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A point in many triangles

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Every set P of n points in Rd in general position determines d-simplices. Let p be another point in Rd. Let C(P,p) be the number of the simplices containing p. Boros and Füredi [2] constructed a set P of n points in R2 for which C(P,p)≤ for every point p. They also proved that there is always a point p for which C(P,p)≥ for every point p. Here we present a new simpler proof of the existence of such a point p.

A point in many triangles A point in many triangles Boris Bukh Abstract We give a simpler proof of the result of Boros and Füredi that for any finite set of points in the plane in general position there is a point lying in 2/9 of all the triangles determined by these points. Introduction Every set P of n points in R d in general position determines d -simplices. Let p be another point in R d . Let C ( P , p ) be the number of the simplices containing p . Boros and Füredi [ 2 ] constructed a set P of n points in R 2 for which C ( P , p )≤ for every point p . They also proved that there is alway

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