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 alsoElliptic Cone,
Elliptic Cylinder,
Paraboloid Explore with Wolfram|Alpha ReferencesBeyer, 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. Referenced on Wolfram|AlphaElliptic Paraboloid Cite this as:Weisstein, Eric W. "Elliptic Paraboloid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EllipticParaboloid.html
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