Author | Jennings, George A. author |
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Title | Modern Geometry with Applications [electronic resource] / by George A. Jennings |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0855-6 |
Descript | VIII, 204 p. 150 illus. online resource |
1 Euclidean Geometry -- 1.1 Euclidean Space -- 1.2 Isometries and Congruence -- 1.3 Reflections in the Plane -- 1.4 Reflections in Space -- 1.5 Translations -- 1.6 Rotations -- 1.7 Applications and Examples -- 1.8 Some Key Results of High School Geometry: The Parallel Postulate, Angles of a Triangle, Similar Triangles, and the Pythagorean Theorem -- 1.9 SSS, ASA, and SAS -- 1.10 The General Isometry -- 1.11 Appendix: The Planimeter -- 2 Spherical Geometry -- 2.1 Geodesics -- 2.2 Geodesics on Spheres -- 2.3 The Six Angles of a Spherical Triangle -- 2.4 The Law of Cosines for Sides -- 2.5 The Dual Spherical Triangle -- 2.6 The Law of Cosines for Angles -- 2.7 The Law of Sines for Spherical Triangles -- 2.8 Navigation Problems -- 2.9 Mapmaking -- 2.10 Applications of Stereographic Projection -- 3 Conics -- 3.1 Conic Sections -- 3.2 Foci of Ellipses and Hyperbolas -- 3.3 Eccentricity and Directrix; the Focus of a Parabola -- 3.4 Tangent Lines -- 3.5 Focusing Properties of Conics -- 3.6 Review Exercises: Standard Equations for Smooth Conics -- 3.7 LORAN Navigation -- 3.8 Keplerโs Laws of Planetary Motion -- 3.9 Appendix: Reduction of a Quadratic Equation to Standard Form -- 4 Projective Geometry -- 4.1 Perspective Drawing -- 4.2 Projective Space -- 4.3 Desarguesโ Theorem -- 4.4 Cross Ratios -- 4.5 Projections in Coordinates -- 4.6 Homogeneous Coordinates and Duality -- 4.7 Homogeneous Polynomials, Algebraic Curves -- 4.8 Tangents -- 4.9 Dual Curves -- 4.10 Pascalโs and Brianchonโs Theorems -- 5 Special Relativity -- 5.1 Spacetime -- 5.2 Galilean Transformations -- 5.3 The Failure of the Galilean Transformations -- 5.4 Lorentz Transformations -- 5.5 Relativistic Addition of Velocities -- 5.6 Lorentz-FitzGerald Contractions1 -- 5.7 Minkowski Geometry -- 5.8 The Slowest Path is a Line -- 5.9 Hyperbolic Angles and the Velocity Addition Formula -- 5.10 Appendix: Circular and Hyperbolic Functions -- References