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Dimension

From left to right, the square, the cube, and the tesseract. The square is bounded by 1-dimensional lines, the cube by 2-dimensional areas, and the tesseract by 3-dimensional volumes. A projection of the cube is given since it is viewed on a two-dimensional screen. The same applies to the tesseract, which additionally can only be shown as a projection even in three-dimensional space.
A diagram showing the first four spatial dimensions.

In [mathematics] and [physics] , the dimension of a [space] or [object] is informally defined as the minimum number of [coordinates] needed to specify each [point] within it. Thus a [line] has a dimension of one because only one coordinate is needed to specify a point on it. 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, to locate a point on the surface of a sphere you need both its [latitude] and its [longitude] ). The inside of a [cube] , a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces.

The concept of dimension is not restricted to physical objects. [High-dimensional space] s occur in mathematics and the sciences for many reasons, frequently as [configuration space] s such as in [Lagrangian] or [Hamiltonian mechanics] ; these are abstract spaces, independent of the physical space we live in. Some physical theories are also high-dimensional, such as the 4-dimensional [general relativity] and higher-dimensional [string theories] . Indeed, the state-space of [quantum mechanics] is an infinite-dimensional [function space] .

In mathematics

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