Lobachevski illuminated

by Braver, Seth

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Title Statements

Full title :Lobachevski illuminated / by Seth Braver.

Summary

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).

Edition Statements

Publication Date:©2011.

Publication Statements

Publisher(s):Mathematical Association of America
Place of Publication:Washington, DC
Language:eng
Publication Date:©2011.

The Physical Object

Description:xx, 227 pages : : illustrations ; : 26 cm

Edition Identifiers

ISBN:0883855739, 9780883855737, 9781470456405, 1470456400
oclc:ocn696296739
LC Classification:QA685
Dewey Decimal:516.9

Lobachevski's introduction -- Preliminary Theorems (1-15) -- Theory of Parallels 16: The definition of parallelism -- Theory of Parallels 17: Parallelism is well-defined -- Theory of Parallels 18: Parallelism is symmetric -- Theory of Parallels 19: The Saccheri-Legendre Theorem -- Theory of Parallels 20: The Three Musketeers Theorem -- Theory of Parallels 21: A little Lemma -- Theory of Parallels 22: Common perpendiculars -- Theory of Parallels 23: The [pi]-function -- Theory of Parallels 24: Convergence of parallels -- Theory of Parallels 25: Parallelism is transitive -- Theory of Parallels 26: Spherical triangles -- Theory of Parallels 27: Solid angles -- Theory of Parallels 28: The prism theorem -- Theory of Parallels 29: Circumcircles or lack thereof (Part I) -- Theory of Parallels 30: Circumcircles or lack thereof (Part II) -- Theory of Parallels 31: The horocycle defined -- Theory of Parallels 32: The horocycle as a limit-circle -- Theory of Parallels 33: Concentric horocycles -- Theory of Parallels 34: The horosphere -- Theory of Parallels 35: Spherical trigonometry -- Theory of Parallels 36: The fundamental formula -- Theory of Parallels 37: Plane trigonometry -- Appendix:…

Subjects

Géométrie non-euclidienne Geometry, Non-Euclidean Lobačevskij, Nikolaj I. Lobachevskii, N. I., (Nikolai Ivanovich) Nichteuklidische Geometrie Parallelen Parallèles (Géométrie) Parallels (Geometry)