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Lobachevski Illuminated

Lobachevski Illuminated


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  • Author: Seth Braver, South Puget Sound Community College
  • Date Published: July 2011
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Paperback
  • isbn: 9780883855737

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About the Authors
  • 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).

    • Introduces readers to classical non-Euclidean geometry through one of its original sources
    • A new translation of the 170-year-old text
    • Made accessible to the modern reader through the author's extensive commentary
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    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780883855737
    • length: 248 pages
    • dimensions: 254 x 174 x 12 mm
    • weight: 0.45kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    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

  • Author

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

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