pa·rab·o·loid

P0056600 (pə-răb′ə-loid′)n. A surface having parabolic sections parallel to a single coordinate axis and elliptic or circular sections perpendicular to that axis.

pa·rab′o·loi′dal (-loid′l) adj.

paraboloid

(pəˈræbəˌlɔɪd) n (Mathematics) a geometric surface whose sections parallel to two coordinate planes are parabolic and whose sections parallel to the third plane are either elliptical or hyperbolic. Equations x²/a² ± y²/b² = 2cz paˌraboˈloidal adj

pa•rab•o•loid

(pəˈræb əˌlɔɪd)

n. a surface that can be put into a position such that its sections parallel to at least one coordinate plane are parabolas. [1650–60] pa•rab`o•loi′dal, adj.

Thesaurus

Noun

paraboloid - a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axisplane figure, two-dimensional figure - a two-dimensional shape

paraboloid

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.

paraboloid

pa·rab·o·loid

paraboloid

pa•rab•o•loid

paraboloid

paraboloid

Paraboloid

paraboloid

paraboloid

Words related to paraboloid

noun a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis

Related Words