A lower bound for Heilbronn's triangle-problem
Metric Geometry
2025-11-13 v12 Number Theory
Abstract
Let n points be placed on a closed convex domain on the plane, no three points on a straight line. A conjecture by H. A. Heilbronn (before 1950) stated that on the convex domain of unit area the smallest triangle defined by these points has an area not larger than O(n^-2). Here is shown a construction of a set of n points on a unit circle where any of the triangles have an area not less than O(n^-3/2 * (log n)^-7/2).
Cite
@article{arxiv.1703.03297,
title = {A lower bound for Heilbronn's triangle-problem},
author = {Gabor Ellmann},
journal= {arXiv preprint arXiv:1703.03297},
year = {2025}
}
Comments
7 pages, 2 figures