Originally Posted by

**MagiMaster**
Does anyone know if there are any conformal maps of the hyperbolic plane that map to the whole Euclidean plane, or if such a thing is provably impossible?

I know about the disc and half-plane models, but having those areas near the line or the boundary where tiny changes in the Euclidean coordinates make huge (unbounded) differences in the hyperbolic position really throws off any hope of storing object positions in a simulation of a hyperbolic universe.

The other option would be to use a third or fourth coordinate, but I can't figure that out either.