Another way to represent coordinate transformations in Cartesian coordinates is through affine transformations. The map overlays indicated the trajectories of various objects in geographic coordinates. The mathematics of the relationship between joint angles and actual spatial coordinates is called kinematics. They also include the geographical coordinates of . Euler's formula provides a means of conversion between cartesian coordinates and polar coordinates. Cartesian coordinates in position and velocity, and include lunisolar acceleration parameters. Now suppose are the coordinates of the vector from the origin to point . Likewise, vectors with covariant components transform in the opposite way as changes in the coordinates. Using and , one can derive a relationship between derivatives in Cartesian and polar coordinates. GPS navigation relies on such geocentric coordinates. This allows easy computation of the inverse of a complex number given in rectangular coordinates. Spinors can be exhibited as concrete objects using a choice of Cartesian coordinates. Bernoulli's work extended to finding the radius of curvature of curves expressed in these coordinates. Usually, Cartesian coordinates formula 174 are used. "Bases" allow one to represent vectors by a sequence of scalars called "coordinates" or "components".