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Full Description
A brilliantly clear and penetrating exposition of developments in physical science and mathematics brought about by the advent of non-Euclidean geometries, including in-depth coverage of the foundations of geometry, the theory of time, Einstein's theory of relativity and its consequences, other key topics.
Contents
Preface
Introduction
Chapter I Space
§ 1. The axiom of the parallels and non-Euclidean geometry
§ 2. Riemannian geometry
§ 3. The problem of physical geometry
§ 4. Coordinative definitions
§ 5. Rigid bodies
§ 6. The distinction between universal and differential forces
§ 7. Technical impossibility and logical impossibility
§ 8. The relativity of geometry
§ 9. The visualization of Euclidean geometry
§ 10. The limits of visualization
§ 11. Visualization of non-Euclidean geometry
§ 12. Spaces with non-Euclidean topological properties
§ 13. Pure visualization
§ 14 Geometry as a theory of relations
§ 15. What is graphical representation?
Chapter II Time
§ 16. The difference between space and time
§ 17. The uniformity of time
§ 18. Clocks used in practice
§ 19. Simultaneity
§ 20. Attempts to determine absolute simultaneity
§ 21. Time order
§ 22. The comparison of time
§ 23. Unreal sequences
Chapter III Space an Time
A. The Space-Time Manifold without Gravitational Fields
§ 24. The problem of a combined theory of space and time
§ 25. The dependence of spatial measurement on the definition of simultaneity
§ 26. Consequences for a centro-symmetrical process of propagation
§ 27. The construction of the space-time metric
§ 28. The indefinite space-type
§ 29. The four-dimensional representation of the space-time geometry
§ 30. The retardation of clocks
§ 31. The Lorentz contraction and the Einstein contraction
§ 32. The principle of the constancy of the velocity of light
§ 33. The addition theorem of velocities
B. Gravitation Filled Space-Time Manifolds
§ 34. The relativity of motion
§ 35. Motion as a problem of a coordinative definition
§ 36. The principle of equivalence
§ 37. Einstein's concept of gravitation
§ 38. The problem of rotation according to Einstein
§ 39. The analytic treatment of Riemannian spaces
§ 40. Gravitation and geometry
§ 41. Space and time in special gravitational fields
§ 42. Space and time in generall gravitational fields
C. The Most General Properties of Space and Time
§ 43. The singular nature of time
§ 44. The number of dimensions of space
§ 45. The reality of space and time
Index
