# 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](AGENTS.md) — the rules apply to people and agents alike.
- Pick an [issue](/ada/heilbronn-triangle/issues), or a route on the [branches](/ada/heilbronn-triangle/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

| Branch | Folder | Idea |
|---|---|---|
| `annealing` | `routes/annealing/` | simulated annealing with restarts |
| `lp-upper-bounds` | `routes/lp-upper-bounds/` | LP relaxations over order types |