Draw a closed curve and place a point — the winding number counts how many times the curve winds around the point (with sign).
Draw curve (click/drag). Place probe point (right-click or Shift+click). Background = winding number field.
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winding number around probe point
Presets:
Left-click drag: draw curve Right-click or Shift+click: place probe
The winding number W(γ, p) = (1/2π)·∮_γ dθ counts how many times a closed curve γ winds around point p. It is always an integer — a topological invariant unchanged by continuous deformation of the curve (as long as it doesn't cross p). W=+1 for counterclockwise loop, W=−1 for clockwise, W=0 if p is outside. The total winding number of a meromorphic function's zeros minus poles equals the winding number of the image curve (argument principle).