# paraboloid

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Related to paraboloidal: Paraboloid of revolution
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 ?
In this section the results for a paraboloidal radome both in the homogeneous and FSS cases are presented.
Examples of these relationships are given by equations (3) and (4) for a paraboloidal (spherical) indentation tip of radius R and for an ideal by conical (pyramidal) tip of semi-apical angle [theta], respectively:
FAST's areal advantage, combined with its paraboloidal focus, should permit the new telescope to probe the radio universe three times deeper, complete surveys 10 times faster, and cover four times more sky than Arecibo can.
SCHROEDINGER'S EQUATION IN PARABOLOIDAL COORDINATES
The Noise and Vibration Control I session covered various topics from the development of noise controls for a shearer drum used in the mining industry, a multinational research effort to develop a gradient thickness plate to focus bending waves, an active Helmholtz resonator for acoustic noise attenuation, and the use of photodeformable materials to control paraboloidal thin shells, just to name a few.
Focusing from a large size paraboloidal reflector, composed of two layers of chiral and/or chiral nihility metamaterials, is studied by utilizing the Maslov's method to give the remedy of GO which fails at caustic.
The paraboloidal reflector has been commonly used as an optical focusing device in the IRAs [1].
Cassegrain system consists of two reflectors, one is paraboloidal main reflector and other is hyperboloidal subreflector as shown in Figure 3.
065 mm long; n = 4), reduced and largely fused with the head capsule, shape rather short and paraboloidal in anterior view, with 2 simple setae on the anterior dorsal region (l = 0.
Overall equality of beamwidth is achieved using an offset paraboloidal reflector with the corrugated feed horn.
In a rotating oven the liquid glass climbs the walls of the mold to form naturally a paraboloidal surface.
In Schroedinger's four articles in a series of title Quantisation as a Problem of Proper Values [1,2,3,4] through which he introduced wave mechanics, he applied his partial-differential equation to the solution of the hydrogen atom in spherical polar and paraboloidal coordinates, and specified a method to calculate the frequencies and intensities of spectral lines.

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