Embedding of $\mathbb R^2$ into the unit sphere $S^2$? How to find an embedding of $\mathbb R^2$ into the unit sphere $S^2$?
I know there is such an embedding because $S^2$ is a one-point compactification of $\mathbb R^2$, but I don't know how to write this embedding explicitly.
Thanks!

Consider the usual 2 charts of the sphere: they give homeomorphisms from $\mathbb{R}^2$ and open disks in $S^2$. They are examples of the embedding you are looking for. 
