Exploring Curvature

Häftad, Engelska, 1996

485 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1996-11-01
Mått:148 x 210 x 17 mm
Vikt:401 g
Format:Häftad
Språk:Engelska
Antal sidor:291
Förlag:Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
ISBN:9783528064754

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

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

Innehållsförteckning

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.