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

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

The volume of the solid that lies between the paraboloid z = 2x2 + 2y2 and the plane z = 8.

From Textbooks • Mar. 30, 2016

The coefficients of x2 and y2 are equal, so the cross-section of the paraboloid perpendicular to the z-axis is a circle.

From Textbooks • Mar. 30, 2016

Let S be the part of paraboloid z = 9 − x2 − y2 with z ≥ 0.

From Textbooks • Mar. 30, 2016

If it lies at the infinity, the plane at infinity is a tangent plane, and the surface is called a paraboloid.

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