Modern Geometry with Applications
List price: $64.95
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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 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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $64.95
Copyright year: 1994
Publication date: 6/12/1997
Size: 6.25" wide x 9.50" long x 0.50" tall
|Isometries and Congruence|
|Reflections in the Plane|
|Reflections in Space|
|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|
|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|
|Applications of Stereographic Projection|
|Foci of Ellipses and Hyperbolas|
|Eccentricity and Directrix; the Focus of a Parabola|
|Focusing Properties of Conics|
|Review Exercises: Standard Equations for Smooth Conics|
|Kepler's Laws of Planetary Motion|
|Appendix: Reduction of a Quadratic Equation to Standard Form|
|Projections in Coordinates|
|Homogeneous Coordinates and Duality|
|Homogeneous Polynomials, Algebraic Curves|
|Pascal's and Brianchon's Theorems|
|The Failure of the Galilean Transformations|
|Relativistic Addition of Velocities|
|The Slowest Path is a Line|
|Hyperbolic Angles and the Velocity Addition Formula|
|Appendix: Circular and Hyperbolic Functions|