A number theoretic question arising in the geometry of plane curves and in billiard dynamics

Details A number theoretic question arising in the geometry of plane curves and in billiard dynamics A number theoretic question arising in the geometry of plane curves and in billiard dynamics

2011-03-25

arxiv.org/abs/1103.5072v1

Mathematics

Number Theory

Scientific paper

We prove that if $\rho\neq1/2$ is a rational number between zero and one,
then there is no integer $n>1$ such that $$ n\tan(\pi\rho)=\tan(n\pi\rho). $$
This has interpretations both in the theory of bicycle curves and that of
mathematical billiards.

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