# Euclidean space

Euclidean space
1. ordinary two- or three-dimensional space.
2. any vector space on which a real-valued inner product is defined.
Also called Cartesian space.
[1880-85]

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In geometry, a two-or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.

The only conception of physical space for over 2,000 years, it remains the most compelling and useful way of modeling the world as it is experienced. Though non-Euclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathematics itself, Euclidean space remains the point of departure for their study.

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Universalium. 2010.

### Look at other dictionaries:

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• Euclidean space — /juˌklɪdiən ˈspeɪs/ (say yooh.klideeuhn spays) noun space that is described within the rules of Euclidean geometry …

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• locally Euclidean space — Math. a topological space in which each point has a neighborhood that is homeomorphic to an open set in a Euclidean space of specified dimension. * * * …   Universalium