Abstract:
The individual who encounters hyperbolic geometry for the first time in such a book as Wolfe's C353 has the stimulating experience of developing the analogue of a substantial part of Euclidean geometry using the same essential spirit and methods as those of Euclid. Other texts, such as Coxeter's [10], approach hyperbolic geometry from the point of view of projective geometry.From the beginners point of view it seems the Poincare Euclidean Model of hyperbolic geometry would be superior to the Klein-Cayley projective model of hyperbolic geometry, if only for the reason that the beginning student is more familiar with Euclidean geometry.The aim of this paper is to present a development of the Poincare Model of hyperbolic geometry following the procedures of first, an analytic Euclidean approach, and then, the Klein or transformation approach. The knowledge assumed of the reader is that of a junior mathematics student.