A quadratic surface which has elliptical cross section. The elliptic paraboloid of height , semimajor
axis ,
and semiminor axis can be specified parametrically by
for
and .
This gives first fundamental form coefficients
of
second fundamental form coefficients of
The Gaussian curvature and mean
curvature are
The Gaussian curvature can be expressed implicitly as
|
(12)
|
See also
Elliptic Cone,
Elliptic
Cylinder,
Paraboloid
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References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 227,
1987.Fischer, G. (Ed.). Plate 66 in Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, p. 61, 1986.JavaView. "Classic Surfaces from
Differential Geometry: Elliptic Paraboloid." http://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_EllipticParaboloid.html.
Cite this as:
Weisstein, Eric W. "Elliptic Paraboloid."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EllipticParaboloid.html
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