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Eight Surface

The Surface of Revolution given by the parametric equations

$\displaystyle x(u,v)$ $\textstyle =$ $\displaystyle \cos u\sin(2v)$ (1)
$\displaystyle y(u,v)$ $\textstyle =$ $\displaystyle \sin u\sin(2v)$ (2)
$\displaystyle z(u,v)$ $\textstyle =$ $\displaystyle \sin v$ (3)

for $u\in[0,2\pi)$ and $v\in[-\pi/2, \pi/2]$.

See also Eight Curve


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 209-210 and 224, 1993.

© 1996-9 Eric W. Weisstein