In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system, it can be represented by the equation
This is an elliptical paraboloid which opens upward.
This is a hyperbolic paraboloid that opens up along the x-axis and down along the y-axis.
With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis. It is the shape of the parabolic reflectors used in mirrors, antenna dishes, and the like; and is also the shape of the surface of a rotating liquid, a principle used in liquid mirror telescopes. It is also called a circular paraboloid.
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.
The hyperbolic paraboloid is a ruled surface: it contains two families of mutually skew lines. The lines in each family are parallel to a common plane, but not to each other. The Pringles potato chip gives a good physical approximation to the shape of a hyperbolic paraboloid.
The elliptic paraboloid, parametrized simply as
The hyperbolic paraboloid, when parametrized as
The two paraboloidal functions
Agency Reviews Patent Application Approval Request for "Pressure Vessel with Multi Membrane Modules in Parallel"
Jul 25, 2013; By a News Reporter-Staff News Editor at Politics & Government Week -- A patent application by the inventors Drivarbekk, Kristin...
Patent Issued for Reflective Display Device Including Polymer-Dispersed Liquid Crystals Having Particular Light-Absorbing Member
Sep 25, 2013; From Alexandria, Virginia, VerticalNews journalists report that a patent by the inventors Lee, Gae-hwang (Hwaseong-si, KR);...