Heilbronn's Problem of Eight Points in the Square

Lydia Dehbi, Zhenbing Zeng

Abstract: In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the \(\left(\begin{array}{c}8\\ 3\end{array}\right)\) triangles formed by them is maximal. Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution. All computations are done using Maple.