Orthogonality and Spacetime Geometry

1 A Trip On Einstein's Train. - 2 Planes. - 2. 1 Affine Planes and Fields. - 2. 2 Metric Vector Spaces. - 2. 3 Metric Planes. - 2. 4 The Singular Plane. - 2. 5 The Artinian Plane. - 2. 6 Constants of Orthogonality. - 2. 7 The Three Real Metric Planes. - 3 Projective Transformations. - 3. 1 Projective Planes. - 3. 2 Projectivities and Involutions. - 3. 3 Matrix-Induced Projectivities. - 3. 4 Projective Collineations. - 3. 5 Correlations and Polarities. - 4 Threefolds. - 4. 1 Affine Spaces. - 4. 2 Metric Affine Spaces. - 4. 3 Singular Threefolds. - 4. 4 Nonsingular Threefolds. - 5 Fourfolds. - 5. 1 Artinian Four-Space. - 5. 2 Affine Fourfolds and Projective Three-Space. - 5. 3 Nonsingular Fourfolds. - 5. 4 The Three Real Fourfolds. - Appendix A Metageometry. Language: English