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We study the asymptotic behaviour of the sequence of sine products$P_n(\alpha) = \prod_{r=1}^n |2\sin \pi r \alpha|$ for real quadraticirrationals $\alpha$. In particular, we study the subsequence$Q_n(\alpha)=\prod_{r=1}^{q_n} |2\sin \pi r \alpha|$, where $q_n$ is the $n$thbest approximation denominator of $\alpha$, and show that this subsequenceconverges to a periodic sequence whose period equals that of the continuedfraction expansion of $\alpha$. This verifies a conjecture recently posed byMestel and Verschueren.

Asymptotic behaviour of the Sudler product of sines for quadratic irrationals