The German-Canadian mathematician Hans Arnold Heilbronn (1908–1975) specialized in number theory. The conjecture bearing his name belongs to discrete geometry: the Heilbronn triangle problem asks how to place N points in a predetermined set so that the smallest area of the triangles they form is as large as possible.
The optimization therefore concerns the triangles whose vertices are three of the N points (with N ≥ 3).
The original problem was posed for the unit square (of area 1), with the points allowed anywhere in its interior or on its boundary. The optimal area sought is called the Heilbronn number and is denoted by H(N). The problem was subsequently extended to all kinds of shapes.
No general solution to Heilbronn's problem is known: the optimal placement of the points and the optimal area are known for only a few values of N. Current research focuses on estimates and approximation methods.
The square
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