An Expedition to Geometry / S. Kumaresan and G.Santhanam
Material type: TextLanguage: English Publication details: New Delhi : Hindustan Book Agency, c2005.Description: 232p.: illISBN:- 9789380250113
- 510 KUM
Item type | Current library | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
Project book | CUTN Central Library | Non-fiction | 510 KUM (Browse shelf(Opens below)) | Checked out to Renuka Devi V (20019T) | 31/01/2024 | 48864 |
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510 KOS Discrete Mathematics with Applications/ | 510 KOS Discrete Mathematics with Applications/ | 510 KOS Discrete Mathematics with Applications/ | 510 KUM An Expedition to Geometry / | 510 MAR Mathematics for physicists / | 510 PEN Collected works | 510 RAY The construction of logical space |
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
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.
Geometric intuition is emphasized throughout the book. Figures are included wherever needed. The book has several exercises varying from computational problems to investigative or explorative open questions.
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