          # Dimension

• from left to right: the square, the cube and the tesseract. the two-dimensional (2d) square is bounded by one-dimensional (1d) lines; the three-dimensional (3d) cube by two-dimensional areas; and the four-dimensional (4d) tesseract by three-dimensional volumes. for display on a two-dimensional surface such as a screen, the 3d cube and 4d tesseract require projection. the first four spatial dimensions, represented in a two-dimensional picture.
1. two points can be connected to create a line segment.
2. two parallel line segments can be connected to form a square.
3. two parallel squares can be connected to form a cube.
4. two parallel cubes can be connected to form a tesseract.

in physics and mathematics, the dimension of a mathematical space (or object) 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 a plane or the surface 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. 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.

in classical mechanics, space and time are different categories and refer to absolute space and time. that conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. the four dimensions (4d) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. minkowski space first approximates the universe without gravity; the pseudo-riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6d hyperspace + 4d), 11 dimensions can describe supergravity and m-theory (7d hyperspace + 4d), and the state-space of quantum mechanics is an infinite-dimensional function space.

the concept of dimension is not restricted to physical objects. high-dimensional spaces frequently occur in mathematics and the sciences. they may be parameter spaces or configuration spaces such as in lagrangian or hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

• in mathematics
• in physics
• networks and dimension
• in literature
• in philosophy
• more dimensions
## This article is about the dimension of a space. For the dimension of an object, see size. For the dimension of a quantity, see Dimensional analysis. For other uses, see Dimension (disambiguation). From left to right: the square, the cube and the tesseract. The two-dimensional (2D) square is bounded by one-dimensional (1D) lines; the three-dimensional (3D) cube by two-dimensional areas; and the four-dimensional (4D) tesseract by three-dimensional volumes. For display on a two-dimensional surface such as a screen, the 3D cube and 4D tesseract require projection. The first four spatial dimensions, represented in a two-dimensional picture. Two points can be connected to create a line segment.Two parallel line segments can be connected to form a square.Two parallel squares can be connected to form a cube.Two parallel cubes can be connected to form a tesseract. Geometry Projecting a sphere to a plane. OutlineHistory Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence ConceptsFeaturesDimension Straightedge and compass constructions Angle Curve Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line segment ray Length Two-dimensional Plane Area Polygon Triangle Altitude Hypotenuse Pythagorean theorem Parallelogram Square Rectangle Rhombus Rhomboid Quadrilateral Trapezoid Kite Circle Diameter Circumference Area Three-dimensional Volume Cube cuboid Cylinder Pyramid Sphere Four- / other-dimensional Tesseract Hypersphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Present day Atiyah Gromov vt In physics and mathematics, the dimension of a mathematical space (or object) 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 a plane or the surface 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. 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. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space. The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in. Contents 1 In mathematics 1.1 Vector spaces 1.2 Manifolds 1.2.1 Complex dimension 1.3 Varieties 1.4 Krull dimension 1.5 Topological spaces 1.6 Hausdorff dimension 1.7 Hilbert spaces 2 In physics 2.1 Spatial dimensions 2.2 Time 2.3 Additional dimensions 3 Networks and dimension 4 In literature 5 In philosophy 6 More dimensions 7 See also 7.1 Topics by dimension 8 References 9 Further reading 10 External links  