Euclidean Space

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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 ?
The one ethnic proportion variable that remains in the model is still not in the Euclidean space.
Let M be an n-dimensional (n [greater than or equal to] 3) submanifold of a Euclidean space [E.
While the result is quite intuitive in Euclidean space, it holds in all normed vector spaces (even if the indifferent set is thick somewhere).
Atomic objects are real-valued vectors in n-dimensional Euclidean space, in practice represented by n-tuples of components taken in some basis.
Yaprak, The minimal translation surfaces in Euclidean space, Soochow J.
Their approach places the discrete optimization problem into the Euclidean space of locations of TSP.
In mathematics, a surface can be defined to be a 2-D submanifold of 3-D Euclidean space.
As a scientist, he would believe in the totality of the Euclidean space.
Delineating buffers on a terrain surface requires that distance is measured on the surface rather than in 2D Euclidean space.
Odio frees her characters, allowing them to leave Euclidean space and enter instead into a new and unknown cosmic conscience.
For the sphere of the divine increasingly assumes the form of an infinite plenitude of which the whole infinite universe is the seal, shadow, or reflection, while the three spheres of Neoplatonic being merge into the three dimensions of Euclidean space.
Therefore, this proposal aims at developing an alternative technique for the representation, analysis and numerical treatment of subsets of the Euclidean space.