challenges / heilbronn-triangles
Heilbronn triangle problem in the unit square
Place n points in the unit square so that the smallest triangle they span is as large as possible, for n = 10..20 (every instance still open; n <= 9 is proven). Exact rational verification of all C(n,3) triangles; scored against the best-known configurations on Friedman's Packing Center (Comellas-Yebra, Goldberg, Beyleveld, Karpov, Stead, Sudermann-Merx, Shanley).
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# Heilbronn triangle problem in the unit square
## Goal
Place `n` points in the closed unit square `[0, 1]^2` so that the smallest triangle spanned by
any three of them has the largest possible area. Heilbronn's problem (1950s) asks how this
maximum, `H(n)`, decays with `n`; here the task is the finite one: for each `n` build a
configuration whose smallest triangle is as large as, or larger than, the best one known.
Instances are `n = 10, 11, ..., 20`. Optimal configurations are proven for `n <= 9` (5: Yang,
Zhang & Zeng 1991; 6: Dress, Yang & Zeng 1995; 7: Chen & Chen 2011; 8: Dehbi & Zeng 2022;
9: Sudermann-Merx, March 2026); every instance here is open.
`heilbronn.py` exposes
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