Cartographers use a wide variety of projections from the sphere to the plane, which have a very rich structure studied in differential geometry. Particularly interesting examples are conformal maps, in which angles are preserved but not lengths. References:

1. Feeman, TG 2002 Portraits of the Earth: A Mathematician Looks at Maps American Mathematical Society.
2. McCleary, J 1994 Geometry from a Differentiable Viewpoint Cambridge University Press.

Supervisor: Professor Stephen Huggett