Why Hyperbolic Geometry?

Abstract

In this first chapter, I shall introduce the unfamiliar reader to hyperbolic geometry. Section 1.1 is a very short survey about the history of this geometry. This history is a very important step in the general history of sciences. But this would require almost a whole book. Another summary can be found in [34] where much interesting information is given about hyperbolic geometry, in particular from an aesthetic point of view. In Section 1.2, I give a few general indications on this geometry. In Section 1.3, I introduce the Poincaré’s model which is intensively used in the other chapters of the book.