See homothety in All languages combined, or Wiktionary
Download JSON data for homothety meaning in English (3.8kB)
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"etymology_text": "From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).",
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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.",
"type": "quotation"
},
{
"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": "quotation"
},
{
"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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"An isotropic scaling transformation of an affine space with a single fixed point."
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"(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point."
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"sense": "isotropic scaling transformation with a fixed point",
"word": "homothecy"
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{
"sense": "isotropic scaling transformation with a fixed point",
"word": "homogeneous dilation"
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{
"sense": "isotropic scaling transformation with a fixed point",
"word": "homothetic transformation"
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"translations": [
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"code": "eo",
"lang": "Esperanto",
"sense": "scaling transformation",
"word": "homotetio"
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{
"code": "fr",
"lang": "French",
"sense": "scaling transformation",
"tags": [
"feminine"
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"word": "homothétie"
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{
"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"
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{
"code": "es",
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"sense": "scaling transformation",
"tags": [
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"word": "homothety"
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},
{
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"4": "setting, placement, arrangement"
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"expansion": "θέσις (thésis, “setting, placement, arrangement”)",
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],
"etymology_text": "From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).",
"forms": [
{
"form": "homotheties",
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"text": "The product of two homotheties with the same centre is a homothety with that centre.",
"type": "quotation"
},
{
"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": "quotation"
},
{
"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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"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": [
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"word": "homotecia"
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],
"word": "homothety"
}
This page is a part of the kaikki.org machine-readable English 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.
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