Modern Geometry with Applications

ISBN-10: 038794222X
ISBN-13: 9780387942223
Edition: 1994
List price: $64.95 Buy it from $4.60 Rent it from $28.05
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Description: This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides  More...

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Book details

List price: $64.95
Copyright year: 1994
Publisher: Springer
Publication date: 6/12/1997
Binding: Paperback
Pages: 204
Size: 6.25" wide x 9.50" long x 0.50" tall
Weight: 0.638
Language: English

This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important ares of non-Euclidean goemetry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics and teachers, who need to know how geometry is used in addition to its formal theory.

Foreword
Euclidean Geometry
Euclidean Space
Isometries and Congruence
Reflections in the Plane
Reflections in Space
Translations
Rotations
Applications and Examples
Some Key Results of High School Geometry: The Parallel Postulate, Angles of a Triangle, Similar Triangles, and the Pythagorean Theorem
SSS, ASA, and SAS
The General Isometry
Appendix: The Planimeter
Spherical Geometry
Geodesics
Geodesics on Spheres
The Six Angles of a Spherical Triangle
The Law of Cosines for Sides
The Dual Spherical Triangle
The Law of Cosines for Angles
The Law of Sines for Spherical Triangles
Navigation Problems
Mapmaking
Applications of Stereographic Projection
Conics
Conic Sections
Foci of Ellipses and Hyperbolas
Eccentricity and Directrix; the Focus of a Parabola
Tangent Lines
Focusing Properties of Conics
Review Exercises: Standard Equations for Smooth Conics
LORAN Navigation
Kepler's Laws of Planetary Motion
Appendix: Reduction of a Quadratic Equation to Standard Form
Projective Geometry
Perspective Drawing
Projective Space
Desargues' Theorem
Cross Ratios
Projections in Coordinates
Homogeneous Coordinates and Duality
Homogeneous Polynomials, Algebraic Curves
Tangents
Dual Curves
Pascal's and Brianchon's Theorems
Special Relativity
Spacetime
Galilean Transformations
The Failure of the Galilean Transformations
Lorentz Transformations
Relativistic Addition of Velocities
Lorentz-FitzGerald Contractions
Minkowski Geometry
The Slowest Path is a Line
Hyperbolic Angles and the Velocity Addition Formula
Appendix: Circular and Hyperbolic Functions
References
Index

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