More Parametrizations of Surfacesa. A torus of revolution
Chapter 16, Problem 31E(choose chapter or problem)
Problem 31E
More Parametrizations of Surfaces
a. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz-plane about the z-axis in space. (See the accompanying figure.) If C has radius r > 0 and center (R, 0, 0), show that a parametrization of the torus is
where are the angles in the figure.
b. Show that the surface area of the torus is
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