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frustum

From Wiktionary, the free dictionary

English

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A frustum of a decagonal pyramid
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Etymology

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Borrowed fromLatinfrustum(morsel).

Pronunciation

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Noun

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frustum (pluralfrustumsorfrusta)

  1. Acone orpyramid whosetip has beentruncated by aplaneparallel to itsbase.
    • 1742, Colin MacLaurin,A Treatise of Fluxions, volume 1,page25:
      In a parabolic conoid this difference vaniſhes, thefruſtum being always equal to a cylinder of the ſame height upon the ſection of the conoid that biſects the altitude of thefruſtum and is parallel to its baſes.
    • 1809,William Nicholson, “FRUSTUM”, inThe British Encyclopedia, or Dictionary of Arts and Sciences; [], volumeIII (E … I), London: Printed byC[harles] Whittingham, []; forLongman, Hurst, Rees, and Orme, [],→OCLC:
      This theorem holds good for complete solids as well asfrustums, whether right or oblique, and not only of the solids generated from the conic sections, but also of all pyramids, cones, and in short of any solid, whose parallel sections are similar figures.
    • 1974,Stanisław Lem, translated byMichael Kandel,The Cyberiad:
      Come, everyfrustum longs to be a cone,
      And every vector dreams of matrices.
    • 2006, Pawan Harish Nirnimesh, P. J. Narayanan,Culling an Object Hierarchy to aFrustum 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 viewfrustums (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,page122:
      Here, the dynamics of the fluid-filledfrusta of cones are considered (see Figure 5.5). Thefrusta are clamped at their roots and free at their ends.
  2. A portion of asphere, or in general anysolid,delimited by twoparallelplanes.
    • 1840, James Blundell,Observations on Some of the More Important Diseases of Women,page131:
      In some women it[the os uteri] is flat, in many more tuberose, and forming, as it were, afrustum of a sphere;[].
    • 2014, John Bird,Engineering Mathematics,page183:
      Problem 22. Determine the volume of afrustum of a sphere of diameter 49.74 cm if the diameter[sic] of the ends of thefrustum are 24.0 and 40.0 cm, and the height of thefrustum is 7.00 cm.

Usage notes

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The misspellingfrustrum is by incorrect analogy withfrustrate, also of Latin origin.[1]

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

Derived terms

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Related terms

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Translations

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truncated cone or pyramid

References

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  1. ^James A. H. Murrayet al., editors (1884–1928), “Frustum”, inA New English Dictionary on Historical Principles (Oxford English Dictionary), London:Clarendon Press,→OCLC.

Latin

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Etymology

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FromProto-Italic*frustom, fromProto-Indo-European*bʰrus-tós, from*bʰrews-(to break up, cut).[1]

Pronunciation

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The etymology is consistent with the /u/ in the first syllable being short, and the word is shown without a macron in De Vaan's dictionary.[1] Although Bennett 1907 says "ū acc. to the Romance",[2] there are related words in Romance that point to short u in the descendants of the derivative *frŭstiāre,[3] such as Old Frenchfroissier.

Noun

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frū̆stum n (genitivefrū̆stī);second declension

  1. apiece,bit;crumb,morsel,scrap offood

Declension

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Second-declension noun (neuter).

singularplural
nominativefrū̆stumfrū̆sta
genitivefrū̆stīfrū̆stōrum
dativefrū̆stōfrū̆stīs
accusativefrū̆stumfrū̆sta
ablativefrū̆stōfrū̆stīs
vocativefrū̆stumfrū̆sta

Synonyms

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Derived terms

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Descendants

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References

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  1. 1.01.1De Vaan, Michiel (2008) “frustum”, inEtymological Dictionary of Latin and the other Italic Languages (Leiden Indo-European Etymological Dictionary Series; 7), Leiden, Boston: Brill,→ISBN,page245
  2. ^Charles E. Bennett (1907) “Hidden Quantity”, inThe Latin Language – a historical outline of its sounds, inflections, and syntax, Boston: Allyn and Bacon,page59
  3. ^Walther von Wartburg (1928–2002) “*frustiare”, inFranzösisches Etymologisches Wörterbuch, volumes3: D–F,page831

Further reading

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  • frustum”, inCharlton T. Lewis and Charles Short (1879)A Latin Dictionary, Oxford: Clarendon Press
  • frustum”, inCharlton T. Lewis (1891)An Elementary Latin Dictionary, New York: Harper & Brothers
  • "frustum", in Charles du Fresne du Cange’sGlossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius and others, edited by Léopold Favre, 1883–1887)
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