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Elliptic Paraboloid

A Quadratic Surface which has Elliptical Cross-Section. The elliptic paraboloid of height $h$, Semimajor Axis $a$, and Semiminor Axis $b$ can be specified parametrically by

$\displaystyle x$ $\textstyle =$ $\displaystyle a \sqrt{u}\,\cos v$  
$\displaystyle y$ $\textstyle =$ $\displaystyle b \sqrt{u}\,\sin v$  
$\displaystyle z$ $\textstyle =$ $\displaystyle u.$  

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

See also Elliptic Cone, Elliptic Cylinder, Paraboloid


Fischer, G. (Ed.). Plate 66 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 61, 1986.

© 1996-9 Eric W. Weisstein