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arXiv · 1103.5072

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

Van Cyr
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Abstract

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

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Van Cyr. 2011-03-25. A number theoretic question arising in the geometry of plane curves and in billiard dynamics. https://arxiv.org/abs/1103.5072

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