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).
Rezensionen / Stimmen
Seth Braver doesn't just interpret the existing contents of Lobachevski's Theory of Parallels, but he continually adds to it by way of making it more mathematically coherent. In this respect, his achievement is first rate and it is equalled by his eloquently inspiring literary style. ... As such, this is a masterly addition to the literature on the history of geometry."" - Peter Ruane, MAA Reviews
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Maße
Höhe: 249 mm
Breite: 178 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-0-88385-573-7 (9780883855737)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
