paraboloid


Also found in: Dictionary, Thesaurus, Medical, Wikipedia.
Related to paraboloid: Paraboloid of revolution
Paraboloid surfaceclick for a larger image
Paraboloid surface

paraboloid

(pă-rab -ŏ-loid) A curved surface formed by the rotation of a parabola about its axis. Cross sections along the central axis are circular. A beam of radiation striking such a surface parallel to its axis is reflected to a single point on the axis (the focus), no matter how wide the aperture (see illustration). A paraboloid mirror is thus free of spherical aberration; it does however suffer from coma. Paraboloid surfaces are used in reflecting telescopes and radio telescopes. Over a small area a paraboloid differs only slightly from a sphere. A paraboloid mirror can therefore be made by deepening the center of a spherical mirror.

Paraboloid

 

an open quadric surface without a center. There are two types of paraboloids—elliptic and hyperbolic (Figure 1). Paraboloids are two of the five main types of quadric surfaces. The intersection of a hyperbolic paraboloid with a plane is

Figure 1. Paraboloids: (a) elliptic, (b) hyperbolic

a hyperbola, a parabola, or a pair of lines. Two rectilinear generators pass through each point of a hyperbolic paraboloid, which consequently is a ruled surface. In contrast to a hyperbolic paraboloid, an elliptic paraboloid does not intersect every plane in space. When it does intersect a plane, the intersection is either an ellipse or a parabola. In an appropriate system of coordinates the equation for an elliptic paraboloid has the form

and the equation for a hyperbolic paraboloid has the form

Here, p > 0 and q > 0.

paraboloid

[pə′rab·ə‚lȯid]
(engineering)
A reflecting surface which is a paraboloid of revolution and is used as a reflector for sound waves and microwave radiation.
(mathematics)
A surface where sections through one of its axes are ellipses or hyperbolas, and sections through the other are parabolas.
References in periodicals archive ?
Paraboloids of revolution have been used for many purposes such as searchlights, radars and other operations concentrating on the broadcasting of waves.
The paraboloid used to delimit chromatic and achromatic zones is the revolution of the parabola given in (4).
Wavien currently offers its unique "Dual Paraboloid Reflector" (DPR(TM)) technology for projectors for desktop and digital cinema applications.
The Paraboloid An extension activity following The Parabola
Low spillover past the paraboloid toward the ground at high elevation angles.
demonstrated that Wavien's patented Dual Paraboloid Reflector (DPR([R])) technology could provide projector lamp life for more than three times the lamp life of other projection technology providers.
ii) Dual axis tracked paraboloid dishes To cover circular and square designs of
FUNNY, but whenever I visit the Market Hall, the last thing that occurs to me is to admire the hyperbolic paraboloid shells forming its roof.
These experiments yielded a spherical surface: the next step would be to create a paraboloid with the right combination of electromagnets.
Parameters Qt, Qbb, Qc, Qz were used to triangulate all non-simplicial facets before generating results, to scale the last coordinate to [0,m] for Delaunay, to keep coplanar points with nearest facet and to add a point above the paraboloid of lifted sites for a Delaunay triangulation (Barber C, 2002).
The eerie sounds and lights of the Poeme Electronique composed by Edgard Varese had filled the sloping walls of the hyperbolic paraboloid structure, designed by Le Corbusier.
Then they must be ground to the desired curved shape (usually a paraboloid of revolution or a piece of a sphere).