Hyperbolic Coordinates

In mathematics, hyperbolic coordinates are a method of locating points in Quadrant I of the Cartesian plane

.

Hyperbolic coordinates take values in the hyperbolic plane defined as:

.

These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion.

For in take

and

.

Sometimes the parameter is called hyperbolic angle and v the geometric mean.

The inverse mapping is

.

This is a continuous mapping, but not an analytic function.