Euclidean space

Math.1. ordinary two or threedimensional space.2. any vector space on which a realvalued inner product is defined.Also called Cartesian space.[188085]
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In geometry, a twoor threedimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.The only conception of physical space for over 2,000 years, it remains the most compelling and useful way of modeling the world as it is experienced. Though nonEuclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathematics itself, Euclidean space remains the point of departure for their study.* * *
Universalium. 2010.
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Euclidean space — Every point in three dimensional Euclidean space is determined by three coordinates. In mathematics, Euclidean space is the Euclidean plane and three dimensional space of Euclidean geometry, as well as the generalizations of these notions to… … Wikipedia
Euclidean space — Euklido erdvė statusas T sritis fizika atitikmenys: angl. Euclidean space vok. euklidischer Raum, m rus. эвклидово пространство, n pranc. espace euclidien, m … Fizikos terminų žodynas
Euclidean space — /juˌklɪdiən ˈspeɪs/ (say yooh.klideeuhn spays) noun space that is described within the rules of Euclidean geometry … Australian English dictionary
Euclidean space — noun a space in which Euclid s axioms and definitions apply; a metric space that is linear and finite dimensional • Hypernyms: ↑metric space * * * noun Usage: often capitalized E : the space to which Euclid s axioms and definitions (as of… … Useful english dictionary
Euclidean space — noun a) Ordinary two or three dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines. b) Any real vector space on which a real valued inner product (and, consequently … Wiktionary
Euclidean space — Euclid′ean space′ n. math. ordinary two or three dimensional space • Etymology: 1880–85 … From formal English to slang
euclidean space — noun Usage: often capitalized E Date: 1883 a space in which Euclid s axioms and definitions (as of straight and parallel lines and angles of plane triangles) apply … New Collegiate Dictionary
PseudoEuclidean space — A pseudo Euclidean space is a finite dimensional real vector space together with a non degenerate indefinite quadratic form. Such a quadratic form can, after a change of coordinates, be written as : q(x) = left(x 1^2+cdots + x k^2 ight) left(x… … Wikipedia
Fixed points of isometry groups in Euclidean space — A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.For an object, any unique center and, more… … Wikipedia
locally Euclidean space — Math. a topological space in which each point has a neighborhood that is homeomorphic to an open set in a Euclidean space of specified dimension. * * * … Universalium