"homothety" meaning in All languages combined

See homothety on Wiktionary

Noun [English]

Forms: homotheties [plural]
Etymology: From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”). Etymology templates: {{cog|grc|ὁμο-||same}} Ancient Greek ὁμο- (homo-, “same”) Head templates: {{en-noun}} homothety (plural homotheties)
  1. (mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point. Categories (topical): Geometry, Mathematics Synonyms (isotropic scaling transformation with a fixed point): homothecy, homogeneous dilation, homothetic transformation Translations (scaling transformation): homotetio (Esperanto), homothétie [feminine] (French), homotecia [feminine] (Galician), omotetia [feminine] (Italian), jednokładność [feminine] (Polish), homotetia [feminine] (Polish), homotetia (Portuguese), homotecia [feminine] (Spanish)
    Sense id: en-homothety-en-noun-K637mviE Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, 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 Disambiguation of English entries with incorrect language header: 89 11 Disambiguation of Entries with translation boxes: 94 6 Disambiguation of Pages with 1 entry: 87 13 Disambiguation of Terms with Esperanto translations: 92 8 Disambiguation of Terms with French translations: 88 12 Disambiguation of Terms with Galician translations: 89 11 Disambiguation of Terms with Italian translations: 91 9 Disambiguation of Terms with Polish translations: 88 12 Disambiguation of Terms with Portuguese translations: 89 11 Disambiguation of Terms with Spanish translations: 92 8 Topics: geometry, mathematics, sciences Disambiguation of 'isotropic scaling transformation with a fixed point': 93 7 Disambiguation of 'scaling transformation': 94 6
  2. (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).
    Sense id: en-homothety-en-noun-Ar~hxDjl
The following are not (yet) sense-disambiguated
Related terms: homothetic

Inflected forms

Alternative forms

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          "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.",
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          "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.",
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        {
          "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.",
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        "(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point."
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          "word": "homotetio"
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      "code": "eo",
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      "sense": "scaling transformation",
      "word": "homotetio"
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    {
      "code": "fr",
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      "word": "homotetia"
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    {
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      "sense": "scaling transformation",
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}

Download raw JSONL data for homothety meaning in All languages combined (4.2kB)

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  "subsection": "noun",
  "title": "homothety",
  "trace": ""
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{
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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 2024-09-22 from the enwiktionary dump dated 2024-09-20 using wiktextract (af5c55c and 66545a6). 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.