Dimension

Definition

In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

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Abbott Eight-dimensional space Einstein notation Einstein tensor Electromagnetic tensor Electromagnetism Elliptic geometry Elwin Bruno Christoffel Embedding (mathematics)Encyclopædia Britannica Eleventh Edition Engineering Entropy Euclid Euclidean geometry Euclidean plane Euclidean space Event (relativity)Exterior calculus Exterior covariant derivative Exterior derivative Exterior dimension Exterior form Exterior product Extra dimensions F-theory Felix Klein Fiber bundle Finite geometry Five-dimensional space Flatland Force Four-dimensional space Fourth dimension in art Fourth dimension in literature Fractal Fractal dimension Free module Function space Fundamental forces Gauge theory General relativity Geodesic Geographic coordinate system Geographic information systems Geometric point Geometric primitive Geometric topology Geometry Glossary of tensor theory Gluon field strength tensor Graph (discrete mathematics)Gravity Great circle Gregorio Ricci-Curbastro Group action Habilitationsschrift Hamel dimension Hamiltonian mechanics Harold Scott MacDonald Coxeter Hausdorff dimension Henri Poincaré Hermann Grassmann Hermann Minkowski Hermann Weyl Hiding in the Mirror Hilbert space Hodge star operator Homeomorphic Homotopy Hurst exponent Hyperbolic geometry Hyperbolic triangle Hypercomplex number Hypercube Hyperplane Hyperpyramid Hyperrectangle Hyperspace Hyperspace (book)Hyperspace (disambiguation)Hypersphere Hypersurface Hypotenuse Ian Stewart (mathematician)Ibn al-Yasamin Icosahedron Id est Imaginary part Incidence geometry Index notation Inductive dimension Integer Interpolation Intrinsic dimension Isolated point Isoperimetric dimension Jan Arnoldus Schouten John T. 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