This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

1989 Romania Team Selection Test, 2
Let $P$ be a point on a circle $C$ and let $\phi$ be a given angle incommensurable with $2\pi$. For each $n \in N, P_n$ denotes the image of $P$ under the rotation about the center $O$ of $C$ by the angle $\alpha_n = n \phi$. Prove that the set $M = \{P_n | n \ge 0\}$ is dense in $C$.
circles dense set rotation set combinatorics geometry