Foreword | |
Euclidean Geometry | p. 1 |
Euclidean Space | p. 1 |
Isometries and Congruence | p. 2 |
Reflections in the Plane | p. 3 |
Reflections in Space | p. 5 |
Translations | p. 7 |
Rotations | p. 9 |
Applications and Examples | p. 11 |
Some Key Results of High School Geometry: The Parallel Postulate, Angles of a Triangle, Similar Triangles, and the Pythagorean Theorem | p. 17 |
SSS, ASA, and SAS | p. 27 |
The General Isometry | p. 36 |
Appendix: The Planimeter | p. 39 |
Spherical Geometry | p. 43 |
Geodesics | p. 43 |
Geodesics on Spheres | p. 46 |
The Six Angles of a Spherical Triangle | p. 48 |
The Law of Cosines for Sides | p. 54 |
The Dual Spherical Triangle | p. 55 |
The Law of Cosines for Angles | p. 59 |
The Law of Sines for Spherical Triangles | p. 62 |
Navigation Problems | p. 63 |
Mapmaking | p. 66 |
Applications of Stereographic Projection | p. 77 |
Conics | p. 83 |
Conic Sections | p. 83 |
Foci of Ellipses and Hyperbolas | p. 86 |
Eccentricity and Directrix; the Focus of a Parabola | p. 90 |
Tangent Lines | p. 93 |
Focusing Properties of Conics | p. 96 |
Review Exercises: Standard Equations for Smooth Conics | p. 98 |
LORAN Navigation | p. 99 |
Kepler's Laws of Planetary Motion | p. 101 |
Appendix: Reduction of a Quadratic Equation to Standard Form | p. 110 |
Projective Geometry | p. 115 |
Perspective Drawing | p. 115 |
Projective Space | p. 120 |
Desargues' Theorem | p. 122 |
Cross Ratios | p. 126 |
Projections in Coordinates | p. 133 |
Homogeneous Coordinates and Duality | p. 136 |
Homogeneous Polynomials, Algebraic Curves | p. 140 |
Tangents | p. 143 |
Dual Curves | p. 145 |
Pascal's and Brianchon's Theorems | p. 148 |
Special Relativity | p. 153 |
Spacetime | p. 153 |
Galilean Transformations | p. 155 |
The Failure of the Galilean Transformations | p. 158 |
Lorentz Transformations | p. 159 |
Relativistic Addition of Velocities | p. 165 |
Lorentz-FitzGerald Contractions | p. 167 |
Minkowski Geometry | p. 169 |
The Slowest Path is a Line | p. 174 |
Hyperbolic Angles and the Velocity Addition Formula | p. 176 |
Appendix: Circular and Hyperbolic Functions | p. 178 |
References | p. 183 |
Index | p. 185 |
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