Description
This introductory book is organized around a collection of simple experiments which the reader can perform at home or in a classroom setting. Methods for physically exploring the intrinsic geometry of commonplace curved objects (such as bowls, balls and watermelons) are described. The concepts of Gaussian curvature, parallel transport, and geodesics are treated. Dr. J. Casey ist Professor an der University of California, Berkeley Department of Mechanical Engineering. 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.
