I wonder if we can say that, similar to Euclidean 2D space, there are two equivalent views on the coordinates of the points, Cartesian $(x,y)$ and Polar $(r, \phi)$ with correspondence:
$$x = r\cos\phi$$ $$y = r\sin\phi$$
Or, there is no such 2 views on coordinates in Poincare disk? Or maybe, their correspondence is different?
Note, that my question is not about matching between Euclidean and Hyperbolic spaces, but rather on the view solely in Poincare disk.