@WillieWong has kindly pointed out that there are 2 definitions of stereographic projection. One with the unit sphere placed on top of the plane, the other where the plane is at the equator of the sphere. When do we use which? In particular when we are using the projections to investigate corresponding Möbius maps and cross ratios etc, since clearly they have different effects. For the second definition where is the "source of projection"? Thank you.