# 7 Projections

Now let’s take a closer look at the process of drawing a map. If you’re drawing a map of a classroom, you can assume the floor is flat like a piece of paper. (If not, the district is going to need to up its facilities budget.) That makes mapping it straightforward; a seating chart or other floor plan is just a two-dimensional map of a two-dimensional floor.

Cartographers mapping the earth’s surface don’t get off so easy, because the earth’s surface isn’t flat.^{1} That makes accurately representing the earth’s surface in two dimensions difficult — or impossible, depending on how you define “accurate.” Of course, you could simply make a globe, but globes aren’t terribly convenient. They’re big and bulky — in order to distinguish Raleigh from Durham you’d need a globe almost three feet across^{2} — and they don’t fold up, unless you’re *very* good at origami.

To make a two-dimensional map, cartographers have to project the spherical surface of the earth onto a two-dimensional piece of paper or computer screen. Most of us are aware of that fact, at least vaguely, but we may not realize just how many map projections there are or how they impact the way we see the world.

Why do students (and teachers!) need to understand something about map projections? Understanding map projections can help you choose the right map for a given situation. It’s also important in reading maps. Because every projection distorts the earth’s surface in one way or another, knowing what sort of projection we’re looking at can help us interpret a map accurately.

## Projection basics: Peeling the surface of the earth

A common way of demonstrating the need for projections is to draw rough outlines of the continents on an orange, then score it and peel it. Another, slightly more complicated, is to tape paper to the surface of a ball so that the paper just covers the ball. In either activity, students quickly see that the surface of a sphere doesn’t come off as a rectangle.

To turn a spherical surface into a rectangle or other two-dimensional shape, we have to transform it or deform it by stretching it and/or compressing it. To see what happens when you deform a spherical surface, use a balloon. First blow up the balloon and tie it off. then draw rough outlines of the continents on the surface. Carefully cut off the tied end of the balloon and snip through the Pacific Ocean. Now try to flatten it into a useful shape. What does it look like? What happens to the shapes, sizes, and positions of the continents?

Cartographers have better ways to project spherical surfaces onto maps than stretching them by hand, but they’re subject to the same limitations. All projections deform the earth’s surface in some way, which means that **every projection is in some way inaccurate**. The trick in drawing or selecting a map is to find the projection that shows key information for a given region with the least inaccuracy.

## Early maps and the Mercator projection

When people first started drawing maps, they didn’t draw them with mathematical precision, because the necessary mathematics hadn’t been invented yet. The Greeks were the first to do rigorous geometry, and the Greek mathematician Ptolemy (90–168 CE) was the first to develop a map using lines of latitude and longitude and defining locations on a coordinate system. Islamic mapmakers in the Middle Ages built on his ideas, and the Chinese also drew coordinate-based maps to careful scale.

In 1569, the Flemish geographer and cartographer Gerardus Mercator created a map using a mathematical formula to “project” points on the earth’s surface onto a map based on their latitude and longitude. His formula — called the Mercator projection — became the standard means of making maps for navigation, because the directions of the compass corresponded to directions on the map. North, east, south, and west were straight lines on paper, just as they are on the earth’s surface.

The problem with the Mercator projection is that it distorts areas and distances. The North and South Poles are stretched all the way across the top and bottom of the map, and regions to the far north and south appear much larger than they actually are. This isn’t a problem for navigation — Google Maps uses a Mercator projection even today — and the distortion is negligible for maps of small regions (say, of North Carolina). But it can give a false impression of the relative sizes of various countries and continents. For example, on the map below, Greenland is larger than Africa!

Cartographers have developed a number of other projections with various advantages and disadvantages, but the Mercator projection is the vision of the earth that most of us have in our heads more than four centuries later.