EAS Let (mathcal{S}) be the surface with parametrization [ Phi(u, v)=((3+sin v) cos u,(3+sin v) sin u,

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EAS Let \(\mathcal{S}\) be the surface with parametrization
\[
\Phi(u, v)=((3+\sin v) \cos u,(3+\sin v) \sin u, v)
\]
for \(0 \leq u \leq 2 \pi, 0 \leq v \leq 2 \pi\). Using a computer algebra system:
(a) plot \(\mathcal{S}\) from several different viewpoints. Is \(\mathcal{S}\) best described as a "vase that holds water" or a "bottomless vase"?
(b) calculate the normal vector \(\mathbf{N}(u, v)\).

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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