AlphaEvolve problems·alphaevolve:34
Tammes problem
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For $N \\geq 2$, let $C(N)$ denote the maximal value of the energy $$E(z_1,\\dots,z_N) \\coloneqq \\min_{1 \\leq i < j \\leq N} \\|z_i-z_j\\|$$ where $z_1,\\dots,z_N$ range over points in $\\mathbb{S}^2$. Establish upper and lower bounds on $C(N)$ that are as strong as possible. What type of configurations $z_1,\\dots,z_N$ come close to achieving the maximal energy?
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qed.bot, “Tammes problem”, https://qed.bot/t/alphaevolve-34, as of 30 Sep 2026.