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 ?
where [phi](t) is instantaneous angle between vectors of the IV of current and voltage in the arithmetic 3-dimensional space [X.
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.
It can track a ball in 3-dimensional space and measures the ball's entire 3D trajectory.
We can also characterize the type of defect involved and its depth in 3-dimensional space.
Jiu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J.

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