This is problem 1.12 in Armstrong's Basic Topology:
’Stereographic projection’ $\pi$ from the sphere minus the north pole to the plane.
Work out a formula for $\pi$ and check that $\pi$ is a homeomorpism. Notice that $\pi$ provides us with a homeomorphism from the sphere with the north and south poles removed to the plane minus the origin.
I am struggling to even get started on this one.
Can anyone give me a hint about the first step i should take to find this projection?