Map projection

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A map projection is a way of showing the surface of a three-dimensional sphere on a plane. Such projections are necessary to create maps. The problem with projections is that they change the surface in some way; this is called distorsion. Depending on the purpose of the map, some distorsions may be acceptable. For this reason, there are different map projections that serve different purposes.

Carl Friedrich Gauss showed that is not possible to project the surface of a sphere to a plane, without distorting it. This theorem is known as Theorema egregium today.

To understand the projections, it is easier to imagine a light source, a globe, and another geometric object. The light source shines "a shadow" of each point of the globe onto the geometric object. At the end the surface of the geometric object is unrolled, this yields the map. It is possible to tell the projections apart by the type of helper object used.

  • Using a plane gives azimuthal projections.
  • Using a cone gives conical projections.
  • Using a cylinder gives cylindrical ones.