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 - Bengaluru > University Publications > At Right Angles |
| Full Text Status: | Public |
| URI: | http://publications.azimpremjiuniversity.edu.in/id/eprint/2132 |
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