Map projections

On a Mercator map Greenland looks about as big as Africa, yet Africa is about 14 times larger.

Why every flat map is wrong somewhere

Try peeling an orange in one piece and pressing the peel flat on a table. It tears or stretches; it never lies flat without changing. A map has the same problem. The method used to move the round surface of the Earth onto a flat page or screen is called a map projection, and every projection has to give something up. Some keep angles and small shapes right, some keep areas right, some keep distances right from one point, and some split the difference so that nothing is far off.

Cartographers name these properties. A conformal projection keeps angles true, so a small island has the right shape. An equal-area projection keeps the sizes of regions in the right proportion, so it is the choice for maps of population or forests. An equidistant projection keeps distances true along certain lines. No projection can be both conformal and equal-area, and the globe above is the only map that is all of these at once.

Mercator’s map for sailors

The Flemish mapmaker Gerardus Mercator published his projection in 1569. He wanted a map on which a line of constant compass bearing is straight, so a navigator could lay a ruler between two ports, read the angle and steer that heading. To make that work the map stretches east to west more and more as latitude rises, and then stretches north to south by the same amount to keep shapes right. The stretch factor is 1 ÷ cos(latitude): lengths are doubled at 60 degrees, so areas there look four times too large, and at the poles the stretch becomes infinite, which is why Mercator maps cut off before them.

That is how Greenland, at about 72 degrees north, swells on the map. Its true area is about 2.17 million square kilometres, while Africa covers about 30.1 million, so Africa is about 14 times larger. On the Mercator drawing above, computed from the same outlines as the globe, Greenland actually comes out a little larger than Africa. Antarctica, stretched across the whole bottom edge, looks like the largest continent of all, which is why the drawing leaves it out. National Geographic notes that many popular online maps, including Google Maps, use a variant of Mercator, because keeping angles right matters when you zoom in on streets.

Equal-area and compromise maps

The second drawing uses an equal-area cylindrical projection. Every region keeps its true proportion of area, so Greenland shrinks back to about 7 percent of Africa, but the price is shape: land near the poles is squashed flat and land near the equator is pulled tall. Other equal-area designs bend the meridians to soften that. The Mollweide projection draws the world as an ellipse, and USGS notes that the sinusoidal projection is often used in atlases to show distribution patterns.

For general world maps many publishers pick a compromise that is neither conformal nor equal-area but keeps all errors moderate. National Geographic’s own choices show how this changed. The society used the Van der Grinten projection, which draws the world inside a circle, from 1922 to 1988. It then switched to the Robinson projection, presented by Arthur Robinson in 1963 and designed to make the world look right. In the 1990s it moved again, to the Winkel tripel, which reduces the distortion of land masses near the poles.