Exploring Curvature

James Casey

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English

Vieweg+Teubner Verlag
01 November 1996

This introductory text is exploratory in nature, and is intended as a bridge between Euclid's geometry and the modern geometry of curved spaces. It 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. The book also contains biographical chapters on Gauss, Riemann and Levi-Civita.

By: James Casey
Imprint: Vieweg+Teubner Verlag
Country of Publication: Germany
Edition: Softcover reprint of the original 1st ed. 1996
Dimensions: Height: 210mm, Width: 148mm, Spine: 16mm
Weight: 451g
ISBN: 9783528064754
ISBN 10: 3528064757
Pages: 291
Publication Date: 01 November 1996
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.

Dr. J. Casey ist Professor an der University of California, Berkeley Department of Mechanical Engineering.