dimensions

This article is about dimensions of space. For the dimension of a quantity, see Dimensional analysis. For other uses, see Dimension (disambiguation).

From left to right: the square, the cubeand 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.

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 ofcoordinates needed to specify any point within it.^[1][2] Thus a line has a dimension of one 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 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 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 afour-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetimeconsist 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. Ten dimensions are used to describe string theory, 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 abstractspaces, independent of the physical space we live i