Euclidean space

(redirected from N-dimensional Euclidean space)
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Related to N-dimensional Euclidean space: Euclidean vector space

Euclid′ean space′

ordinary two- or three-dimensional space.
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Noun1.Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
metric 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
euklidovský prostor
espacio euclideoespacio euclídeoespacio euclidiano
euklidinen avaruus
euklidski prostor
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.