Lobachevski illuminated
著者
書誌事項
Lobachevski illuminated
（MAA spectrum）
Mathematical Association of America, c2011
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注記
Includes bibliographical references (p. 197-198) and index
Parent title from cover
内容説明・目次
内容説明
Lobachevski Illuminated provides a historical introduction to non-Euclidean geometry. Lobachevski's trailblazing explorations of non-Euclidean geometry constitute a crucial episode in the history of mathematics, but they were not widely recognized as such until after his death. Within these pages, readers will be guided step-by-step, through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels. Extensive commentary situates Lobachevski's work in its mathematical, historical and philosophical context, thus granting readers a vision of the mysteries and beautiful world of non-Euclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170-year-old text is challenging to read on its own, Seth Braver's carefully arranged 'illuminations' render this classic accessible to modern readers (student, professional mathematician or layman).
目次
- Introduction
- Note to the reader
- 1. Theory of parallels - Lobachevski's introduction
- 2. Theory of parallels - preliminary theorems (1-15)
- 3. Theory of parallels 16: the definition of parallelism
- 4. Theory of parallels 17: parallelism is well-defined
- 5. Theory of parallels 18: parallelism is symmetric
- 6. Theory of parallels 19: the Saccheri-Legendre theorem
- 7. Theory of parallels 20: the Three Musketeers theorem
- 8. Theory of parallels 21: a little lemma
- 9. Theory of parallels 22: common perpendiculars
- 10. Theory of parallels 23: the Pi function
- 11. Theory of parallels 24: Convergence of parallels
- 12. Theory of parallels 25: parallelism is transitive
- 13. Theory of parallels 26: spherical triangles
- 14. Theory of parallels 27: solid angles
- 15. Theory of parallels 28: the Prism theorem
- 16. Theory of parallels 29: circumcircles or lack thereof (Part I)
- 17. Theory of parallels 30: circumcircles or lack thereof (Part II)
- 18. Theory of parallels 31: the horocycle defined
- 19. Theory of parallels 32: the horocycle as a limit circle
- 20. Theory of parallels 33: concentric horocycles
- 21. Theory of parallels 34: the horosphere
- 22. Theory of parallels 35: spherical trigonometry
- 23. Theory of parallels 36: the fundamental formula
- 24. Theory of parallels 37: plane trigonometry
- Bibliography.
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