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.

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

References in periodicals archive ?
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).
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.
It is necessary to go beyond the Euclidian space with three orthogonal axes.