English

A frustum of a decagonal pyramid

Noun

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

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

• frustum culling
• view frustum
• viewing frustum

Related terms

• bifrustum

Translations

References

1. ↑ James A. H. Murray [et al.], editor (1884–1928) A New English Dictionary on Historical Principles (Oxford English Dictionary), London: Clarendon Press, OCLC 15566697; and The Oxford English Dictionary; being a Corrected Re-issue with an Introduction, Supplement, and Bibliography of A New English Dictionary on Historical Principles (the First Supplement), Oxford: Clarendon Press, 1933, OCLC 2748467.

Latin

Etymology

From Proto-Italic *frustom, from Proto-Indo-European *bʰrus-tós, from *bʰrews- ‎(“to break up, cut”).

Pronunciation

• (Classical) IPA^(key): /ˈfrus.tum/, [ˈfrʊs.tũ]

Noun

frustum n ‎(genitive frustī); second declension

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

Inflection

Second declension.

Synonyms

• (piece): fragmentum, segmentum
• (crumb): mīca

Derived terms

• frustulentus

Descendants

• English: frustum
• Italian: frusta
• Spanish: frusto, frusta

References

• frustum in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
• frustum in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• FRUSTUM in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition, 1883–1887)