An unusual proof of the centroid theorem

Venkatasubban, Rajatadri (2019) An unusual proof of the centroid theorem. At Right Angles (5). pp. 34-36. ISSN 2582-1873

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Abstract

In this article, I present an unusual proof of the Centroid Theorem. (The theorem states: For any triangle, the three medians meet in a point. Moreover, the common point of intersection is a point of trisection of each median.) The standard methods (see [3], pg 65 for a much shorter proof that uses the same base results as this one, or [1], pg 7 for one that uses Ceva’s theorem) require nothing but elementary geometry. Another vector-based approach (see [2], pg 19) also exists. This one, however, makes use of an infinite geometric progression to achieve its result.

Item Type: Articles in APF Magazines
Uncontrolled Keywords: Median, centroid theorem, Ceva’s theorem, vector, infinite geometric series
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 17 Dec 2019 14:44
Last Modified: 17 Dec 2019 14:44
URI: http://publications.azimpremjifoundation.org/id/eprint/2132
Publisher URL:

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