Hyperbolic analogs of spherical projections

Cartographers need to project the surface of Earth to a flat paper. However, since the surface of Earth is curved, there is no perfect way to do this. Some projections will be conformal (map angles and small shapes faithfully), equidistant (map distances along SOME lines faithfully), equal-area (map areas proportionally), etc., but no map will be all at once. Cartographers use many projections. Interestingly, most of them have natural analogs in hyperbolic plane H²! This video shows 22 projections and their H² analogs. 0:00 sphere and hyperboloid