Let $\alpha(n)$ be the smallest non-negative angle such that for any $n\geq3$ distinct points in the plane, there exists points $A,B,C$ such that $\angle ABC\leq\alpha(n)$.

My conjecture is $\alpha(n)=\frac{\pi}{n}$ for all $n\geq3$.

If the points are in convex configuration, it's easy to prove by Pigeonhole Principle. Also $n=3,4,5,6$ cases are doable in every configuration. I could not go any further. But is this true for all $n$ and every configuration? Or is there a counter example to disprove it?

## A conjecture about random angles formed between n points

- Anindya Biswas
**Posts:**264**Joined:**Fri Oct 02, 2020 8:51 pm**Location:**Magura, Bangladesh-
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"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

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**John von Neumann**