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Paraboloid vs Hyperboloid - What's the difference?

paraboloid | hyperboloid |

As nouns the difference between paraboloid and hyperboloid

is that paraboloid is a surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola while hyperboloid is a particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.

paraboloid

English

Noun

(en noun)
  • (mathematics) A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola.

    • Derived terms

    * elliptic paraboloid * hyperbolic paraboloid * paraboloidal

    hyperboloid

    English

    Noun

    (en noun)
  • A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.

    • Usage notes

    * If the hyperboloid is a connected surface, it is said to be (term); otherwise, it has two components and is said to be (term). *

    Derived terms

    *hyperboloidal

    External links

    * (wikipedia "hyperboloid")