Coordinates/Linear and curvy/Remark

Linear coordinates give a bijective relation between points and number tuples. Due to linearity, such a bijection respects addition and scalar multiplication. In many different contexts, also nonlinear (curvilinear) coordinates are important. These put points of a space and number tuples into a bijective relation. Examples are polar coordinates, cylindrical coordinates, and spherical coordinates. By choosing suitable coordinates, mathematical problems, like the computation of volumes, can be simplified.