A Simple Non-Euclidean Geometry and Its Physical Basis An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity
There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics de...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1979, 1979
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| Edition: | 1st ed. 1979 |
| Series: | Heidelberg Science Library
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. What is geometry?
- 2. What is mechanics?
- I. Distance and Angle; Triangles and Quadrilaterals
- 3. Distance between points and angle between lines
- 4. The triangle
- 5. Principle of duality; coparallelograms and cotrapezoids
- 6. Proof s of the principle of duality
- II. Circles and Cycles
- 7. Definition of a cycle; radius and curvature
- 8. Cyclic rotation; diameters of a cycle
- 9. The circumcycle and incycle of a triangle
- 10. Power of a point with respect to a circle or cycle; inversion
- Conclusion
- 11. Einstein’s principle of relativity and Lorentz transformations
- 12. Minkowskian geometry
- 13. Galilean geometry as a limiting case of Euclidean and Minkowskian geometry
- Supplement A. Nine plane geometries
- Supplement B. Axiomatic characterization of the nine plane geometries
- Supplement C. Analytic models of the nine plane geometries
- Answers and Hints to Problems and Exercises
- Index of Names
- Index of Subjects