Stereographic projection

Stereographic projection is a way to map points from the surface of a sphere onto a plane. Imagine placing a sphere so that it touches a flat plane at its 'south pole.' For any point on the sphere (except the 'north pole'), draw a straight line from the north pole through that point. The line will meet the plane at exactly one point. This point on the plane is the stereographic projection of the original point on the sphere.

Important properties

• Stereographic projection is one-to-one except at the north pole, which maps to infinity.

• Circles on the sphere map to circles or straight lines on the plane.

• Angles are preserved (the projection is conformal).

• The projection is not area-preserving.