• anonymous
HARVARD/MIT STUDENT DAY: A median of a triangle is a segment joining a vertex to the midpoint of the opposite side. Show that the centroid of the triangle lies on each of its medians, at a distance two-thirds down from the vertex. Then use this fact to prove that the three medians intersect at a single point. Hint: Simplify the calculation by assuming that one vertex lies at the origin and another at the X axis.
  • Stacey Warren - Expert
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  • schrodinger
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  • zzr0ck3r
I bet you can do this with convex analysis, and sub differentials without geometry.

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