Mercator Projection

Have you ever peeled an orange and tried to press the peel flat on the table as a perfect rectangle, with no tears? However gently you press, the edges rip or bunch up in lumps. Moving the Earth, a 3D ball, onto flat 2D paper without wrinkles runs into exactly the same math problem.

Gerardus Mercator, a 16th-century mapmaker, came up with a clever fix. Picture wrapping a cylinder of paper around a globe like a scroll and then unrolling it. The farther you get from the equator, the more the lines of longitude spread apart sideways. So he stretched the vertical spacing by the same ratio, and he worked out the math so that shapes at every point stay undistorted.

Near the equator, where the paper touches the globe, everything prints at its true size. But toward the poles, the sideways spread gets bigger and the vertical stretch grows right along with it. Small areas keep their shapes and angles, but the trade-off is a distortion where area swells by the square of that ratio.

Mathematically, no flat map of a sphere can get area, angles, shape, and distance all right at once. Mercator gave up everything else and chose to keep one thing perfect for sailors crossing the sea: angles.

The world map many of us grew up with, on classroom walls and in online map apps, is exactly this Mercator projection. Look closely and Greenland, the huge icy island near the Arctic, looks about as big as the vast continent of Africa.

But check a globe or the real numbers and you get a shock. Africa covers about 30 million square kilometers, a full 14 times more than Greenland's roughly 2.16 million. Europe gets the same treatment. South America is actually about 1.7 times bigger than Europe, yet on this map the two look similar in size, because Europe has been blown up.

A Mercator map inflates continents sharply as you move away from the equator toward higher latitudes. The poles themselves stretch to infinite size mathematically, so they can't be drawn on the map at all. That's why this map is a poor choice for comparing the true sizes of countries or continents.

The size ranking you see on the map isn't the Earth's real size ranking. It only shows how far a place is from the equator.

Even with area this distorted, the Mercator projection was a huge help for navigation. Here's why. It gave up the size of land, but for any small region, the angles and shapes of borders and coastlines stay accurate instead of getting twisted.

For a navigator drifting across open ocean with water on every side, the most urgent information isn't how big the land is. It's the right direction, so they don't get lost. On a Mercator map, you just lay a ruler between your starting point and your destination, draw a straight line, and read the compass angle (the bearing) that line makes.

Then you steer so the compass needle stays at the angle you set when you left. Apart from currents and wind, that gets you to your destination. This kind of straight route is called a rhumb line, a path with a constant compass bearing.

This path isn't the shortest route over the round Earth, which is called the 'great-circle route.' But sailors didn't have to recalculate the compass angle every hour. For sailors who trusted their lives to a single compass on rough seas, it was a lifesaving map.