The familiar Mercator projection is useful for navigation, but it exaggerates the size of regions at high latitudes. Greenland, for example, appears to be the same size as South America, when in fact it’s only one eighth as large.

An equal-area projection such as the Mollweide, below, distorts the shapes of regions but preserves their relative size. This reveals some surprising facts: Russia is larger than Antarctica, Mexico is larger than Alaska, and Africa is just mind-bogglingly huge — larger than the former Soviet Union, larger than China, India, Australia, and the United States put together.