"quaternion" meaning in All languages combined

See quaternion on Wiktionary

Noun [English]

IPA: /kwəˈtɜːni.ən/ [UK], /kwɑˈtɜɹniɑn/ [US], /kwə-/ [US], /-ən/ [US] Forms: quaternions [plural]
Etymology: From Middle English quaternioun, from Late Latin quaterniō, from quaternī (“four each”) + -iō, from quater (“four times”). Doublet of kern. The mathematics sense was coined by Irish mathematician and astronomer William Rowan Hamilton in 1843. Etymology templates: {{inh|en|enm|quaternioun}} Middle English quaternioun, {{der|en|LL.|quaterniō}} Late Latin quaterniō, {{m|la|quaternus|quaternī|t=four each}} quaternī (“four each”), {{m|la|-iō}} -iō, {{m|la|quater||four times}} quater (“four times”), {{doublet|en|kern}} Doublet of kern, {{coin|en|Q11887|in=1843|nocap=1}} coined by Irish mathematician and astronomer William Rowan Hamilton in 1843 Head templates: {{en-noun}} quaternion (plural quaternions)
  1. A group or set of four people or things.
    Sense id: en-quaternion-en-noun-3DhkVSMe
  2. A word of four syllables.
    Sense id: en-quaternion-en-noun-nvqjJWMb
  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. Categories (topical): Mathematics, Four, Higher-dimensional geometry Translations (a four-dimensional hypercomplex number): quaternió [masculine] (Catalan), quaternion [neuter] (Dutch), kvaternio (Finnish), quaternion [masculine] (French), Quaternion [feminine] (German), τετραδόνιο (tetradónio) [neuter] (Greek), τετράνιο (tetránio) [neuter] (Greek), fertala [feminine] (Icelandic), quaternione [masculine] (Italian), 四元数 (shigensū) (Japanese), quaternio (Latin), kwaternion [masculine] (Polish), quaternião [masculine] (Portuguese), кватернион (kvaternion) [masculine] (Russian), cuaternión [masculine] (Spanish)
    Sense id: en-quaternion-en-noun-0VgRU8FI Disambiguation of Four: 22 28 49 Disambiguation of Higher-dimensional geometry: 8 5 87 Categories (other): English entries with incorrect language header, English entries with language name categories using raw markup, English entries with topic categories using raw markup Disambiguation of English entries with incorrect language header: 3 3 94 Disambiguation of English entries with language name categories using raw markup: 3 4 93 Disambiguation of English entries with topic categories using raw markup: 3 5 93 Topics: mathematics, sciences Disambiguation of 'a four-dimensional hypercomplex number': 1 1 98
The following are not (yet) sense-disambiguated
Synonyms: tetrad, quartet Synonyms (group of four): foursome Hypernyms: hypercomplex number [mathematics, sciences] Hyponyms: versor [mathematics, sciences] Derived forms: hyperbolic quaternion, quaternionic Related terms: octonion [mathematics, sciences], sedenion [mathematics, sciences], trigintaduonion [mathematics, sciences]
Disambiguation of 'group of four': 52 45 3

Noun [French]

Audio: LL-Q150 (fra)-Poslovitch-quaternion.wav Forms: quaternions [plural]
Head templates: {{fr-noun|m}} quaternion m (plural quaternions)
  1. (mathematics) quaternion Tags: masculine Categories (topical): Four, Mathematics
    Sense id: en-quaternion-fr-noun-re5mY1di Categories (other): French entries with incorrect language header Topics: mathematics, sciences

Inflected forms

Download JSON data for quaternion meaning in All languages combined (10.0kB)

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  "derived": [
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      "_dis1": "0 0 0",
      "word": "hyperbolic quaternion"
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      "_dis1": "0 0 0",
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  "etymology_templates": [
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      "args": {
        "1": "en",
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      "expansion": "Middle English quaternioun",
      "name": "inh"
    },
    {
      "args": {
        "1": "en",
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        "3": "quaterniō"
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    {
      "args": {
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      "name": "m"
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      "args": {
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      "expansion": "-iō",
      "name": "m"
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      "args": {
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        "2": "quater",
        "3": "",
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      },
      "expansion": "quater (“four times”)",
      "name": "m"
    },
    {
      "args": {
        "1": "en",
        "2": "kern"
      },
      "expansion": "Doublet of kern",
      "name": "doublet"
    },
    {
      "args": {
        "1": "en",
        "2": "Q11887",
        "in": "1843",
        "nocap": "1"
      },
      "expansion": "coined by Irish mathematician and astronomer William Rowan Hamilton in 1843",
      "name": "coin"
    }
  ],
  "etymology_text": "From Middle English quaternioun, from Late Latin quaterniō, from quaternī (“four each”) + -iō, from quater (“four times”). Doublet of kern.\nThe mathematics sense was coined by Irish mathematician and astronomer William Rowan Hamilton in 1843.",
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  "hyponyms": [
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      "_dis1": "0 0 0",
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      "word": "versor"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "_dis1": "0 0 0",
      "topics": [
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        "sciences"
      ],
      "word": "octonion"
    },
    {
      "_dis1": "0 0 0",
      "topics": [
        "mathematics",
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      "word": "sedenion"
    },
    {
      "_dis1": "0 0 0",
      "topics": [
        "mathematics",
        "sciences"
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      "word": "trigintaduonion"
    }
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          "ref": "1885, Alexander Roberts, James Donaldson, Arthur Cleveland Coxe, Philip Schaff, Nicene and Post-Nicene Fathers: Series II, volume 2, book 6, chapter 13, translation of Historia Ecclesiastica by Socrates of Constantinople",
          "text": "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.",
          "type": "quotation"
        },
        {
          "ref": "2004, Jason Glenn, Politics and History in the Tenth Century: The Work and World of Richer of Reims, Cambridge: Cambridge University Press, page 140",
          "text": "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.",
          "type": "quotation"
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      ],
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      ],
      "id": "en-quaternion-en-noun-3DhkVSMe",
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    },
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        {
          "ref": "1815, Sir Walter Scott, chapter 13, in Guy Mannering",
          "text": "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.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A word of four syllables."
      ],
      "id": "en-quaternion-en-noun-nvqjJWMb",
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          "_dis": "8 5 87",
          "kind": "topical",
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          "name": "Higher-dimensional geometry",
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          "ref": "2004, David H. Eberly, 3D Game Engine Architecture: Engineering Real-Time Applications with Wild Magic",
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          "real number"
        ],
        [
          "imaginary",
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        [
          "square root",
          "square root"
        ],
        [
          "vector",
          "vector"
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        [
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      "raw_glosses": [
        "(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."
      ],
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      "translations": [
        {
          "_dis1": "1 1 98",
          "code": "ca",
          "lang": "Catalan",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "quaternió"
        },
        {
          "_dis1": "1 1 98",
          "code": "nl",
          "lang": "Dutch",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "neuter"
          ],
          "word": "quaternion"
        },
        {
          "_dis1": "1 1 98",
          "code": "fi",
          "lang": "Finnish",
          "sense": "a four-dimensional hypercomplex number",
          "word": "kvaternio"
        },
        {
          "_dis1": "1 1 98",
          "code": "fr",
          "lang": "French",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "quaternion"
        },
        {
          "_dis1": "1 1 98",
          "code": "de",
          "lang": "German",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "feminine"
          ],
          "word": "Quaternion"
        },
        {
          "_dis1": "1 1 98",
          "code": "el",
          "lang": "Greek",
          "roman": "tetradónio",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "neuter"
          ],
          "word": "τετραδόνιο"
        },
        {
          "_dis1": "1 1 98",
          "code": "el",
          "lang": "Greek",
          "roman": "tetránio",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "neuter"
          ],
          "word": "τετράνιο"
        },
        {
          "_dis1": "1 1 98",
          "code": "is",
          "lang": "Icelandic",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "feminine"
          ],
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        },
        {
          "_dis1": "1 1 98",
          "code": "it",
          "lang": "Italian",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "quaternione"
        },
        {
          "_dis1": "1 1 98",
          "code": "ja",
          "lang": "Japanese",
          "roman": "shigensū",
          "sense": "a four-dimensional hypercomplex number",
          "word": "四元数"
        },
        {
          "_dis1": "1 1 98",
          "code": "la",
          "lang": "Latin",
          "sense": "a four-dimensional hypercomplex number",
          "word": "quaternio"
        },
        {
          "_dis1": "1 1 98",
          "code": "pl",
          "lang": "Polish",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "kwaternion"
        },
        {
          "_dis1": "1 1 98",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "quaternião"
        },
        {
          "_dis1": "1 1 98",
          "code": "ru",
          "lang": "Russian",
          "roman": "kvaternion",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "кватернион"
        },
        {
          "_dis1": "1 1 98",
          "code": "es",
          "lang": "Spanish",
          "sense": "a four-dimensional hypercomplex number",
          "tags": [
            "masculine"
          ],
          "word": "cuaternión"
        }
      ]
    }
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      "tags": [
        "UK"
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      "ipa": "/kwɑˈtɜɹniɑn/",
      "tags": [
        "US"
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        "US"
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      "tags": [
        "US"
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    {
      "_dis1": "52 45 3",
      "sense": "group of four",
      "word": "foursome"
    },
    {
      "_dis1": "0 0 0",
      "word": "tetrad"
    },
    {
      "_dis1": "0 0 0",
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  "word": "quaternion"
}

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  "etymology_text": "From Middle English quaternioun, from Late Latin quaterniō, from quaternī (“four each”) + -iō, from quater (“four times”). Doublet of kern.\nThe mathematics sense was coined by Irish mathematician and astronomer William Rowan Hamilton in 1843.",
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  "lang_code": "en",
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      "word": "octonion"
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          "ref": "1885, Alexander Roberts, James Donaldson, Arthur Cleveland Coxe, Philip Schaff, Nicene and Post-Nicene Fathers: Series II, volume 2, book 6, chapter 13, translation of Historia Ecclesiastica by Socrates of Constantinople",
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          "type": "quotation"
        },
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          "ref": "2004, Jason Glenn, Politics and History in the Tenth Century: The Work and World of Richer of Reims, Cambridge: Cambridge University Press, page 140",
          "text": "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.",
          "type": "quotation"
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      ],
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    {
      "categories": [
        "English terms with quotations"
      ],
      "examples": [
        {
          "ref": "1815, Sir Walter Scott, chapter 13, in Guy Mannering",
          "text": "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.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A word of four syllables."
      ],
      "links": [
        [
          "syllable",
          "syllable"
        ]
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2004, David H. Eberly, 3D Game Engine Architecture: Engineering Real-Time Applications with Wild Magic",
          "text": "The right-hand side of the quaternion equation requires scalar multiplication and quaternion addition.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "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."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "hypercomplex number",
          "hypercomplex number"
        ],
        [
          "real",
          "real number"
        ],
        [
          "imaginary",
          "imaginary number"
        ],
        [
          "square root",
          "square root"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "rotation",
          "rotation"
        ]
      ],
      "raw_glosses": [
        "(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."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/kwəˈtɜːni.ən/",
      "tags": [
        "UK"
      ]
    },
    {
      "ipa": "/kwɑˈtɜɹniɑn/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/kwə-/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/-ən/",
      "tags": [
        "US"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "group of four",
      "word": "foursome"
    },
    {
      "word": "tetrad"
    },
    {
      "word": "quartet"
    }
  ],
  "translations": [
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "quaternió"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "neuter"
      ],
      "word": "quaternion"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "a four-dimensional hypercomplex number",
      "word": "kvaternio"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "quaternion"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "feminine"
      ],
      "word": "Quaternion"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "tetradónio",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "neuter"
      ],
      "word": "τετραδόνιο"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "tetránio",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "neuter"
      ],
      "word": "τετράνιο"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "feminine"
      ],
      "word": "fertala"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "quaternione"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "shigensū",
      "sense": "a four-dimensional hypercomplex number",
      "word": "四元数"
    },
    {
      "code": "la",
      "lang": "Latin",
      "sense": "a four-dimensional hypercomplex number",
      "word": "quaternio"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "kwaternion"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "quaternião"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "kvaternion",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "кватернион"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "a four-dimensional hypercomplex number",
      "tags": [
        "masculine"
      ],
      "word": "cuaternión"
    }
  ],
  "wikipedia": [
    "quaternion"
  ],
  "word": "quaternion"
}

{
  "forms": [
    {
      "form": "quaternions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "m"
      },
      "expansion": "quaternion m (plural quaternions)",
      "name": "fr-noun"
    }
  ],
  "lang": "French",
  "lang_code": "fr",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "French countable nouns",
        "French entries with incorrect language header",
        "French lemmas",
        "French masculine nouns",
        "French nouns",
        "French terms with audio links",
        "fr:Four",
        "fr:Mathematics"
      ],
      "glosses": [
        "quaternion"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "quaternion",
          "quaternion#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) quaternion"
      ],
      "tags": [
        "masculine"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "audio": "LL-Q150 (fra)-Poslovitch-quaternion.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/1/1e/LL-Q150_%28fra%29-Poslovitch-quaternion.wav/LL-Q150_%28fra%29-Poslovitch-quaternion.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/1/1e/LL-Q150_%28fra%29-Poslovitch-quaternion.wav/LL-Q150_%28fra%29-Poslovitch-quaternion.wav.ogg",
      "text": "Audio"
    }
  ],
  "word": "quaternion"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.