## Euclidean spaceAny n-dimensional mathematical space that is a generalization of
the familiar two- and three-dimensional spaces described by the axioms of
Euclidean geometry. The term "n-dimensional
Euclidean space" (where n is any positive whole number) is usually
abbreviated to "Euclidean n-space", or even just "n-space".
Formally, Euclidean n-space is the set R^{n}
(where R is the set of real numbers)
together with the distance function, which is obtained
by defining the distance between two points (x_{1}, ...,
x_{n}) and (y_{1}, ...,y_{n})
to be the square root of (sigma) (x - _{i}y)_{i}^{2},
where the sum is over i = 1, ..., n. This distance function
is based on Pythagoras' theorem
and is called the Euclidean metric. ## Related categories• GEOMETRY• SPACE AND TIME | |||||

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