For questions about winding numbers. The winding number of a continuous curve counts how many times it "loops" around a given point.
Consider a curve in the plane parameterized in polar coordinates by $r = r(t)$ and $\theta = \theta(t)$, with $0 \le t \le 1$. Assuming that $r$ and $\theta$ are continuous, and the curve does not pass through the origin, we can define the winding number to be
$$\text{winding number} = \frac{\theta(1) - \theta(0)}{2\pi}$$
This counts the change in angle as a point moves along the curve containing the origin: Adding $1$ every counterclockwise loop, and subtracting $1$ for every counterclockwise loop.
Alternatively, in the complex plane, the winding number of a curve $\gamma$ not passing through a point $a$ can be defined as
$$\text{winding number} = \oint_{\gamma} \frac{dz}{z - a}$$
This can be generalized in geometry and algebraic topology, and the winding number of a map can also be called its degree.
