Here's an atypical conformal model of the hyperbolic plane.
Here's an atypical conformal model of the hyperbolic plane. The Poincaré disk is mapped to the entire plane via the Joukowsky transformation ( https://www.johndcook.com/blog/2016/01/31/joukowsky-transformation/ ), compressing the boundary-at-infinity to the interval [-1,1] on the real axis. Has this model appeared in the literature? If so, what is it named?