See Euclidean distance on Wiktionary
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for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as" ], "id": "en-Euclidean_distance-en-noun-83t06lkQ", "links": [ [ "geometry", "geometry" ], [ "distance", "distance" ], [ "point", "point" ], [ "square root", "square root" ], [ "sum", "sum" ], [ "square", "square" ], [ "difference", "difference" ], [ "coordinate", "coordinate" ], [ "two-dimensional", "two-dimensional" ], [ "Euclidean geometry", "Euclidean geometry" ] ], "raw_glosses": [ "(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:" ], "tags": [ "countable", "uncountable" ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "50 50", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Japanese translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:\n d( textbf a, textbf b)=√", "d( textbf a, textbf b)=√" ], "id": "en-Euclidean_distance-en-noun-ZRVM3zo7", "links": [ [ "geometry", "geometry" ], [ "distance", "distance" ], [ "point", "point" ], [ "square root", "square root" ], [ "sum", "sum" ], [ "square", "square" ], [ "difference", "difference" ], [ "coordinate", "coordinate" ], [ "two-dimensional", "two-dimensional" ], [ "Euclidean geometry", "Euclidean geometry" ] ], "raw_glosses": [ "(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:" ], "tags": [ "countable", "uncountable" ], "topics": [ "geometry", "mathematics", "sciences" ] } ], "synonyms": [ { "_dis1": "49 51", "word": "Cartesian distance" }, { "_dis1": "49 51", "tags": [ "US" ], "word": "euclidean distance" } ], "translations": [ { "_dis1": "50 50", "code": "fi", "lang": "Finnish", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "word": "euklidinen etäisyys" }, { "_dis1": "50 50", "code": "de", "lang": "German", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "tags": [ "masculine" ], "word": "euklidischer Abstand" }, { "_dis1": "50 50", "code": "hu", "lang": "Hungarian", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "word": "euklideszi távolság" }, { "_dis1": "50 50", "code": "it", "lang": "Italian", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "tags": [ "feminine" ], "word": "distanza euclidea" }, { "_dis1": "50 50", "code": "ja", "lang": "Japanese", "roman": "Yūkuriddo kyori", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "word": "ユークリッド距離" }, { "_dis1": "50 50", "code": "ro", "lang": "Romanian", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "tags": [ "feminine" ], "word": "distanță euclidiană" }, { "_dis1": "50 50", "code": "es", "lang": "Spanish", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "tags": [ "feminine" ], "word": "distancia euclidiana" }, { "_dis1": "50 50", "code": "sv", "lang": "Swedish", "sense": "distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points", "tags": [ "neuter" ], "word": "euklidiskt avstånd" } ], "wikipedia": [ "Euclidean distance" ], "word": "Euclidean distance" }
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