Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Euclidean_space> ?p ?o }
- Euclidean_space abstract "In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. 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 one dimension, this is the real line; in two dimensions, 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 wikiPageLength "29694".
- Euclidean_space wikiPageOutDegree "244".
- Euclidean_space wikiPageRevisionID "681868374".
- Euclidean_space wikiPageWikiLink 2_31_polytope.
- Euclidean_space wikiPageWikiLink 3-dimensional_space.
- Euclidean_space wikiPageWikiLink 3-sphere.
- Euclidean_space wikiPageWikiLink 3_(number).
- Euclidean_space wikiPageWikiLink Abelian_group.
- Euclidean_space wikiPageWikiLink Abstraction.
- Euclidean_space wikiPageWikiLink Addition.
- Euclidean_space wikiPageWikiLink Affine_geometry.
- Euclidean_space wikiPageWikiLink Affine_space.
- Euclidean_space wikiPageWikiLink Algebra.
- Euclidean_space wikiPageWikiLink Analytic_geometry.
- Euclidean_space wikiPageWikiLink Arccosine.
- Euclidean_space wikiPageWikiLink Axiom.
- Euclidean_space wikiPageWikiLink Axis–angle_representation.
- Euclidean_space wikiPageWikiLink Ball_(mathematics).
- Euclidean_space wikiPageWikiLink Base_(topology).
- Euclidean_space wikiPageWikiLink Calculus.
- Euclidean_space wikiPageWikiLink Canonical_form.
- Euclidean_space wikiPageWikiLink Cartesian_coordinate_system.
- Euclidean_space wikiPageWikiLink Cartesian_coordinates.
- Euclidean_space wikiPageWikiLink Cartesian_plane.
- Euclidean_space wikiPageWikiLink Cartesian_product.
- Euclidean_space wikiPageWikiLink Category:Euclidean_geometry.
- Euclidean_space wikiPageWikiLink Category:Linear_algebra.
- Euclidean_space wikiPageWikiLink Category:Norms_(mathematics).
- Euclidean_space wikiPageWikiLink Category:Topological_spaces.
- Euclidean_space wikiPageWikiLink Circle.
- Euclidean_space wikiPageWikiLink Circle_group.
- Euclidean_space wikiPageWikiLink Classical_mechanics.
- Euclidean_space wikiPageWikiLink Complete_metric_space.
- Euclidean_space wikiPageWikiLink Complex_number.
- Euclidean_space wikiPageWikiLink Complex_numbers.
- Euclidean_space wikiPageWikiLink Conformal_geometry.
- Euclidean_space wikiPageWikiLink Congruence_(geometry).
- Euclidean_space wikiPageWikiLink Continuous_function.
- Euclidean_space wikiPageWikiLink Coordinate_hypersurface.
- Euclidean_space wikiPageWikiLink Coordinate_space.
- Euclidean_space wikiPageWikiLink Coordinate_system.
- Euclidean_space wikiPageWikiLink Coordinate_vector.
- Euclidean_space wikiPageWikiLink Covering_space.
- Euclidean_space wikiPageWikiLink Cube.
- Euclidean_space wikiPageWikiLink Curvature.
- Euclidean_space wikiPageWikiLink Curved_space.
- Euclidean_space wikiPageWikiLink Curvilinear_coordinates.
- Euclidean_space wikiPageWikiLink Degeneracy_(mathematics).
- Euclidean_space wikiPageWikiLink Degree_(angle).
- Euclidean_space wikiPageWikiLink Diffeomorphic.
- Euclidean_space wikiPageWikiLink Diffeomorphism.
- Euclidean_space wikiPageWikiLink Differentiable_manifold.
- Euclidean_space wikiPageWikiLink Differential_geometry.
- Euclidean_space wikiPageWikiLink Dimension.
- Euclidean_space wikiPageWikiLink Dimension_(mathematics).
- Euclidean_space wikiPageWikiLink Dimensional_analysis.
- Euclidean_space wikiPageWikiLink Dimensionless_quantity.
- Euclidean_space wikiPageWikiLink Displacement_(vector).
- Euclidean_space wikiPageWikiLink Dodecahedron.
- Euclidean_space wikiPageWikiLink Dot_product.
- Euclidean_space wikiPageWikiLink Double_cover_(topology).
- Euclidean_space wikiPageWikiLink E7_(mathematics).
- Euclidean_space wikiPageWikiLink Equation.
- Euclidean_space wikiPageWikiLink Equilateral_triangle.
- Euclidean_space wikiPageWikiLink Euclid.
- Euclidean_space wikiPageWikiLink Euclidean_distance.
- Euclidean_space wikiPageWikiLink Euclidean_geometry.
- Euclidean_space wikiPageWikiLink Euclidean_vector.
- Euclidean_space wikiPageWikiLink Field_(mathematics).
- Euclidean_space wikiPageWikiLink Flat_(geometry).
- Euclidean_space wikiPageWikiLink Frame_of_reference.
- Euclidean_space wikiPageWikiLink Function_composition.
- Euclidean_space wikiPageWikiLink Function_of_several_real_variables.
- Euclidean_space wikiPageWikiLink G2_(mathematics).
- Euclidean_space wikiPageWikiLink Galilean_invariance.
- Euclidean_space wikiPageWikiLink Galilean_relativity.
- Euclidean_space wikiPageWikiLink General_position.
- Euclidean_space wikiPageWikiLink General_relativity.
- Euclidean_space wikiPageWikiLink Geometric_algebra.
- Euclidean_space wikiPageWikiLink Geometric_shape.
- Euclidean_space wikiPageWikiLink Geometry.
- Euclidean_space wikiPageWikiLink Glide_reflection.
- Euclidean_space wikiPageWikiLink Greek_mathematics.
- Euclidean_space wikiPageWikiLink Group_(mathematics).
- Euclidean_space wikiPageWikiLink Group_action.
- Euclidean_space wikiPageWikiLink Group_theory.
- Euclidean_space wikiPageWikiLink Hausdorff_space.
- Euclidean_space wikiPageWikiLink Higher_dimension.
- Euclidean_space wikiPageWikiLink Hilbert_space.
- Euclidean_space wikiPageWikiLink History_of_geometry.
- Euclidean_space wikiPageWikiLink Homeomorphic.
- Euclidean_space wikiPageWikiLink Homeomorphism.
- Euclidean_space wikiPageWikiLink Hyperbolic_space.
- Euclidean_space wikiPageWikiLink Hyperplane.
- Euclidean_space wikiPageWikiLink Icosahedron.
- Euclidean_space wikiPageWikiLink Identity_component.
- Euclidean_space wikiPageWikiLink Identity_function.