Goursat's Theorem

We prove Goursat's Theorem. It asserts that if f is holomorphic on a region which contains a triangle, then the integral around that triangle of the function is zero. This result is true for any triangle contained in the region! This is an incredible result that is among the most beautiful in mathematics. We bisect the triangle over and over and estimate at each phase. The result is a beautiful example of cancelation and convergence. This is the first step into an incredible theory. #mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis