Editing Coordinate system (section)

==Transformations==
{{Broader|Geometric transformation}}
{{Main list|List of common coordinate transformations}}
{{See also|Active and passive transformation}}

There are often many different possible coordinate systems for describing geometrical figures. The relationship between different systems is described by ''coordinate transformations'', which give formulas for the coordinates in one system in terms of the coordinates in another system. For example, in the plane, if Cartesian coordinates (''x'',&nbsp;''y'') and polar coordinates (''r'',&nbsp;''θ'') have the same origin, and the polar axis is the positive ''x'' axis, then the coordinate transformation from polar to Cartesian coordinates is given by ''x''&nbsp;=&nbsp;''r''&nbsp;cos''θ'' and ''y''&nbsp;=&nbsp;''r''&nbsp;sin''θ''.

With every [[bijection]] from the space to itself two coordinate transformations can be associated:
* Such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the formulas for the mapping are the inverse of those for the coordinate transformation)
* Such that the old coordinates of the image of each point are the same as the new coordinates of the original point (the formulas for the mapping are the same as those for the coordinate transformation)

For example, in [[dimension|1D]], if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to −3, so that the coordinate of each point becomes 3 more.