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In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation:
- (elliptic paraboloid),
or
- (hyperbolic paraboloid).
-
- Hyperbolic paraboloid.
There are two kinds of paraboloid: elliptic and hyperbolic. The elliptic paraboloid is shaped like a cup and can have a maximum or minimum point. The hyperbolic
paraboloid is shaped like a saddle and can have a critical point called a saddle point.
It is a ruled surface.
With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a
parabola around its axis. It the shape used by the parabolic reflectors used in mirrors, antenna dishes, and the like.
It is also called a circular paraboloid.
-
-
- Paraboloid of revolution.
A point light source at the focal point produces a parallel light beam. This also works the other way around: a parallel beam
of light incident on the paraboloid is concentrated at the focal point. This applies also for other waves, hence parabolic antennas.
See also: ellipsoid, hyperboloid.
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