Exploring Curvature (Paperback, Softcover Repri)

1. The Evolution of Geometry.- 2. Basic Operations.- 3. Intersecting with a Closed Ball.- 4. Mappings.- 5. Preserving Closeness: Continuous Mappings.- 6. Keeping Track of Magnitude, Direction and Sense: Vectors.- 7. Curves.- 8. Arc Length.- 9. Tangent.- 10. Curvature of Curves.- 11. Surfaces.- 12. Surface Measurements.- 13. Intrinsic Geometry of a Surface.- 14. Gauss (1777-1855).- 15. Normal Sections.- 16. Gaussian Curvature.- 17. Riemann (1826-1866).- 18. Levi-Civita (1873-1941).- 19. Parallel Transport of a Vector on a Surface.- 20. Geodesics.- 21. Geometry and Reality.