Claims

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1960_01_01_erdos_szekeres: Every configuration of $2^n$ points in the plane, $n\ge3$, contains an angle greater than $\pi(1-1/n)$, so with Szekeres's construction $\alpha_{2^n}=\pi(1-1/n)$; also gives the values of $\alpha_N$ for $N\le8$.

1993_01_01_sendov: Determines $\alpha_N$ for every $N\ge4$: $\pi(1-1/n)$ when $2^{n-1}+2^{n-3}<N\le2^n$ and $\pi(1-2/(2n-1))$ when $2^{n-1}<N\le2^{n-1}+2^{n-3}$, refuting the Erdős–Szekeres guess.

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