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Sylvester's Four-Point Problem

Let $q(R)$ be the probability that four points chosen at random in a region $R$ have a Convex Hull which is a Quadrilateral. For an open, convex subset of the Plane of finite Area,

0.667 \approx {\textstyle{2\over 3}} \leq q(R) \leq 1-{35\over 12\pi^2} \approx 0.704.


Schneinerman, E. and Wilf, H. S. ``The Rectilinear Crossing Number of a Complete Graph and Sylvester's `Four Point' Problem of Geometric Probability.'' Amer. Math. Monthly 101, 939-943, 1994.

© 1996-9 Eric W. Weisstein