# Euclidean Space

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## euclidean space

[yü′klid·ē·ən ′spās]
(mathematics)
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

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These datasets are all reduced to a low-dimensional Euclidean space and aligned according to certain rules.
It is easier to answer this question for hyperbolic spaces than for Euclidean spaces since there is a family of non-crystallographic tilings of [H.
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Thus, while work in Hong Kong became valued for its closeness to the PRC in Euclidean space, this proximity was not the only (or even the primary) thing that made it interesting.
With Vectors 1 and 2 of Euclidean space (see Figure 1), the first set of dimensions seemed to be dominated by the Conventional-Authentic dimension.
While balls in Euclidean space are rotation invariant, the same is not true in spaces endowed with other metrics.
In Euclidean space, these integrals are obtained by showing that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Yaprak, The minimal translation surfaces in Euclidean space, Soochow J.
The classical Weierstrass formulae for minimal surfaces immersed in the three-dimensional Euclidean space [R.
An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space.
ToC is based on the use of continuous geometrical 3-space or more typically an n-space volume (a Euclidean space [R.

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