The Heilbronn Problem: New Records Push the Limits of Point Placement

The Heilbronn problem asks how to place n points in a unit-area region so that the smallest triangle formed by any three points is as large as possible. This site tracks the best known configurations for squares, triangles, and optimal convex regions, with exact coordinates, symmetry analysis, and a rational arithmetic verifier. Recent records include a 3.74% gain for the square with n=25 and a 3.46% gain for the convex case with n=31, found with the help of Opus 5.5.