Hyperbolic spiral ($r=a/(\theta -{\theta }_0)$)

A hyperbolic spiral is a plane curve whose radial distance in polar coordinates is inversely proportional to the angular displacement from a fixed angle: $r=a/(\theta -{\theta }_0)$, on a branch where $r>0$. For $a>0$ and $\theta >{\theta }_0$, it winds infinitely often towards the origin as $\theta \to \infty$. Its geometric winding alone does not determine whether a moving particle traverses it in finite time: that also requires a law for the angular velocity.