## The loxodrome and two projections of the sphere

### Sphere projection

A projection* of the sphere is a mathematical technique that allows us to obtain a representation of the points of the sphere on the plane.

There exist several types of projection and, since the sphere and the plane are not locally isometric, these projections come with a certain degree of distortion. Depending on the purpose, one chooses a suitable type of projection, taking into account their properties.

Example of a map that preserves areas, that is, the value of the area of a region on the map is the same as the area of the same region mapped on the sphere. However, the projection used is non-conformal.

The two projections analysed in this work preserve angles, that is, given two curves intersecting at one point and making a certain angle, their projections also intersect making an angle with the same amplitude. A projection with this property is said to be conformal.

Mercator's projection

Stereographic projection

*Is a continuous injective function defined on a subset of the sphere onto the plane.