Exploring Curvature

Exploring Curvature

by James Casey
     
 

ISBN-10: 3528064757

ISBN-13: 9783528064754

Pub. Date: 01/01/1996

Publisher: Vieweg Verlag

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.  See more details below

Overview

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.

Product Details

ISBN-13:
9783528064754
Publisher:
Vieweg Verlag
Publication date:
01/01/1996
Pages:
291
Product dimensions:
5.80(w) x 8.34(h) x 0.45(d)

Table of Contents

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.

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