See quaternion on Wiktionary
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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": "quote" } ], "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." ], "id": "en-quaternion-en-noun-0VgRU8FI", "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" ], "translations": [ { "_dis1": "1 2 97", "code": "ca", "lang": "Catalan", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "quaternió" }, { "_dis1": "1 2 97", "code": "cs", "lang": "Czech", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "kvaternion" }, { "_dis1": "1 2 97", "code": "nl", "lang": "Dutch", "sense": "a four-dimensional hypercomplex number", "tags": [ "neuter" ], "word": "quaternion" }, { "_dis1": "1 2 97", "code": "fi", "lang": "Finnish", "sense": "a four-dimensional hypercomplex number", "word": "kvaternio" }, { "_dis1": "1 2 97", "code": "fr", "lang": "French", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "quaternion" }, { "_dis1": "1 2 97", "code": "de", "lang": "German", "sense": "a four-dimensional hypercomplex number", "tags": [ "feminine" ], "word": "Quaternion" }, { "_dis1": "1 2 97", "code": "el", "lang": "Greek", "roman": "tetradónio", "sense": "a four-dimensional hypercomplex number", "tags": [ "neuter" ], "word": "τετραδόνιο" }, { "_dis1": "1 2 97", "code": "el", "lang": "Greek", "roman": "tetránio", "sense": "a four-dimensional hypercomplex number", "tags": [ "neuter" ], "word": "τετράνιο" }, { "_dis1": "1 2 97", "code": "hi", "lang": "Hindi", "roman": "catuṣṭayī", "sense": "a four-dimensional hypercomplex number", "word": "चतुष्टयी" }, { "_dis1": "1 2 97", "code": "is", "lang": "Icelandic", "sense": "a four-dimensional hypercomplex number", "tags": [ "feminine" ], "word": "fertala" }, { "_dis1": "1 2 97", "code": "it", "lang": "Italian", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "quaternione" }, { "_dis1": "1 2 97", "code": "ja", "lang": "Japanese", "roman": "shigensū", "sense": "a four-dimensional hypercomplex number", "word": "四元数" }, { "_dis1": "1 2 97", "code": "la", "lang": "Latin", "sense": "a four-dimensional hypercomplex number", "word": "quaternio" }, { "_dis1": "1 2 97", "code": "pl", "lang": "Polish", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "kwaternion" }, { "_dis1": "1 2 97", "code": "pt", "lang": "Portuguese", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "quaternião" }, { "_dis1": "1 2 97", "code": "ru", "lang": "Russian", "roman": "kvaternion", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "кватернион" }, { "_dis1": "1 2 97", "code": "es", "lang": "Spanish", "sense": "a four-dimensional hypercomplex number", "tags": [ "masculine" ], "word": "cuaternión" } ] } ], "sounds": [ { "ipa": "/kwəˈtɜːni.ən/", "tags": [ "UK" ] }, { "ipa": "/kwɑˈtɜɹniɑn/", "tags": [ "US" ] }, { "ipa": "/kwə-/", "tags": [ "US" ] }, { "ipa": "/-ən/", "tags": [ "US" ] } ], "synonyms": [ { "_dis1": "51 44 4", "sense": "group of four", "word": "foursome" }, { "_dis1": "0 0 0", "word": "tetrad" }, { "_dis1": "0 0 0", "word": "quartet" } ], "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": [ { "kind": "other", "name": "French entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 2 entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "fr", "name": "Four", "orig": "fr:Four", "parents": [ "Numbers", "All topics", "Terms by semantic function", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "fr", "name": "Mathematics", "orig": "fr:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "quaternion" ], "id": "en-quaternion-fr-noun-re5mY1di", "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" } ], "word": "quaternion" }
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-03-09 from the enwiktionary dump dated 2025-03-02 using wiktextract (32c88e6 and 633533e). 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.
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