Let $\alpha (n)$ be such that every set of $n$ points in the unit disk contains three points which determine a triangle of area at most $\alpha (n)$. Estimate $\alpha (n)$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let (D={(x,y):x^{2}+y^{2}\le 1}). For a given $n$-point set (P\subset D), write [ m(P):=\min_{{p,q,r}\subset P}\operatorname{Area}(\triangle pqr). ] Your (\alpha(n)) is exactly the extremal quantity [ \alpha(n)=\sup_{|P|=n,P\subset D} m(P), ] i.e. the **largest possible value of the smallest triangle area** forced amon…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.