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Dimension (Latin, ‘measuring across’), in mathematics, is one of the most fundamental concepts of geometry. The dimension of a mathematical object is the least number of co-ordinates needed to describe every possible member of the object (see Cartesian co-ordinate systems). For example, a line has dimension 1 (because one number is all that is needed to express the position of a point on the line), whereas the system describing the movement of the Earth around the Sun has twelve (three each for the positions of the Sun and the Moon, and another three each for their velocities). There are systems that need infinitely many co-ordinates (some complex descriptions of the flow of fluids, for example).
Recently, mathematicians have also discovered fractals: objects which have fractional dimensions. It is perhaps one of the most paradoxical-sounding ideas in modern mathematics, that some objects take, for instance, one and a half numbers to describe the position of points in them. Because of the way that fractals are generated from (usually) lines of dimension one, they are too complex to be described by just one number, but they do not fill space in the way they would have to in order to be of dimension two. SMcL |
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