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- Euclidean_space abstract "In mathematics, particularly in geometry, the concept of a Euclidean space encompasses Euclidean plane and the three-dimensional space of Euclidean geometry as spaces of dimensions 2 and 3 respectively. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term “Euclidean” distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions.Classical Greek geometry defined the Euclidean plane and Euclidean three-dimensional space using certain postulates, while the other properties of these spaces were deduced as theorems. Geometric constructions are also used to define rational numbers. When algebra and mathematical analysis became developed enough, this relation reversed and now it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry. It means that points of the space are specified with collections of real numbers, and geometric shapes are defined as equations and inequalities. This approach brings the tools of algebra and calculus to bear on questions of geometry, and has the advantage that it generalizes easily to Euclidean spaces of more than three dimensions.From the modern viewpoint, there is essentially only one Euclidean space of each dimension. With Cartesian coordinates it is modelled by the real coordinate space (Rn) of the same dimension. In dimension one this is the real line; in dimension two it is the Cartesian plane; and in higher dimensions it is a coordinate space with three or more real number coordinates. Mathematicians denote the n-dimensional Euclidean space by En if they wish to emphasize its Euclidean nature, but Rn is used as well, since the latter is assumed to have the standard Euclidean structure and these two structures are not always distinguished. Euclidean spaces have finite dimension.".
- Euclidean_space thumbnail Sphere_wireframe.svg?width=300.
- Euclidean_space wikiPageID "9697".
- Euclidean_space wikiPageRevisionID "606558060".
- Euclidean_space hasPhotoCollection Euclidean_space.
- Euclidean_space id "p/e036380".
- Euclidean_space title "Euclidean space".
- Euclidean_space subject Category:Euclidean_geometry.
- Euclidean_space subject Category:Linear_algebra.
- Euclidean_space subject Category:Norms_(mathematics).
- Euclidean_space subject Category:Topological_spaces.
- Euclidean_space type Abstraction100002137.
- Euclidean_space type Attribute100024264.
- Euclidean_space type MathematicalSpace108001685.
- Euclidean_space type Set107999699.
- Euclidean_space type Space100028651.
- Euclidean_space type TopologicalSpaces.
- Euclidean_space comment "In mathematics, particularly in geometry, the concept of a Euclidean space encompasses Euclidean plane and the three-dimensional space of Euclidean geometry as spaces of dimensions 2 and 3 respectively. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term “Euclidean” distinguishes these spaces from other types of spaces considered in modern geometry.".
- Euclidean_space label "Espace euclidien".
- Euclidean_space label "Espacio euclídeo".
- Euclidean_space label "Espaço euclidiano".
- Euclidean_space label "Euclidean space".
- Euclidean_space label "Euclidische ruimte".
- Euclidean_space label "Euklidischer Raum".
- Euclidean_space label "Przestrzeń euklidesowa".
- Euclidean_space label "Spazio euclideo".
- Euclidean_space label "Евклидово пространство".
- Euclidean_space label "فضاء إقليدي".
- Euclidean_space label "ユークリッド空間".
- Euclidean_space label "欧几里得空间".
- Euclidean_space sameAs Eukleidovský_prostor.
- Euclidean_space sameAs Euklidischer_Raum.
- Euclidean_space sameAs Espacio_euclídeo.
- Euclidean_space sameAs Euklidestar_espazio.
- Euclidean_space sameAs Espace_euclidien.
- Euclidean_space sameAs Ruang_euklides.
- Euclidean_space sameAs Spazio_euclideo.
- Euclidean_space sameAs ユークリッド空間.
- Euclidean_space sameAs 유클리드_공간.
- Euclidean_space sameAs Euclidische_ruimte.
- Euclidean_space sameAs Przestrzeń_euklidesowa.
- Euclidean_space sameAs Espaço_euclidiano.
- Euclidean_space sameAs m.02n21.
- Euclidean_space sameAs Q17295.
- Euclidean_space sameAs Q17295.
- Euclidean_space sameAs Euclidean_space.
- Euclidean_space wasDerivedFrom Euclidean_space?oldid=606558060.
- Euclidean_space depiction Sphere_wireframe.svg.
- Euclidean_space isPrimaryTopicOf Euclidean_space.