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Beskrivning
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.
PrefaceIntroductionChapter 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 sequencesChapter III Space an TimeA. 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 velocitiesB. 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 fieldsC. 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 timeIndex
