Circle metric
= Circle metric
{title2=$d(x,y)=\|x-y\|_{\mathbb R/\mathbb Z}$}
The quotient metric of circumference one uses the shorter distance around the circle: $\|x\|=\min_{m\in\mathbb Z}|\widetilde x-m|$. It also measures separation across the identified endpoints. This is the metric used by <circular spacing> in the <analytic large sieve inequality>.