The surface of the Earth is a sphere S = {(x, y, z) R 3 : x 2 y 2 z 2 = R 2 } where R = 6371. 2. The set S is parametrized by the map g : [0, 2] [0,] R 3 given by g(,) = (Rcos sin,Rsin sin,Rcos)