See homothety on Wiktionary
{ "etymology_templates": [ { "args": { "1": "grc", "2": "ὁμο-", "3": "", "4": "same" }, "expansion": "Ancient Greek ὁμο- (homo-, “same”)", "name": "cog" } ], "etymology_text": "From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).", "forms": [ { "form": "homotheties", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "homothety (plural homotheties)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "_dis1": "0 0", "word": "homothetic" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "90 10", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "94 6", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "88 12", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "95 5", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "93 7", "kind": "other", "name": "Terms with Esperanto translations", "parents": [], "source": "w+disamb" }, { "_dis": "89 11", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "90 10", "kind": "other", "name": "Terms with Galician translations", "parents": [], "source": "w+disamb" }, { "_dis": "92 8", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "89 11", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "91 9", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "93 7", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:", "text": "The product of two homotheties with the same centre is a homothety with that centre.", "type": "quote" }, { "ref": "1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:", "text": "One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.", "type": "quote" }, { "ref": "2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:", "text": "Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ.", "type": "quote" } ], "glosses": [ "An isotropic scaling transformation of an affine space with a single fixed point." ], "id": "en-homothety-en-noun-K637mviE", "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "isotropic", "isotropic" ], [ "scaling", "scaling" ], [ "affine space", "affine space" ], [ "fixed point", "fixed point" ] ], "raw_glosses": [ "(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point." ], "synonyms": [ { "_dis1": "93 7", "sense": "isotropic scaling transformation with a fixed point", "word": "homothecy" }, { "_dis1": "93 7", "sense": "isotropic scaling transformation with a fixed point", "word": "homogeneous dilation" }, { "_dis1": "93 7", "sense": "isotropic scaling transformation with a fixed point", "word": "homothetic transformation" } ], "topics": [ "geometry", "mathematics", "sciences" ], "translations": [ { "_dis1": "94 6", "code": "eo", "lang": "Esperanto", "sense": "scaling transformation", "word": "homotetio" }, { "_dis1": "94 6", "code": "fr", "lang": "French", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homothétie" }, { "_dis1": "94 6", "code": "gl", "lang": "Galician", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotecia" }, { "_dis1": "94 6", "code": "it", "lang": "Italian", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "omotetia" }, { "_dis1": "94 6", "code": "pl", "lang": "Polish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "jednokładność" }, { "_dis1": "94 6", "code": "pl", "lang": "Polish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotetia" }, { "_dis1": "94 6", "code": "pt", "lang": "Portuguese", "sense": "scaling transformation", "word": "homotetia" }, { "_dis1": "94 6", "code": "es", "lang": "Spanish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotecia" } ] }, { "glosses": [ "A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case)." ], "id": "en-homothety-en-noun-Ar~hxDjl", "links": [ [ "commutative algebra", "commutative algebra" ], [ "homomorphism", "homomorphism" ], [ "module", "module" ] ], "qualifier": "commutative algebra", "raw_glosses": [ "(commutative algebra, Bourbakist) A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case)." ] } ], "wikipedia": [ "Homothetic transformation" ], "word": "homothety" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Esperanto translations", "Terms with French translations", "Terms with Galician translations", "Terms with Italian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Spanish translations" ], "etymology_templates": [ { "args": { "1": "grc", "2": "ὁμο-", "3": "", "4": "same" }, "expansion": "Ancient Greek ὁμο- (homo-, “same”)", "name": "cog" } ], "etymology_text": "From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).", "forms": [ { "form": "homotheties", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "homothety (plural homotheties)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "homothetic" } ], "senses": [ { "categories": [ "English terms with quotations", "Quotation templates to be cleaned", "en:Geometry", "en:Mathematics" ], "examples": [ { "ref": "1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:", "text": "The product of two homotheties with the same centre is a homothety with that centre.", "type": "quote" }, { "ref": "1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:", "text": "One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.", "type": "quote" }, { "ref": "2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:", "text": "Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ.", "type": "quote" } ], "glosses": [ "An isotropic scaling transformation of an affine space with a single fixed point." ], "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "isotropic", "isotropic" ], [ "scaling", "scaling" ], [ "affine space", "affine space" ], [ "fixed point", "fixed point" ] ], "raw_glosses": [ "(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point." ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "glosses": [ "A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case)." ], "links": [ [ "commutative algebra", "commutative algebra" ], [ "homomorphism", "homomorphism" ], [ "module", "module" ] ], "qualifier": "commutative algebra", "raw_glosses": [ "(commutative algebra, Bourbakist) A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case)." ] } ], "synonyms": [ { "sense": "isotropic scaling transformation with a fixed point", "word": "homothecy" }, { "sense": "isotropic scaling transformation with a fixed point", "word": "homogeneous dilation" }, { "sense": "isotropic scaling transformation with a fixed point", "word": "homothetic transformation" } ], "translations": [ { "code": "eo", "lang": "Esperanto", "sense": "scaling transformation", "word": "homotetio" }, { "code": "fr", "lang": "French", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homothétie" }, { "code": "gl", "lang": "Galician", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotecia" }, { "code": "it", "lang": "Italian", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "omotetia" }, { "code": "pl", "lang": "Polish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "jednokładność" }, { "code": "pl", "lang": "Polish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotetia" }, { "code": "pt", "lang": "Portuguese", "sense": "scaling transformation", "word": "homotetia" }, { "code": "es", "lang": "Spanish", "sense": "scaling transformation", "tags": [ "feminine" ], "word": "homotecia" } ], "wikipedia": [ "Homothetic transformation" ], "word": "homothety" }
Download raw JSONL data for homothety meaning in All languages combined (4.2kB)
{ "called_from": "form_descriptions/1831", "msg": "unrecognized sense qualifier: commutative algebra, Bourbakist", "path": [ "homothety" ], "section": "English", "subsection": "noun", "title": "homothety", "trace": "" } { "called_from": "form_descriptions/1831", "msg": "unrecognized sense qualifier: commutative algebra, Bourbakist", "path": [ "homothety" ], "section": "English", "subsection": "noun", "title": "homothety", "trace": "" }
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.