# paraboloid

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Related to paraboloid: 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 ?
The quadric surface we discuss in this paper will be an ellipsoid, an elliptic paraboloid, a hyperboloid of two sheets or a cone; however, we will leave it to reader to explore the case when quadric surface is a cone.
Theory of diffraction by a paraboloid of revolution," Diffraction of Electromagnetic Waves by Some Bodies of Revolution, 5-56, Soviet Radio, Moscow, 1957.
In this case, the architectural idea of the indoor continuity and outdoor innovation, it is elaborated through conical shapes and hyperbolic paraboloids.
for cylinder, paraboloid, conoid, and neiloid, respectively (Graves, 1906).
The library's saw-tooth roof is also a response to built context, amplified here with playful interlocking arrangements of high and low gables that produce hyperbolic paraboloid sections.
The first function is a 2D quadratic function, the graph of which is a paraboloid above a quarter of the unit circle on the x-y plane (Fig 2).
Previously in CACTUS we considered simple constructions to study the reflective property of a parabola and of a paraboloid.
Their redesign of the Lincoln Center performing-arts complex, set to be unveiled later this year, includes an undulating paraboloid lawn that doubles as the roof for a 250-seat restaurant, which will save on heating and cooling costs (not to mention sponging up rainwater that would otherwise run off into the sewer system).
Previous attempts to estimate three dimensional (3D) characteristics of fire ant mounds, such as above-ground volume, have relied on assumptions that mounds are consistent, and conform to a specific, definable shape such as a semi-ellipsoid or an elliptic paraboloid (Porter et al.
The object of the study is the spatially-rod shell with Gauss's positive curvature with the surface in the shape of elliptic paraboloid.
Consider a concave mirror of elliptic paraboloid shape.
Its elaborate roof, known as a hyperbolic paraboloid, is one of the trademarks of architect Sam Scorer, who died last year at the age of 80.

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