.
[5] Jian Liu, “International Electronic Journal,” A New Proof of the Erdős Mordell Inequality, vol. 4, no. 2, pp. 114-119, 2011.
[2] Mordell L. J. and Barrow D. F., “American Mathematical Monthly,” Solution to 3740, vol. 44, pp. 252-254, 1937.
[3] Claudi Alsina and Roger B. Nelsen, “Forum Geometricorum,” A Visual Proof of the Erdös-Mordell Inequality, vol. 7, pp. 99-102, 2007.
[4] Michigan Math J., “The Michigan Mathematical Journal,” A Simple Proof of the Erdős-Mordell Inequality for Triangles, vol. 4, pp. 97-98, 1957.
[5] Jian Liu, “International Electronic Journal,” A New Proof of the Erdős Mordell Inequality, vol. 4, no. 2, pp. 114-119, 2011.