ABSTRACT
There are three types of homogeneous two-dimensional geometries, as illustrated in Figure 10.1. Two of these are already familiar. The first geometry shown is the familiar geometry of a sphere. This ge ometry is often called elliptic geometry, and is said to have positive curvature. The second geometry is the familiar geometry of the Euclidean plane. It is called Euclidean geometry and is said to have zero curvature. The third geometry shown is, loosely speaking, a sad dle shaped geometry. It is less familiar than elliptic or Euclidean geometry, but certainly no less important.
