Exploring Curvature

Häftad, Engelska, 1996

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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

Utgivningsdatum1996-11-01
Mått148 x 210 x 17 mm
Vikt401 g
FormatHäftad
SpråkEngelska
Antal sidor291
FörlagFriedrich Vieweg & Sohn Verlagsgesellschaft mbH
ISBN9783528064754

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

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.