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.
A third reflecting area consisting of an aggregation of paraboloid-of-revolution segments forms a pattern contributing to the formation of a cut line tilted a given angle with respect to the horizontal line in the distribution pattern of a passing beam.
Further, to provide a reflecting area contributing to the formation of a cut line tapered with respect to the horizontal line to form a passing light beam, two-sheet hyperbolic paraboloid or paraboloid of revolution reflecting segments are used.
The hyperbolic paraboloid plane 3 is parabolic in both the horizontal and vertical cross sections.
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