## Winding Number (Contour)

Denoted and defined as the number of times a path curve passes around a point.

The contour winding number was part of the inspiration for the idea of the Degree of a Map between two Compact, oriented Manifolds of the same Dimension. In the language of the Degree of a Map, if is a closed curve (i.e., ), then it can be considered as a Function from to . In that context, the winding number of around a point in is given by the degree of the Map

from the Circle to the Circle.