Geometry

   

Triangle Inscribed-Triangle Picking

Authors: Arman Maesumi

Given a triangle ABC, the average area of an inscribed triangle RST whose vertices are uniformly distributed on BC, CA and AB, is proven to be one-fourth of the area of ABC. The average of the square of the area of RST is shown to be one-twelfth of the square of the area of ABC, and the average of the cube of the ratio of the areas is 5/144. A Monte Carlo simulation confirms the theoretical results, as well as a Maxima program which computes the exact averages.

Comments: 5 Pages.

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Submission history

[v1] 2017-03-28 19:09:13

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