# Euclidean space

Euclidean space is the fundamental space of classical geometry. Originally, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any nonnegative integer dimension, including the three-dimensional space and the Euclidean plane (dimension two). It was introduced by the Ancient Greek mathematician Euclid of Alexandria, and the qualifier Euclidean is used to distinguish it from other spaces that were later discovered in physics and modern mathematics.

There is essentially only one Euclidean space of each dimension; that is, all Euclidean spaces of a given dimension are isomorphic. Therefore, in many cases, it is possible to work with a specific Euclidean space, which is generally the real n-space $\mathbb {R} ^{n},$ equipped with the dot product. An isomorphism from a Euclidean space to $\mathbb {R} ^{n}$ associates with each point an n-tuple of real numbers which locate that point in the Euclidean space and are called the Cartesian coordinates of that point.