Why are map projections so different

Compare map projections

The earth is a sphere.
(Well, no exact Sphere, but close enough.)
The only correct representation of the earth's surface is to be found on a globe.

A globe shows the earth as it is - greatly reduced in size for practical reasons, because most people don't have room on their desks for a globe with a diameter of about 12,742 kilometers.
But the shapes and proportions of the land masses and oceans, their position in relation to one another - all of this is correct.

But now it is impossibleto represent the earth's surface correctly on a flat map, which Leonhard Euler proved mathematically as early as 1777. A common everyday example is to imagine you wanted to lay the peeled peel of an orange flat on a table: the peel will bulge in some places and tear in others.

So since that doesn't work, you can do it with one projection:
Imagine the earth is translucent, you have a light source and a large (correct large!) piece of paper, which is wrapped around the earth and which acts as a canvas on which the picture is thrown.

The schematic diagram shows this arrangement.
That should make it clear how you have to imagine it - and why you should think of cardsprojections speaks. And if you look at Greenland (the purple island at the top of the globe on the map), you immediately see the distortions that this process leads to.

But the illustration only shows a possible way of capturing the projection.
Depending on Where you place the light source, how you wrap the paper around the earth - if you wrap it around at all and don't lay it flat next to the earth -, at which point the paper touches the earth (if at all), etc., a very different image is thrown onto the canvas. In this picture, for example, Greenland is not distorted, but perhaps Africa.

Most importantly, most map network designs don't even work that way!
They could not be made with the help of an optical projection; Instead, they capture the spherical surface of the earth on the flat map based on purely mathematical formulas. In such cases, cartographers do not speak of a »map projection«, but rather of a (map) network design or map representation.
 
On this website, however, the terms are used as synonyms: I also say »map projection« if, according to cartographic terminology, it is not a projection! (I have explained the reasons for this in detail in Actually It Is Called Map Network Draft.)

So you have the most varied of options to capture the earth's surface on a flat map, but one thing always remains the same:

Man can the earth not exactly represent, so you try them approximately to represent. To do this, one is forced to stretch some parts of the earth's surface, to compress others, perhaps to bend them. That leads to distortions.
It is important to realize that every map of the world has some form of distortion!

But you can distort different parts of the world, you can choose different types of distortion. A specific combination of these possibilities is called projection. And there are hundreds of different projections, each with its own unique type and location of the distortion, in many different forms.


 

 
From left to right and top to bottom: Miller, Wagner IV, Mollweide, Canters W14.
 

And no of these different projections is really accurate, none is wrong, none is inherently better or worse than the others. you are differently, they serve different purposes, they want to emphasize different aspects.

You can say that you have chosen a wrong projection for a certain representation - but only the wrong one for this particular purpose; in other situations the "wrong" projection may be exactly the right one.

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