Definition from Wiktionary, the free dictionary
Jump to: navigation, search


A frustum of a decagonal pyramid
Wikipedia has an article on:


Wikipedia has an article on:



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 notes[edit]

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.

Derived terms[edit]

Related terms[edit]



  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 terms[edit]