Lobachevski Illuminated (Spectrum)

Lobachevski Illuminated (Spectrum)

By: Seth Braver (author)Paperback

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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).

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About Author

Seth Braver teaches mathematics at South Puget Sound Community College in Olympia, Washington.


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.

Product Details

  • publication date: 07/07/2011
  • ISBN13: 9780883855737
  • Format: Paperback
  • Number Of Pages: 248
  • ID: 9780883855737
  • weight: 450
  • ISBN10: 0883855739

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