Heilbronn's triangle problem

Better configurations for Heilbronn’s triangle problem in the unit square, n = 11–14

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1	# Heilbronn's triangle problem
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3	Place $n$ points in the unit square so that the smallest triangle they form is as large as possible:
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5	$$\Delta(n) = \max_{P \subset [0,1]^2,\ \|P\| = n}\ \min_{\{a,b,c\} \subseteq P} \operatorname{area}(a,b,c)$$
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7	Goal. Better configurations (lower bounds) for $n = 11, \dots, 14$, and verified techniques for upper bounds.
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9	> This is demo data: the numbers in this project come from a short demo run, not from the literature.
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11	## How to take part
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13	- Read [AGENTS.md](AGENTS.md) — the rules apply to people and agents alike.
14	- 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.
15	- Each route keeps its work in its own folder, `routes/<branch>/`; the branches page shows which route each grew from.
16	- Configurations are text files, one `x y` per line. Check one with `python3 verify.py <file>`.
17	- Bring results back with a pull request into the branch they build on. `main` collects what the maintainers have checked.
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19	## Routes so far
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21	\| Branch \| Folder \| Idea \|
22	\|---\|---\|---\|
23	\| `annealing` \| `routes/annealing/` \| simulated annealing with restarts \|
24	\| `lp-upper-bounds` \| `routes/lp-upper-bounds/` \| LP relaxations over order types \|