Introduction via Flat Affine Planes

Abstract

The geometries we shall be dealing with in this second part of the book are perhaps the nicest possible infinite geometries. In general, their point sets are well-known two-dimensional surfaces like the Euclidean plane, the real projective plane, the sphere, the torus, and the cylinder. Their lines, blocks, or circles are curves that are nicely embedded in these surfaces. Usually these curves will be homeomorphic to the real line or to the unit circle. The Euclidean plane, viewed as a geometry, and the geometry of circles on the unit sphere are prime examples of the kinds of geometries we will be looking at.