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From left to right, the square has two dimensions, the cube has three and the tesseract has four.
From left to right, the square has two dimensions, the cube has three and the tesseract has four.

In mathematics the dimension of a manifold (a type of abstract topological space) is the mimimum number of coordinates needed to specify every point within it[1], a concept which is formalized as the Lebesgue covering dimension. In the physical world there are known to be four dimensions: three in space and one in time[2].

Dimensions can be thought of as the axes in a Cartesian coordinate system, which in a three-dimensional system run left-right, up-down and forward-backward. A set of three co-ordinates on these axes, or any other three dimensional coordinate system, specifies the position of a particular point in space[3]. According to the theory of relativity the fourth dimension is time, which runs before-after. An event’s position in space and time is specified if four co-ordinates are given.

The spatial position of a point in three dimensions can be given using either the Cartesian, Spherical or Cylindrical co-ordinate systems (shown here left to right). Whichever system is used, every point needs three numbers to be located.
The spatial position of a point in three dimensions can be given using either the Cartesian, Spherical or Cylindrical co-ordinate systems (shown here left to right). Whichever system is used, every point needs three numbers to be located.

On surfaces such as a plane or the surface of a sphere, a point can be specified using just two numbers and so this space is said to be two-dimensional. Similarly a line is one-dimensional because only one co-ordinate is needed, whereas a point has no dimensions. In mathematics, spaces with more than three dimensions are used to describe other manifolds. In these n-dimensional spaces a point is located by a set of n co-ordinates {n1, n2, … nn}. Some theories, such as those used in fractal geometry, make use of a non-integer or negative number of dimensions.

The concept of dimensions and co-ordinate spaces can be generalized to describe abstract parameters in other systems. For example in economics, dimensions are used to model economic parameters, such as demand, supply and price. The position of a point in this model would then refer to a particular set of values of those parameters.

[edit] References

  1. ^ Curious About Astronomy
  2. ^ Oxford Dictionary of English, Second Edition
  3. ^ Oxford Illustrated Encyclopedia: The Physical World