## Texts and Readings in Mathematics

An Expedition to Geometry

S. Kumaresan and G.Santhanam

This book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry.

Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a rigorous footing. It may be considered as an explication of the Kleinian view of geometry a la Erlangen Programme. The treatment in the book, however, goes beyond the Kleinian view of geometry.

Some noteworthy topics presented include ...

- various results about triangles (including results on areas of geodesic triangles) in Euclidean, hyperbolic, and spherical planes
- affine and projective classification of conics
- twopoint homogeneity of the three planes and
- the fact that the set of distance preserving maps (isometries) are essentially the same as the set of lengths preserving maps of these planes.

Contents:

1. Introduction 2. Affine Geometry

3. Projective Geometry

4. Classification of Conics

5. Euclidean Geometry

6. Hyperbolic Plane Geometry

7. Spherical Plane Geometry

8. Theory of Surfaces

9. A Group Action

Texts and Readings in Mathematics/ 30

Reprint 2011, 978-93-80250-11-3, Softcover, Rs.360.00

Reprint 2011, 978-93-80250-11-3, Softcover, Rs.360.00