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.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

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.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

Mentioned in

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.

Paraboloids for maximum solar energy collection

This design procedure is based on previously established conditions[11,12] and is similar to a previously described design.[13] The procedure was especially designed to upgrade existing single reflector configurations and is applied to the just fully offset paraboloid to determine the corresponding low cross-polarized dual configuration.

Computer-aided design of reflector antennas

Jones, "Paraboloid reflector and hyperboloid lens antennas," Transactions of the IRE Professional Group on Antennas and Propagation, vol.

Ka-Band Lightweight High-Efficiency Wideband 3D Printed Reflector Antenna

A paraboloid reflector is defined to provide a sharp focus to the rays of light reflected from its surface, when the incident light consists of rays parallel to the axis of the paraboloid.

Determination of Performance Measuring Parameters of an Improved Dual Paraboloid Solar Cooker

The external and internal surfaces of the PDL may be presented with the circular hyperboloid or paraboloid

Mathematical Model for Analysis of Translational Displacements of Tooth Root

which again is readily classified as a hyperbolic paraboloid with a vertex centred at (q, r, s).

Visualising the roots of quadratic equations with complex coefficients

The calculation is carried out for the offset paraboloid, as shown in Fig.

Plane-wave synthesis for compact antenna test range by feed scanning

This astonishing cynosure, nearly 70ft high, is paraboloid rather than pineapple (or gherkin) shaped, perhaps owing its origin to the mathematical interests of the Savilian professor.

Drawing conclusions: this catalogue of drawings from Wren's office triumphs in its 'seemingly impossible task'

The second presents a similar construction for a circular paraboloid using Cabri 3D.

The ubiquitous parabola

The paraboloid extends the special case of the parabola to the three dimensional problem.

Analytic, geometric, and numeric analysis of the Shrinking Circle and Sphere Problems

Their analyses were in turn based upon relationships developed by Sneddon [38] for the penetration of a flat elastic half space by different probes with particular axisymmetric shapes (e.g., a flat-ended cylindrical punch, a paraboloid of revolution, and a cone).

Review of instrumented indentation