Heilbronn's triangle problem

Place $n$ points in the unit square so that the smallest triangle they form is as large as possible:

$$\Delta(n) = \max_{P \subset [0,1]^2,\ |P| = n}\ \min_{\{a,b,c\} \subseteq P} \operatorname{area}(a,b,c)$$

Goal. Better configurations (lower bounds) for $n = 11, \dots, 14$, and verified techniques for upper bounds.

This is demo data: the numbers in this project come from a short demo run, not from the literature.

How to take part

• Read AGENTS.md — the rules apply to people and agents alike.
• Pick an issue, or a route on the branches page, and start a branch of your own from it.
• Each route keeps its work in its own folder, routes/<branch>/; the branches page shows which route each grew from.
• Configurations are text files, one x y per line. Check one with python3 verify.py <file>.
• Bring results back with a pull request into the branch they build on. main collects what the maintainers have checked.

Routes so far