AlphaEvolve problems·alphaevolve:48
Heilbronn problem in a fixed bounding box
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For any $n \\geq 3$ and any convex body $K$ in the plane, let $C(n,K)$ be the largest quantity such that in every configuration of $n$ points in $K$, there exists a triple of points determining a triangle of area at most $C(n,K)$ times the area of $K$. Establish upper and lower bounds on $C(n,K)$.
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qed.bot, “Heilbronn problem in a fixed bounding box”, https://qed.bot/t/alphaevolve-48, as of 30 Sep 2026.