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.)
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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?
Mariano Suárez-Álvarez
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I'm sorry, I am new to these things now, and I don't understand a word of your answer (at least from my knowledge of first two sections of first chapter of Uniform Distribution of Sequences by Kuipers and Niederreiter after which this exercise appears). I guess, the link you provided to equidistribution theorem simply says that $(n\theta)$ is ud mod 1 for irrational $\theta$. But, I have no idea of how we can "project to the imaginary axis". Can you please make your answer a little more elaborate and better accessible? – Sayan Dutta Sep 23 '22 at 21:25
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Beautiful idea. – K.defaoite Nov 28 '22 at 15:33