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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 Kepler's 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 Desargues' 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 Pascal's and Brianchon's 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 theVelocity Addition Formula.-
5.10 Appendix: Circular and Hyperbolic Functions.- References.