A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid
is a surface of revolution obtained by rotating
a hyperbola about the perpendicular bisector to the
line between the foci, while the two-sheeted
hyperboloid is a surface of revolution
obtained by rotating a hyperbola about the line joining
the foci (Hilbert and Cohn-Vossen 1991, p. 11).
See also
Barrel,
Catenoid,
Confocal Ellipsoidal Coordinates,
Confocal Quadrics,
Cylinder,
Doubly Ruled Surface,
Ellipsoid,
Elliptic Hyperboloid,
Hyperbola,
Hyperboloid Embedding,
One-Sheeted
Hyperboloid,
Paraboloid,
Ruled
Surface,
Spaghetti Bundle,
Trihyperboloid,
Two-Sheeted Hyperboloid
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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.). Plates 67 and 69 in Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, pp. 62 and 64, 1986.Gray, A. "The Hyperboloid
of Revolution." §20.5 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, p. 470, 1997.Harris, J. W. and Stocker,
H. "Hyperboloid of Revolution." §4.10.3 in Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, p. 112,
1998.Hilbert, D. and Cohn-Vossen, S. Geometry
and the Imagination. New York: Chelsea, pp. 10-11, 1999.JavaView.
"Classic Surfaces from Differential Geometry: Hyperboloid." http://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_Hyperboloid.html.Steinhaus,
H. Mathematical
Snapshots, 3rd ed. New York: Dover, 1999.Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
pp. 112-113, 1991.
Cite this as:
Weisstein, Eric W. "Hyperboloid." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hyperboloid.html
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