Cauchy theorem for a triangle
= Cauchy theorem for a triangle
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{title2=$\oint_{\partial T}f(z)\,dz=0$}
A <holomorphic function> on an open neighbourhood of a closed triangle has zero <contour integral> around its boundary. Goursat's subdivision proof uses complex differentiability alone: repeatedly choose a quarter-size triangle carrying at least one quarter of the integral, and subtract the affine expansion at the limiting point. No continuity of the derivative is assumed.