Winding Number around origin
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Winding number n(γ, z₀) counts how many times a curve γ wraps around point z₀.
By the Cauchy integral formula:
n(γ, z₀) = (1/2πi) ∮ dz/(z−z₀)
Residue theorem: ∮ f(z)dz = 2πi Σ Res(f, zₖ)·n(γ, zₖ)
Click canvas to add points. Red dot = origin (pole). Green dots = added poles.