Before we get started, let's think a little bit about map projections. We have already seen the visualized data showing population density in the United States:
It is known that the earth is a sphere, but your screen is not a sphere, it's actually a flat Euclidean plane. So, translating points from the surface of a sphere onto the points on the surface of this flat plane is actually non-trivial. We can't unroll a sphere into a flat plane without tearing or distorting that sphere, and so, most of the time when you're dealing with a map, you're actually looking at a projection.
But Mercator is only one of many projections. There are other alternative projections, and even projections that don't necessarily end up giving you square edges for your globe, as shown here:
One of the key things when setting up a map is choosing which...