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AuthorCasey, James. author
TitleExploring Curvature [electronic resource] / by James Casey
ImprintWiesbaden : Vieweg+Teubner Verlag, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-322-80274-3
Descript XVI, 291p. online resource

SUMMARY

This introductory book, which is intuitive and exploratory in nature, 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


CONTENT

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 (1777โ{128}{147}1855) -- 15. Normal Sections -- 16. Gaussian Curvature -- 17. Riemann (1826โ{128}{147}1866) -- 18. Levi-Civita (1873โ{128}{147}1941) -- 19. Parallel Transport of a Vector on a Surface -- 20. Geodesics -- 21. Geometry and Reality


Mathematics Geometry Mathematics Geometry Mathematics general



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