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