See Möbius group on Wiktionary
{ "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.", "forms": [ { "form": "Möbius groups", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "Möbius group (plural Möbius groups)", "name": "en-noun" } ], "hypernyms": [ { "_dis1": "52 48", "word": "Lie group" } ], "lang": "English", "lang_code": "en", "meronyms": [ { "_dis1": "52 48", "word": "Möbius transformation" } ], "pos": "noun", "related": [ { "_dis1": "52 48", "word": "Möbius strip" }, { "_dis1": "52 48", "word": "Möbius transformation" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Group theory", "orig": "en:Group theory", "parents": [ "Algebra", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "67 33", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "82 18", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "69 31", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "77 23", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "71 29", "kind": "other", "name": "Terms with Dutch translations", "parents": [], "source": "w+disamb" }, { "_dis": "76 24", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "64 36", "kind": "other", "langcode": "en", "name": "Non-Euclidean geometry", "orig": "en:Non-Euclidean geometry", "parents": [], "source": "w+disamb" } ], "glosses": [ "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere." ], "id": "en-Möbius_group-en-noun-J0is7NYn", "links": [ [ "group theory", "group theory" ], [ "projective general linear group", "projective general linear group" ], [ "Möbius transformations", "Möbius transformations" ], [ "Riemann sphere", "Riemann sphere" ] ], "raw_glosses": [ "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere." ], "topics": [ "group-theory", "mathematics", "sciences" ], "translations": [ { "_dis1": "94 6", "code": "nl", "lang": "Dutch", "sense": "PGL(2,C)", "tags": [ "feminine", "masculine" ], "word": "Möbius-groep" }, { "_dis1": "94 6", "code": "es", "lang": "Spanish", "sense": "PGL(2,C)", "tags": [ "masculine" ], "word": "grupo de Möbius" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Group theory", "orig": "en:Group theory", "parents": [ "Algebra", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant." ], "id": "en-Möbius_group-en-noun-ohRFK8Nm", "links": [ [ "group theory", "group theory" ], [ "group", "group" ], [ "hypersphere", "hypersphere" ], [ "invariant", "invariant" ] ], "raw_glosses": [ "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant." ], "topics": [ "group-theory", "mathematics", "sciences" ] } ], "synonyms": [ { "_dis1": "52 48", "word": "Moebius group" }, { "_dis1": "52 48", "word": "Mobius group" } ], "wikipedia": [ "Möbius group" ], "word": "Möbius group" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English nouns", "English terms spelled with Ö", "English terms spelled with ◌̈", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Dutch translations", "Terms with Spanish translations", "en:Non-Euclidean geometry" ], "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.", "forms": [ { "form": "Möbius groups", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "Möbius group (plural Möbius groups)", "name": "en-noun" } ], "hypernyms": [ { "word": "Lie group" } ], "lang": "English", "lang_code": "en", "meronyms": [ { "word": "Möbius transformation" } ], "pos": "noun", "related": [ { "word": "Möbius strip" }, { "word": "Möbius transformation" } ], "senses": [ { "categories": [ "en:Group theory" ], "glosses": [ "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere." ], "links": [ [ "group theory", "group theory" ], [ "projective general linear group", "projective general linear group" ], [ "Möbius transformations", "Möbius transformations" ], [ "Riemann sphere", "Riemann sphere" ] ], "raw_glosses": [ "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere." ], "topics": [ "group-theory", "mathematics", "sciences" ] }, { "categories": [ "en:Group theory" ], "glosses": [ "For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant." ], "links": [ [ "group theory", "group theory" ], [ "group", "group" ], [ "hypersphere", "hypersphere" ], [ "invariant", "invariant" ] ], "raw_glosses": [ "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant." ], "topics": [ "group-theory", "mathematics", "sciences" ] } ], "synonyms": [ { "word": "Moebius group" }, { "word": "Mobius group" } ], "translations": [ { "code": "nl", "lang": "Dutch", "sense": "PGL(2,C)", "tags": [ "feminine", "masculine" ], "word": "Möbius-groep" }, { "code": "es", "lang": "Spanish", "sense": "PGL(2,C)", "tags": [ "masculine" ], "word": "grupo de Möbius" } ], "wikipedia": [ "Möbius group" ], "word": "Möbius group" }
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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 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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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