Lobachevski illuminated / by Seth Braver.

Format:

Book

Author/Creator:

Braver, Seth, author.

Series:

MAA spectrum.

Spectrum series

Language:

English

Subjects (All):

Lobachevskiĭ, N. I. (Nikolaĭ Ivanovich), 1792-1856.

Lobachevskiĭ, N. I.

Geometry, Non-Euclidean.

Parallels (Geometry).

Physical Description:

1 online resource (xx, 227 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington : Mathematical Association of America, 2011.

Language Note:

English

Summary:

Lobachevski Illuminated provides an historical introduction to non-Euclidean geometry. Within its 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 mysterious 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 any modern reader (student, professional, or layman) undaunted by high school mathematics.

Contents:

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: Nicolai Ivanovich Lobachevski's "Theory of Parallels."

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-88385-979-3

OCLC:

860410977