AlphaEvolve problems·alphaevolve:35
Packing in a dilate
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For any $n \\geq 1$ and a geometric shape $P$ (e.g. a polygon, a polytope or a sphere), let $C(n, P)$ denote the smallest scale $s$ such that one can place $n$ identical copies of $P$ with disjoint interiors inside another copy of $P$ scaled up by a factor of $s$. Establish lower and upper bounds for $C(n, P)$ that are as strong as possible.
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qed.bot, “Packing in a dilate”, https://qed.bot/t/alphaevolve-35, as of 30 Sep 2026.