different between quaternion vs quaternary

English

Etymology

From Middle English quaternioun, from Late Latin quaterni?, from quatern?, ablative form of quater (“four times”) + -i?n. The mathematics sense was coined by William Rowan Hamilton in 1843.

Pronunciation

• (UK) IPA^(key): /kw??t??ni.?n/

Noun

quaternion (plural quaternions)

1. A group or set of four people or things.
2. A word of four syllables.
3. (mathematics) A four-dimensional hypercomplex number that consists of a real dimension and three imaginary ones (i, j, k) that are each an independent square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.

Synonyms

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

Hypernyms

• hypercomplex number

Derived terms

• quaternionic

Translations

See also

• (mathematics):
  • octonion
  • sedenion
  • trigintaduonion

Further reading

• Cayley–Dickson construction on Wikipedia.Wikipedia

References

English

Etymology

From the Latin quatern?rius (“containing or consisting of four”), from quatern? (“four each”, “four at a time”) + -?rius (whence the English suffix -ary); compare the French quaternaire.

Pronunciation

• (UK) IPA^(key): /kw??t??n??i/; (rare) IPA^(key): /?kw??t?n(?)?i/
• (US) IPA^(key): /?kw??t??n???i/

Adjective

quaternary (not comparable)

1. Of fourth rank or order

   the quaternary stress in a pronounced word

2. Of a mathematical expression containing e.g. x⁴
3. Relating to or in number base four
4. (organic chemistry) quaternary ammonium
5. (inorganic chemistry) composed of four elements

Usage notes

The fourth ordinal from Latin that might etymologically follow tertiary is quartary, but quaternary (from the distributive number instead) is more usual in English.

Related terms

• quaternion

Derived terms

• bisquaternary
• quaternary ammonium

Translations

See also

• unary, unitary (1)
  • primary (1st)
• binary (2)
  • secondary (2nd)
• ternary or trinary (3)
  • tertiary (3rd)
• quaternary (4)
  • quartary (4th)
  • tetranary (4)
• quinary (5)
• senary (6)
• septenary (7)
• octonary (8)
• novenary (9)
  • nonary (9th)
• denary (10)
• duodenary (12)
• vicenary (20)
• tricenary (30)
• sexagenary (60)
• centenary (100)

Noun

quaternary (plural quaternaries)

1. (chemistry) A quaternary compound.
2. (geology) The Quaternary period or the system of deposits laid down during it.