quaternion

quaternion

English

Etymology

From Middle English quaternioun, from Late Latin quaterniō, from quaternī, ablative form of quater (“four times”) + -iōn.[1][2][3] Doublet of kern.

The mathematics sense was coined by William Rowan Hamilton in 1843.

Pronunciation

• (UK) IPA^(key): /kwəˈtəːni.ən/

Noun

quaternion (plural quaternions)

1. A group or set of four people or things.
   • 1526, Tyndale, William, The Bible, Acts XII, translation of The Bible:

     Then wer the dayes of unlevended breed, and when he had caught hym, he put him in preson, and delyvered hym to iiij. quaternions off soudiers to be kept, entendynge after ester to brynge hym forth to the people.

   • 1885, Roberts, Alexander; Donaldson, James; Coxe, Arthur Cleveland; Schaff, Philip, Nicene and Post-Nicene Fathers: Series II, volume 2, book 6, chapter 13, translation of Historia Ecclesiastica by Socrates of Constantinople:

     This quaternion of revilers has traduced Origen, but not on the same grounds, one having found one cause of accusation against him, and another another; and thus each has demonstrated that what he has taken no objection to, he has fully accepted.

   • 2004, Glenn, Jason, Politics and History in the Tenth Century: The Work and World of Richer of Reims, Cambridge: Cambridge University Press, →ISBN, page 140:

     We saw above that the fourth quire consists of ten folios, two of which (folios 29 and 31) Richer added to a quaternion (folios 23 to 28, 30, 32). Most of the folios Richer added to his manuscript supplement, elaborate, or amend text that he had already composed in the codex.

2. A word of four syllables.
   • 1815, Scott, Sir Walter, chapter 13, in Guy Mannering:

     In his general deportment he was pompous and important, affecting a species of florid elocution, which often became ridiculous from his misarranging the triads and quaternions with which he loaded his sentences.

3. (mathematics) A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.
   • 2004, Eberly, David H., 3D Game Engine Architecture: Engineering Real-Time Applications with Wild Magic:

     The right-hand side of the quaternion equation requires scalar multiplication and quaternion addition.

Synonyms

• (group of four): foursome, tetrad; see also Thesaurus:quartet

Hypernyms

• (mathematics): hypercomplex number

Hyponyms

• (mathematics): versor

Derived terms

• quaternionic

Translations

a four-dimensional hypercomplex number

Catalan: quaternió m Dutch: quaternion (nl) n Finnish: kvaternio (fi) French: quaternion (fr) m German: Quaternion f Greek: τετραδόνιο (el) n (tetradónio), τετράνιο n (tetránio) Icelandic: fertala f Italian: quaternione m Japanese: 四元数 (ja) (shigensū) Latin: quaternio (la) Polish: kwaternion m Portuguese: quaternião m Russian: кватернион (ru) m (kvaternion) Spanish: cuaternión m

See also

• (mathematics):
  • octonion
  • sedenion
  • trigintaduonion

References

1. “quaternion”, in Dictionary.com Unabridged, Dictionary.com, LLC, 1995–present.
2. American Heritage Dictionary of the English Language, fourth edition
3. Concise Oxford English Dictionary, eleventh edition

Further reading

• Cayley–Dickson construction on Wikipedia.Wikipedia

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French

Noun

quaternion m (plural quaternions)

1. (mathematics) quaternion

Further reading

• “quaternion”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.