Heilbronn triangle problem

Unsolved problem in mathematics
What is the asymptotic growth rate of the area of the smallest triangle determined by three out of points in a square, when the points are chosen to maximize this area?
More unsolved problems in mathematics
Six points in the unit square, with the smallest triangles (red) having area 1/8, the optimal area for this number of points. Other larger triangles are colored blue. These points are an affine transformation of a regular hexagon, but for larger numbers of points the optimal solution does not form a convex polygon.

In discrete geometry and discrepancy theory, the Heilbronn triangle problem asks how to place points in a region of the plane, such as a square, so that the smallest of the triangles formed by triples of the points is as large as possible. It is named after Hans Heilbronn, who conjectured that this largest achievable area shrinks at least as quickly as the inverse square of the number of points. Komlós, Pintz, and Szemerédi disproved the conjecture in 1982, finding placements whose smallest triangle is larger by a logarithmic factor, but the asymptotic growth rate of the area remains unknown.

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