In
geometry, a
coordinate system is a system which uses one or more
numbers, or
coordinates, to uniquely determine the position of a
point or other geometric element on a
manifold such as
Euclidean space. The order of the coordinates is significant and they are sometimes identified by their position in an ordered
tuple and sometimes by a letter, as in "the
x-coordinate". The coordinates are taken to be
real numbers in elementary mathematics, but may be
complex numbers or elements of a more abstract system such as a
commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and
vice versa; this is the basis of
analytic geometry.