Euclidean Space

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Related to Euclidian space: Euclidean geometry, Euclidean vector space

euclidean space

[yü′klid·ē·ən ′spās]
A space consisting of all ordered sets (x1, …, xn ) of n numbers with the distance between (x1, …, xn ) and (y1, …, yn ) being given by the number n is called the dimension of the space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Euclidean Space


in mathematics, a space whose properties are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is an n-dimensional vector space, into which several special Cartesian coordinates can be introduced so that its metric is defined in the following manner: If point M has the coordinates (x1x2, …, xn and point M* has the coordinates (x1*, x2*, …, xn*), then the distance between these points is

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Suppose that A is compact and B is closed subset of the Euclidian space ([R.sup.n], [parallel]x[parallel]).
With this spatial enclosure, gravity and Euclidian space are suspended, allowing Dom and Ariadne to walk up a street in a ninety-degree angle, not quite, but almost like Frank Poole (Gary Lockwood) jogging around the Ferris wheel structure of the spaceship in Kubrick's 2001--a Space Odyssey (1968).
This group (more exactly, algebra) is a q-deformation of the universal enveloping algebra U(so(5)) which corresponds to the classical group SO(5) of the rotations in 5-dimensional Euclidian space. The obtained results generalize some of the results on orthogonal polynomials related to representations of the classical group SO(5) [1].
They defined three primary categories of space: topological space, projective space, and Euclidian space. It is Euclidian space that expands our view of how spatial cognition works using imagery.
k is a constant which takes one of three values: 0 for a flat Euclidian space, - 1 for a hyperbolic space, or + 1 for a spherical space.
It is an uneasy mix of new and older perceptual modalities--for example, of itineraries and durations within zones of Euclidian space continually interspersed with the shifting dimensions of digital and video simulation.
The Hausdorff approach states that the dimension of an object is related with the number N(s) of spheres of size s needed to over to object in a DE-dimensional Euclidian space.