More Parametrizations of SurfacesParametrization of a
Chapter 16, Problem 32E(choose chapter or problem)
Problem 32E
More Parametrizations of Surfaces
Parametrization of a surface of revolution Suppose that the parametrized curve C: (ƒ(u), g(u)) is revolved about the x-axis, where
a. Show that
is a parametrization of the resulting surface of revolution, where is the angle from the xy-plane to the point r(u, v) on the surface. (See the accompanying figure.) Notice that ƒ(u) measures distance along the axis of revolution and g(u) measures distance from the axis of revolution.
b. Find a parametrization for the surface obtained by revolving the curve about the x-axis.
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