paraboloid

American  

[puh-rab-uh-loid] / pəˈræb əˌlɔɪd /

noun

Geometry.

1. a surface that can be put into a position such that its sections parallel to at least one coordinate plane are parabolas.

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paraboloid British  

/ pəˈræbəˌlɔɪd /

noun

1. 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 x ²/ a ² ± y ²/ b ² = 2 cz

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paraboloid Scientific  

/ pə-răb′ə-loid′ /

1. A surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis.

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Other Word Forms

• paraboloidal
  adjective

Etymology

Origin of paraboloid

First recorded in 1650–60; parabol(a) + -oid

Example Sentences

See Examples For:

paraboloid

He topped the whole thing off with a swooping, saddle-shaped roof — a hyperbolic paraboloid in design-speak — that gave it a distinct presence.

From New York Times ● Jun. 13, 2023

Figure 5.35 Finding the volume of a solid with a paraboloid cap and a circular base.

From Textbooks ● Mar. 30, 2016

Find the volume of the solid bounded by the paraboloid z = 2 − 9x2 − 9y2 and the plane z = 1.

From Textbooks ● Mar. 30, 2016

The cone is the lower bound for z and the paraboloid is the upper bound.

From Textbooks ● Mar. 30, 2016

Consequently a quadric surface is covered by two sets of straight lines, a pair through every point on it; these are imaginary for the ellipsoid, hyperboloid of two sheets, and elliptic paraboloid.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various