MathDB
the upper bound of number of triangles

Source: 8th IMAR,problem 3

January 1, 2012
geometrygraph theorycombinatorics proposedcombinatorics

Problem Statement

Given an integer n≥2n\ge 2, given n+1n+1 distinct points X0,X1,…,XnX_0,X_1,\ldots,X_n in the plane, and a positive real number AA, show that the number of triangles X0XiXjX_0X_iX_j of area AA does not exceed 4nn4n\sqrt n.
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