Geometries And Transformations
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- Synopsis
-
Euclidean and other geometries are distinguished by the transformations that preserve their essential properties.
Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.
Provides a unified framework for describing Euclidean and non-Euclidean geometries.
Demonstrates the interconnectedness of different geometries using linear algebra.
Includes both classical results and contemporary research, as well as numerous exercises.
- Copyright:
- 2018
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9781108131957
- Publisher:
- Cambridge University Press
- Date of Addition:
- 04/30/18
- Copyrighted By:
- Norman W. Johnson
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.