3. (a) Let S be a compact regular surface. Show that there exists a point p on S such that K(p) > 0. (Hint: find a point p € S that maximizes the distance to the origin in R³. Show that K(p) > 0. You may find do Carmo, 1-5, problem 14 useful.) (b) Let S be a regular surface that is diffeomorphic to a torus. Show that S contains points where the Gauss curvature is positive, zero and negative.

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