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 ?
We can now examine the physical examples which the solutions to Laplace's equations represent in our familiar 3-dimensional space.
Clearly, this case belongs to an infinite line charge distribution in 3-dimensional space, where the electric field diminishes inversely as the radial distance from the line charge.
These are identified as the potential and electric field, respectively, of the electric dipole in 3-dimensional space.
Table I summarizes the solutions of the Laplace's equations in n dimensions and the physical examples they represent in 3-dimensional space.
The hyper-sphere corresponds to two points at a distance of r from the origin in 1-dimensional space, whereas it constitutes a circle of radius r in 2-dimensional plane, and of course, the familiar sphere in 3-dimensional space.
Jiu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J.
The technology allows users to experience the traditional, 2-dimensional sites as 3-dimensional spaces and even convert their profile pages on social network platforms, such as MySpace and Facebook, into 3D environments.

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