The Heilbronn triangle problem is to place n>=3 points in a disk (square, equilateral triangle, etc.) of unit area so as to maximize the area Δ(n) of the smallest of the (n 3) = n(n - 1)(n - 2)/6 triangles determined by the n points. For n = 3 points, there is only a single triangle, so Heilbronn's problem degenerates into finding the largest triangle that can be constructed from points in a square. For n = 4, there are four possible triangles for each configuration, so the problem is to find the configuration of points for which the smallest of these four triangles is the maximum possible.

disk point picking | disk triangle picking | square point picking | square triangle picking | triangle point picking | triangle triangle picking

Hans Arnold Heilbronn