The stereographic projection is a projection from a unit sphere into a plane which plays an important role in mathematics, physics, or geography: Draw a line from the sphere's north pole to any other point (x,y,z) on the sphere. The intersection of this line (or its extension) with the horizontal plane that goes through the sphere's center defines the stereographic projection (X,Y) of that point.  A fascinating property of this projection is that it converts circles on the sphere into circles in the plane.