A lower bound for Heilbronn's triangle-problem

Gabor Ellmann

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arXiv · 1703.03297

A lower bound for Heilbronn's triangle-problem

Gabor Ellmann

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Abstract

Let n points be placed on a closed convex domain on the plane, no three points on a straight line. A conjecture by H. A. Heilbronn (before 1950) stated that on the convex domain of unit area the smallest triangle defined by these points has an area not larger than O(n^-2). Here is shown a construction of a set of n points on a unit circle where any of the triangles have an area not less than O(n^-3/2 * (log n)^-7/2).

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Gabor Ellmann. 2017-03-08. A lower bound for Heilbronn's triangle-problem. https://arxiv.org/abs/1703.03297

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