# Euclidean space

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Related to N-dimensional Euclidean space: Euclidean vector space

## Euclid′ean space′

n.
ordinary two- or three-dimensional space.
[1880–85]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensionalmetric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
Translations
euklidovský prostor
espacio euclideoespacio euclídeoespacio euclidiano
euklidinen avaruus
euklidski prostor
ユークリッド空間
euklidiskt rum
References in periodicals archive ?
Subject to (Eq.) X, where X is an open convex subset of Rn (n-dimensional Euclidean space), (Eq.) and (Eq.) are real-valued functions defined on X, are real-valued functions defined on X, and for each (Eq.) 0 for all x satisfying the constraints of (P).
Let H = [partial derivative]/[partial derivative]t - [DELTA], T be a positive real number, x = ([x.sub.1], [x.sub.2], ..., [x.sub.N]) be a point in the N-dimensional Euclidean space [R.sup.N], B be a N-dimensional ball {x [member of] [R.sup.N] : [absolute value of (x)] < R} centered at the origin with a radius R, dB be the boundary of B, v(x) denote the unit inward normal at x [member of] [partial derivative]B, and [[chi].sub.B](x) be the characteristic function, which is 1 for x [member of] B and 0 for x [member of] [R.sup.N]\B.
Let W be a nonempty subset of n-dimensional Euclidean space [R.sup.n]; the diameter of W is defined as
The graphs can be represented as a set of n points in n-dimensional Euclidean space. The position of a point is described according to its relation to other points and is coded as a vector containing a list of the nearest neighbors.

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