From the moment humans first began exploring the planet, maps have been a ubiquitous aspect of our existence. Maps exist in all cultures and facets of society and can greatly help or hinder our understanding of the world. Throughout these various maps, however, one notices very quickly that these depictions of the Earth rarely look the same. How can this be? We at the American Geographical Society have recently received many questions concerning this topic. The answer lies in the map’s projection.
Earth, being a three-dimensional ellipsoid, cannot be accurately drawn and displayed on a two-dimensional surface. It is mathematically impossible to do so, and its true shape is only preserved on a globe. To compensate, cartographers use what are called projections. These projections are adapting the Earth’s shape onto flat surfaces at the cost of some accuracy. There are four geographic elements that can be preserved or lost via projections: landmass shape and area, and the distance and direction between them. To better illustrate these distortions, we have included what is called Tissot’s Indicatrix, represented as ellipsoids on the maps (Fig. 1). These shapes help display what is being preserved and lost. If the ellipses are all the same shape, yet differ in size, then we see that shape is preserved at the expense of size, as it is on the Mercator Projection. Conversely, as on the Goode Homolosine Projection, we see that while the shapes of the ellipses vary greatly, they all have the same area, meaning that size and area are preserved, not shape.
Shape Preserving: The Mercator projection, despite being widely criticized in the modern world, is one of the most commonly seen projections. Why is this? The answer lies in history. The Mercator projection, as well as other conformal projections, preserves the shapes of landmasses while sacrificing the accuracy of their area (Fig 2). This leads to the monstrously large Greenland, Russia, and Canada while equatorial continents such as Africa and South America are rendered quite small. The coastlines and overall shapes of these countries are preserved, even if the areas nearer to poles are distorted and enlarged. The criticism stems from its lack of relevance today, as the Mercator projection is useful for little else besides navigation. For this reason, many seek to move away from the Mercator projection and to more relevant depictions of the Earth.
Area Preserving: Better suited for thematic topics rather than geospatial, area-preserving maps do just that. The shapes of landmasses may not portray their real counterparts, but their relative sizes remain true. This is generally seen as the better method of displaying most information besides navigation. This lends itself well for thematic use, meaning that specific topics can be explored. Percentages, proportions, raw numbers, and relationships can be very clearly displayed on equal-area maps. The Mollweide and Goode homolosine projections are commonly used equal-area maps (Fig. 3).
Distance Preserving: Distance preserving, or equidistant, projections retain accurate distances of all points of land from a central point. These distances are derived from what are called Great Circles, which are lines drawn around the diameter of the earth radiating from the central origin point. The central points can be placed anywhere on Earth, and the rest of the world will be seen from that perspective such as this map centered on Washington D.C. (Fig. 4). While both land shape and area are sacrificed, their spatial relation to each other is preserved. For this reason, the United Nations decided in 1947 to use the Polar Azimuthal Equidistant projection as their official emblem.
Direction Preserving: Direction is the only geographic element that can be preserved alongside another. Due to this fact, direction is often displayed in conjunction with one of the other three elements. Because of this, rarely is direction the only preserved element in a projection.
Compromise: Everything we have previously looked at preserves at least one geographic element perfectly. But what if nothing was perfectly preserved and everything was only slightly distorted? This is the result of a projection that compromises between the elements. The most famous of these are the Robinson and the Gall stereographic projections, which preserves neither shape nor area perfectly, yet diminishes the normal amount of distortion in both (Fig. 5). This is seen as a useful and accurate compromise when transitioning the Earth’s landmasses from three dimensions to two.