The stereographic projection
A light at the North Pole of a sphere laid on a plane on the South Pole: a family of parallels on the sphere, one of which goes through the North Pole, is projected on the plane in a hyperbolic sheaf of circles. You can see also the particular case of the “horizontal” parallels, i.e. on planes perpenducular to the line which goes through the Poles.
© matematita
immagine di Gian Marco Todesco
The image belongs to the sections...:
Lines and curves in 3d-space (3D geometry)
Sphere (3D geometry)