AlphaEvolve problems·alphaevolve:49
Heilbronn problem in an arbitrary convex bounding box
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For any $n \\geq 3$ let $C(n)$ be the largest quantity such that in every configuration of $n$ points in the plane, there exists a triple of points determining a triangle of area at most $C(n)$ times the area of their convex hull. Establish upper and lower bounds on $C(n)$.
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qed.bot, “Heilbronn problem in an arbitrary convex bounding box”, https://qed.bot/t/alphaevolve-49, as of 30 Sep 2026.