# Euclidean Space

(redirected from*Euclidean spaces*)

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Related to Euclidean spaces: Euclidean vector space, N-dimensional Euclidean space

## euclidean space

[yü′klid·ē·ən ′spās] (mathematics)

A space consisting of all ordered sets (

*x*_{1}, …,*x*_{n }) of*n*numbers with the distance between (*x*_{1}, …,*x*_{n }) and (*y*_{1}, …,*y*_{n }) 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 (*x*_{1}*x*_{2}, …, *x*_{n} and point *M*^{*} has the coordinates (*x*_{1}^{*}, *x*_{2}^{*}, …, *x*_{n}^{*}), then the distance between these points is