From Projective Geometry to Poincaré Disk. How to Carry Out a Non-Euclidean Geometry Model

This chapter is devoted to a first model of Non-Euclidean Geometry. To construct this model, we need to deal with one of the most important transformations of the Euclidean plane, the geometric inversion. We still need some other acquirements, therefore we meet the Projective Geometry. An invariant described by a special projective map of a circle allows us to construct a non-Euclidean distance inside the disk. Elaborating the previous model we highlight the Poincaré disk model.