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A surface constructed by placing a family of figure-eight curves into $\Bbb{R}^3$ such that the first and last curves reduce to points. The surface has parametric equations

$\displaystyle x(u,v)$ $\textstyle =$ $\displaystyle (1-u^2)\sin v$  
$\displaystyle y(u,v)$ $\textstyle =$ $\displaystyle (1-u^2)\sin(2v)$  
$\displaystyle z(u,v)$ $\textstyle =$ $\displaystyle u.$  


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 247-248, 1993.

© 1996-9 Eric W. Weisstein