### Definition of Euclidean space

1. Noun. A space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional.

Generic synonyms: Metric Space

### Definition of Euclidean space

1. Noun. Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines. ¹

2. Noun. (mathematics) Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined. ¹

¹ Source: wiktionary.com

### Euclidean Space Pictures

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### Lexicographical Neighbors of Euclidean Space

 EucharistsEuchiteEuchitesEucinostomusEucinostomus gulaEuclidEuclideanEuclidean algorithmEuclidean distanceEuclidean geometry Euclidean groupEuclidean groupsEuclidean metricEuclidean planeEuclidean planesEuclidean space (current term)Euclidean spacesEuclidianEuclidian spaceEuclidian spaces EudermaEuderma maculataEudora WeltyEudoxianEudoxiansEudromias morinellusEudyptesEuflagellataEugeneEugene Curran Kelly

### Literary usage of Euclidean space

Below you will find example usage of this term as found in modern and/or classical literature:

1. Projective Geometry by Oswald Veblen, John Wesley Young (1918)
"Assumptions for a Euclidean space. A Euclidean space can be characterized completely by means of a set of assumptions stated in terms of order relations. ..."

2. Science by American Association for the Advancement of Science (1899)
"But the text shows that this relation of hyperbolic to Euclidean space can be ... Thus no theory of the flatness of Euclidean space can be founded on it. ..."

3. Geometry of Riemannian Spaces by Elie Cartan (1983)
"The easiest way of determining the geometric properties of this space consists of an identification with Euclidean space in any way possible. ..."

4. The American Mathematical Monthly by Mathematical Association of America (1901)
"Just as the Bolyai plane is utterly independent of the Euclidean plane, so the triply extended space of Bolyai is utterly independent of any Euclidean space ..."

5. The Encyclopedia Americana: A Library of Universal Knowledge (1919)
"All three types of space can be exemplified by the selection of entities from Euclidean space, as we have seen, and the three therefore have an equal ..."

6. Proceedings of the American Philosophical Society Held at Philadelphia for by American Philosophical Society (1920)
"A plane in three-dimensional space may be regarded as Euclidean space of two ... A curved surface in three dimensions, however, is non-Euclidean space of ..."

7. Proceedings of the American Association for the Advancement of Science (1899)
"But the text shows that this relation of hyperbolic to Euclidean space can be ... Thus no theory of the flatness of Euclidean space can be founded on it. ..."