= Hyperbolic spiral
{title2=$r=a/(\theta-\theta_0)$}
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>.
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