Modern Geometry with Applications

Name: Modern Geometry with Applications
Price: 14.22 USD
Availability: InStock
ISBN: 9780387942223

ISBN-10: 038794222X

ISBN-13: 9780387942223

Edition: 1994

Authors: George A. Jennings

List price: $64.99

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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 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…

Book details

List price: $64.99
Copyright year: 1994
Publisher: Springer New York
Publication date: 6/10/1994
Binding: Paperback
Pages: 204
Size: 6.10" wide x 9.25" long x 0.19" tall
Weight: 0.638
Language: English



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