The illusions of the brain. Cartographic projections

Distortion of areas in the Mercator projection

In fact, Africa is larger in area than the United States, China, India, and almost all of Europe combined . But from the generally accepted projections of geographic maps there is an illusion that this is not so. The so-called Mercator projection , which is used for many cards, most distorts the areas closer to the poles. Mostly Greenland (an area smaller than Congo) seems like a giant territory. Antarctica too. The area of ​​Russia is greatly exaggerated relative to the southern countries. Or take the Ukraine, whose area is actually equal to the area of ​​Madagascar.

All the maps of the world have been lying to us for many centuries. Moreover, in different countries - Russia, Europe, USA, China, Australia, Chile, South Africa - the maps of the world are very different .

Distortions on cartographic maps are quite natural, because cartographers need to unwrap the Earth's ellipsoid on a plane. This is basically impossible to do without distortion. The only question is what exactly can be distorted and what cannot.
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Distortions are of four types:

• length distortion;
• corner distortion;
• distortion of areas;
• distortion of forms.

The conventional Mercator projection was invented by the Flemish geographer and cartographer Gerard Mercator in 1569 and is still used as a standard cartographic projection in maritime navigation, because it practically nullifies the distortion of the angles. Allows you to determine the correct azimuth and direction of movement. It is critically important in navigation - to go in the right direction. The trajectory of the ship, going under the same rumba to the meridian, is depicted as a straight line on the map in the Mercator projection.


The true size of Africa compared to different countries. Map author: Kai Krause

Why do most people not realize the true scale of gigantic Africa or the more modest size of Russia, Canada or Greenland? Because for some reason the Mercator projection is used not only in sea navigation, but also in many other geographical maps. These cards are taught in schools, such cards are shown on TV. From here and characteristic cognitive distortion at many inhabitants.

The main thing is that it is not at all necessary for us to use the Mercator projection in everyday life. We are not naval navigators and do not plan air raids on neighboring countries, where you need to fly in a straight line. We are simple peaceful people. Why do we need the perfect exact direction in a straight line between geographic points? If you dream up, then in everyday life it can be convenient only when planning large trips by car for several thousand kilometers. In other cases, few people move on their own transport. In general, people use airplanes and trains, so even travelers do not need to make a route on their own.

Why, then, is the Mercator projection used in school maps, on television, etc.? This is not entirely clear. Perhaps for the modern man in the street is still more important to understand the comparative size of the countries of the world, and not to determine the direct directions of the routes.

As we have already noted, in the Mercator projection, real areas are shown only near the equator, and all other areas on the globe are very distorted. These distortions are the price we pay for knowing the exact directions to navigate.

How can we make a more accurate and fair map of the world with the least distortion of the area? In 2009, designers from AuthaGraph tried to solve this problem. Their job is to apply geometric modeling ideas to practical problems. One of these tasks is to design a more visual map of the world. Then they mapped the AuthaGraph World Map , which most fairly displays the areas of geographic countries and territories.

Here, a variation of the so-called isometric projection is used , in which the distortion coefficient (the ratio of the length of the segment projected on the plane parallel to the coordinate axis to the actual length of the segment) along all three axes is the same in the three-dimensional object mapping onto the plane.

The projection is composed in several stages. First, the elliptical surface of the globe is divided into 96 equal triangles. They are projected onto 96 regions of a modified tetrahedron. Then the tetrahedron is “flattened” to the correct shape and cropped so that it can be turned into a rectangular shape, that is, into a standard rectangular flat map of the usual shape.


Stages of projection AuthaGraph World Map

Of course, it was possible to immediately project a sphere onto a tetrahedron in the usual optical way, but at the same time there are strong distortions that catch the eye. The idea of ​​pre-partitioning into 96 regions was to minimize such distortions and preserve the proportions of the territories relative to each other.

But there is no limit to perfection. Based on the original AuthaGraph map, Japanese designer Hajime Narukawa created a new version that looks great and also maintains the proportions of countries and continents relative to each other, as well as the ratio of the Earth’s mass and the World Ocean.


Hajime Map Narukawa based on AuthaGraph World Map

This more equitable and proportional map can be used both in school textbooks and in the media, since it more accurately shows the projection of the globe on a plane and gives a better idea of ​​what our Earth looks like. Its advantage is that all continents are shown on it without breaking the map, including Antarctica (and of course Japan is in the center, as on many Japanese maps: this is quite normal, on Russian maps the vertical axis of the world also passes through Moscow ). And a few more of these maps are stitched into a single space, so that one can visualize the mutual arrangement of the continents. Here it is clear, for example, which point in European Russia is closest to Alaska.



All existing geographical maps are distortions. Only the globe shows the most accurate picture of the world. But if we are forced to use flat surfaces, then at least we will try to minimize the amount of distortion.