Euclidean Space

(redirected from Euclidean spaces)
Also found in: Dictionary, Thesaurus.
Related to Euclidean spaces: Euclidean vector space, N-dimensional Euclidean 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 ?
Let M be an n-dimensional (n [greater than or equal to] 3) submanifold of a Euclidean space [E.
Let M be an n-dimensional (n [greater than or equal to] 3) submanifold in a Euclidean space satisfying Chen's equality, then
infinity]] (as we shall see these are, respectively, the "perfect substitutes" and "perfect complements" cases) and to the familiar Euclidean space [L.
While balls in Euclidean space are rotation invariant, the same is not true in spaces endowed with other metrics.
The union of the two orthogonal proper (or classical) Euclidean 3-spaces yields a compound six-dimensional proper (or classical) Euclidean space with mutually orthogonal dimensions [x.
1 on a differential manifold in such a way that the properties of self-concordant functions in Euclidean space are preserved.
In all other dimensions, Euclidean spaces have a unique smooth description, which mathematicians have long used and understand well.
A combinatorial decomposition of Euclidean spaces Rn with contribution to visibility.
The winding mapping of Euclidean space onto a sphe-re can be extended to any number of dimensions.
This is a systematic presentation of results concerning the isometric embedding of Riemannian manifolds in local and global Euclidean spaces, especially focused on the isometric embedding of surfaces in a Euclidean space R3 and primarily employing partial differential equation techniques for proving results.
Moreover the minimal surfaces of translation of a higher dimensional Euclidean space are obtained in [13] and of a semi-Euclidean space are investigated in [12].
Terras, Finite analogues of Euclidean space, Journal of Computational and Applied Mathematics, 68 (1996), 221-238.