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Published on Nov 8, 2011
We show that the total curvature of a polyhedron is equal to its Euler number. This only works with the rational formulation of curvature, using an analog of the turn angle suitable for the 2 dimensional sphere. We treat Harriot's theorem on the area of a spherical polygon.
This is the first video in the 16th lecture of this beginner's course in Algebraic Topology, given by N J Wildberger at UNSW.