A frustum of a decagonal pyramid
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Latin frustum ‎(morsel).



frustum ‎(plural frustums or frusta)

  1. A cone or pyramid whose tip has been truncated by a plane parallel to its base.
    • 1742, Colin MacLaurin, A Treatise of Fluxions, Volume 1, page 25,
      In a parabolic conoid this difference vaniſhes, the fruſtum being always equal to a cylinder of the ſame height upon the ſection of the conoid that biſects the altitude of the fruſtum and is parallel to its baſes.
    • 1809, Frustum, entry in William Nicholson, The British Encyclopedia, Volume 3, unnumbered page,
      This theorem holds good for complete solids as well as frustums, whether right or oblique [] .
    • 2006, Pawan Harish Nirnimesh, P. J. Narayanan, Culling an Object Hierarchy to a Frustum Hierarchy, Prem Kalra, Shmuel Peleg (editors), Computer Vision, Graphics and Image Processing: 5th Indian Conference, ICVGIP 2006, Springer, LNCS4338, page 252,
      However, when there are multiple view frustums (as in a tiled display wall), visibility culling time becomes substantial and cannot be hidden by pipelining it with other stages of rendering.
    • 2008, R. Benjamin Davis, Techniques to Assess Acoustic-structure Interaction in Liquid Rocket Engines, page 122,
      Here, the dynamics of the fluid-filled frusta of cones are considered (see Figure 5.5). The frusta are clamped at their roots and free at their ends.
  2. A portion of a sphere delimited by two parallel planes.
    • 1840, James Blundell, Observations on Some of the More Important Diseases of Women, page 131,
      In some women it[the os uteri] is flat, in many more tuberose, and forming, as it were, a frustum of a sphere; [] .
    • 2014, John Bird, Engineering Mathematics, page 183,
      Problem 22. Determine the volume of a frustum of a sphere of diameter 49.74 cm if the diameter[sic] of the ends of the frustum are 24.0 and 40.0 cm, and the height of the frustum is 7.00 cm.

Usage notesEdit

The misspelling frustrum is by incorrect analogy with frustrate, also of Latin origin.[1]

  • (portion of a sphere): The portion of the surface of a sphere delimited by parallel planes (i.e., the curved surface of a frustum) may be called a zone; however, that term is also sometimes used as a synonym of frustum.

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Related termsEdit



  1. ^ Oxford English Dictionary, 1884–1928, and First Supplement, 1933



From Proto-Indo-European *bhruhs-to, from *bhreu ‎(to break up, cut).



frustum n ‎(genitive frustī); second declension

  1. a piece, bit; crumb, morsel, scrap of food


Second declension.

Case Singular Plural
nominative frustum frusta
genitive frustī frustōrum
dative frustō frustīs
accusative frustum frusta
ablative frustō frustīs
vocative frustum frusta


Derived termsEdit


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