How do you prove that $\sin(n)$ with $n=0,1,2...$ is not uniformly distributed mod 1?
(This is an exercise in Uniform Distribution of Sequences by Kuipers and Niederreiter.)
How do you prove that $\sin(n)$ with $n=0,1,2...$ is not uniformly distributed mod 1?
(This is an exercise in Uniform Distribution of Sequences by Kuipers and Niederreiter.)
You know that the sequence of powers of $e^{i}$ are equidistributed in the unit circle of $\mathbb C$. The sequence you have is obtained from this one by projecting to the imaginary axis. Can you see what happens?