ABSTRACT
Geometry comes from the words 'geo' and 'metry', which mean to measure the earth. The Greeks took geometry to a much higher level. It was all part of the Greek tradition of seeking truth through logic and analysis. There are many different models for Hyperbolic geometry and all are essentially the same. The one discussed in this chapter is called the Poincare model. It can be referred as Hyperbolic space, or the Hyperbolic plane, or to be more informal, the Hyperbolic world. Euclid was able to arrive at the results on congruence just from his first four axioms without even discussing parallel lines. This chapter provides a brief overview of a different geometry, which is the geometry of the earth: Spherical geometry. It examines the theorem for Euclidean geometry that states that the exterior angle of a triangle is greater than either of the two remote interior angles.
