Editing Winding number (section)

{{Short description|Number of times a curve wraps around a point in the plane}}
{{Distinguish|Map winding number}}
[[Image:Winding Number Around Point.svg|thumb|right|250px|This curve has winding number two around the point ''p''.]]
{{Complex analysis sidebar}}

In [[mathematics]], the '''winding number''' or '''winding index''' of a [[closed curve]] in the [[plane (mathematics)|plane]] around a given [[point (mathematics)|point]] is an [[integer]] representing the total number of times that the curve travels counterclockwise around the point, i.e., the curve's [[number of turns]]. For certain open [[plane curve]]s, the number of turns may be a non-integer. The winding number depends on the [[curve orientation|orientation]] of the curve, and it is [[negative number|negative]] if the curve travels around the point clockwise.

Winding numbers are fundamental objects of study in [[algebraic topology]], and they play an important role in [[vector calculus]], [[complex analysis]], [[geometric topology]], [[differential geometry]], and [[physics]] (such as in [[string theory]]).