The winding number n(γ, z₀) = (1/2πi)∮_γ dz/(z−z₀) counts how many times a closed curve γ winds around a point z₀. It is a homotopy invariant — continuously deforming the curve without crossing z₀ preserves the winding number. This is the fundamental group π₁(ℂ\{0}) ≅ ℤ.
Draw a closed curve by clicking. Close it with double-click or the Close button. The base point (circle) can be dragged. Winding number = net signed count of counterclockwise loops around the point.