## The loxodrome and two projections of the sphere

### Mercator projection

As it has been stated, in the Discoveries period, navigation was simpler if the route of a ship kept a constant angle with all meridians, that is, following an arc of a loxodrome.

Therefore, with the purpose of planning the trips and determining the best suited angle, a map where loxodromes were represented by straight line would constitute a valuable and useful tool to navigators.

This problem was solved, in 1569, by Gerhardus Mercator, with the construction of Mercator's map. The map is based on a conformal projection of the sphere, that is, a projection that preserves angles.

On a map obtained by Mercator's projection, the geographical parallels are represented by horizontal parallel line segments, with intervals of increasing length in regard to their respective latitudes. A consequence of this is the distortion of areas. As we consider regions closer to the poles, the rate between the projected area and the area on the sphere increases. The meridians are represented by vertical parallel line segments, equally spaced.

Definition

Loxodrome