Let $\mathcal P$ be a the plane.
Let the point $N$ be referred to as the north pole of $\mathbb S$ and $S$ be referred to as the south pole of $\mathbb S$.
Let $A$ be a point on $P$.
Let the line $NA$ be constructed.
Then $NA$ passes through a point of $\mathbb S$.
With this construction, the point $N$ on $\mathbb S$ maps to no point on $\mathbb S$.
- Definition:Spherical Representation of Complex Number, where this technique is used to map the complex plane to the unit sphere.