|Cartography is the science of mapmaking. Therefor the spherical shape of the Earth needs to be put onto a plain piece of paper. As a model for the Earth you take the sphere (or the rotation ellipsoid).
Now the challenge of the (mathematical) cartography consists in finding suitable mapping functions (called projections or map projections) which map the surface of the sphere onto the plane in consideration of certain side conditions as
|As a result of the THEOREMA EGREGIUM by C.F. Gauss it is impossible to construct maps which are an exact image of the Earth's surface.|
Single curves however can be projected lenght-preserving.
The task consists in keeping the possible distortions within tolerable limits.
To get an initial impression of the manifoldness of beautiful map projections I would like to present you one of the many possibilities to systematize map projections. Here it is a matter of division into
See for instance ,  and  under Literature.