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
Authors:	Venkatasubban, Rajatadri
Document Language:	Language English
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
Full Text Status:	Public
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/2132
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