# Maps are all lies – Representing a spherical earth on a flat world map

Mercator projection – Source: Strebe

Is Greenland really bigger than Africa and Australia?

Take a deep breath.  The big map in your high school classroom, the atlas you’ve used to navigate during a road trip and even google maps are all lying to you. They all start with the same big lie, that the earth is flat, two-dimensional, like a pancake. When in fact, as humans have known for a very long time, at least since the time of ancient Greeks, that the earth is spherical (that people thought that the earth was flat at the time of Columbus is a myth). Well, not exactly spherical, the earth is an oblate spheroid: a sphere slightly squashed at the poles, but it’s definitely not flat like a pancake.

A (very) short history of maps

Maps are an incredibly useful tool. They help us orient ourselves and understand our surroundings.

There are several cave paintings, some as old as 12000 BCE, that might represent maps.

Maps became common by the time of the Babylonians who used accurate surveying techniques to draw them.  The earliest known map of the world (or at least the earliest known map of the known world at the time) is a Babylonian map dating to 600 BCE.

Development of maps continued with the Ancient Greeks. In 500 BCE Hekatæus drew a flat world map assuming that the earth was a flat circle with Greece right in the middle. Herodotus also thought the earth was flat (though not circular) and that Greece was the centre of civilisation. The further away you got from it (closer to the edges of the earth) the more savage humans were.

Credit: Dariusz Ciach

It wasn’t until the fourth century BCE that Aristotle first proved that earth was, in fact, spherical. Eratosthenes calculated the circumference of the earth (to 0.5% accuracy!) in the third century BCE by measuring the heights of shadows in different parts of Egypt.

Ptolemy, in the second century CE, first proposed the use of mathematical perspective projection to represent the spherical world on a 2D surface. He also introduced a co-ordinate system to fix geographical features to specific points. This co-ordinate system was composed of parallels for latitude (north to south) and meridians for longitude(east to west). We still use them today.

Curiously, one of Ptolemy’s mistakes was to assume that Eurasia occupied about 180° of the world, seriously underestimating the size of the Earth. This error convinced Christopher Columbus to sail across the Atlantic to try to reach India more quickly than the conventional route. Perhaps if he had considered the correct circumference of the earth he would have never set sail (Columbus also made several calculation errors of his own).

Ptolemy’s map of the world (redrawn in the 15th Century) – Source: British library

Other developments in cartography came from the Chinese, the Arabic world during their golden age, the Mongols and from India. But until the 16th century the most used maps in the west were ones drawn using Ptolemy’s projection and his grid system. A map curved at the edges, using elliptical projections, to preserve the correct distance between places close to the poles.

However, these maps were pretty to look at and to study, but not very functional for the 15th century traveller. Traveling from place to place, especially on long voyages by ship, required constant calculation. Enter Gerardus Mercator, a mathematician, philosopher and globe-maker from Flanders (modern-day Belgium).

The Mercator Projection

To really grasp the issues with a 2D projection of the world, one must understand the difference between parallels and meridians. Parallels, as their name implies, are lines parallel to each other, dividing the world from south to north in flat layers, like the layers of a cake. Meridians divide the world from east to west but, and this is the key difference, they all pass through the geographical poles and are all the same length. They divide the world not in layers, but like the wedges of an orange. Which means that in Ptolemy’s projection they appear like curved lines.

Sailors have a problem with this approach. Ships are very easy to sail by maintaining a constant bearing: a constant angle to each meridian. Basically, you pick a direction on the compass and sail straight. On an elliptical map, the course taken would be curved. If you tried to draw a straight line on the map and attempt to follow it, you would constantly have to adjust the compass bearing, unless you were travelling exactly along a parallel.

The original 1569 Mercator map

Mercator solved this problem by making a rectangular map. Using some nifty geometry (he was a mathematician after all) he projected the earth onto a cylinder and then unrolled it. On his map, meridians are parallel to each other. This means that the earth’s surface gets more and more stretched the further away you get from the equator. At the poles, for example, all meridians converge to a single point, but this projection stretches that point to the length of the equator!

But making meridians parallel is not enough to fix the bearing problem. Mercator also proportionally increased the distance between parallels the further away they were from the equator. The end result is that constant bearing routes are perfectly straight lines. Perfect for navigation.

Mercator never intended his map to be used outside of sailing. However, the Mercator projection became the de facto standard for map making for most of the second half of the second millennium.

Is Greenland bigger than Africa?

The map hung on the wall of your classroom was very likely drawn using a Mercator projection. Google maps still uses the Mercator projection.

The deliberate distortion of the earth’s surface  in Mercator’s map has caused many people to misjudge the true sizes of the various continents. The regions close to the poles appear gigantic and huge land masses like Africa appear tiny in comparison.

Hobo-Dwyer projection – Source: Strebe

The Hobo-Dwyer projection, as seen above, still projects meridians as parallel to each other (and hence stretching the distances close to the poles) but also keeps the areas equal. If you’re used to seeing the Mercator projection it looks weird but it more accurately shows the true sizes of the continents.

In the map at the top of this article Greenland seems to be as big as Africa and at least 3 times bigger than Australia when in reality Australia is 3 and a half times bigger than Greenland and Africa is 14 times bigger than Greenland. In fact, Greenland is about as big as Algeria!

We should really stop using the Mercator projection. It downplays the importance and size of the southern hemisphere: Africa and South America are a lot bigger than most people think they are.

Other crazy projections

There are an infinite number of ways that can be used to project maps, using various mathematical procedures. Wikipedia has a very comprehensive list. Here are a couple of my favourites.

Craig retroazimuthal – Author: Strebe

The map above, the Craig retroazimuthal keeps directions (bearings) correct from any point to any other. The one below does the same.

Hammer retroazimuthal projection – Author: Strebe

The Fuller (or Dymaxion) map below projects the world onto an icosahedron (a polyhedron with 20 triangular surfaces) and then unfolds it. See the animation below the map for reference.

Dymaxion map unfolded

Unfolding of the Dymaxion map

The Mercator map has been misused but it was also the map that allowed humans to easily explore. That was Mercator’s goal. And in that, he succeeded.

Of course, the best way to visualise the correct sizes of the world’s landmasses is to not use a map at all and use a globe instead. Although it is quite difficult to fold a globe and put it in your pocket. In terms of portability maps have definitely an advantage.

For more projections check out this list on Wikipedia.

To further understand how the Mercator projection distorts landmasses you should check out this neat little puzzle.