Have you looked at a world wall map and noticed how big Greenland is? It's huge. It's larger than China, the United States, and Australia, and is about as big as Africa. Too bad it's so cold, or we could fit a lot of people up there. Or could we?

Actually, Australia is about three and a half times as big as Greenland, China is almost four and a half times as big, and Africa is almost fourteen times as large!

What's going on? The Mercator projection is what's going on. It was developed by the Flemish cartographer Gerardus Mercator in 1569. Over time, it's become very popular, at least partially so because it fits nicely onto a rectangular page without wasting a lot of space around the edges, the way some projections do.

A map projection is a transformation of locations on a sphere or ellipsoid onto locations on a plane. You can think of it as a function that transforms latitudes and longitudes of the earth into the x and y coordinates on a sheet of paper. This allows...