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Euclidean and Non-Euclidean Geometry: An Analytic Approach (Softcover)
"This book gives a rigorous treatment of the fundamentals of plane geometry — Euclidean, spherical, elliptical, and hyperbolic — from an analytic point of view." — From the back cover
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GOOD: This book is in good condition, with slightly bent and curled corners. The pages are free of writing.
Continued from the back cover: “[This book] serves several purposes, the most obvious one of which is to acquaint the reader with certain geometrical facts, namely, the classical results of plane Euclidean and non-Euclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition, trigonometrical formulas, and the like. In this capacity, it serves as an appropriate background for teachers of high school geometry. However, its treatment is broader than that: It supplies students not only with facts and an understanding of the structure of the classical geometries but also with an arsenal of computational techniques and a certain attitude toward geometrical investigations. It also provides a concrete and interesting realization of concepts readers have encountered or will encounter in their other mathematics courses. It aims to link classical and modern geometry to prepare students for further study and research in group theory, Lie groups, differential geometry, topology, and mathematical physics. Although the formal mathematical prerequisites are minimal and all the necessary background material is included in the appendixes, readers will find that a familiarity with linear algebra and elementary transcendental functions is helpful to using this book.
“The book will be welcomed by students enrolled in senior undergraduate courses as preparation for high school mathematics teaching or for graduate work in differential geometry, topology, or computer graphics.”
- Historical introduction
- Plane Euclidean geometry
- Affine transformations in the Euclidean plane
- Finite groups of isometries of E2
- Geometry on the sphere
- The projective plane P2
- Distance geometry on P2
- The hyperbolic plane
- The axiomatic approach
- Sets and functions
- Linear Algebra
- Proof of Theorem 2.2
- Trigonometric and hyperbolic functions
The book concludes with References and Index.
- Ryan, Patrick J.
- Cambridge University Press
- Publish Date:
- 2006 (Fifteenth Printing)
- Weight (pounds):
- Dimensions (W”xL”xH”):
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