Winding number
= Winding number
{title2=$\operatorname{wind}(\gamma,w)$}
{wiki}
For a closed piecewise smooth curve $\gamma$ avoiding $w$,
$$
\operatorname{wind}(\gamma,w)
=\frac1{2\pi i}\int_\gamma\frac{dz}{z-w}.
$$
It is the net change of a continuous argument divided by $2\pi$ and is an integer.