| Softcover ISBN: | 978-1-4704-5640-5 |
| Product Code: | SPEC/69 |
| List Price: | $35.00 |
| MAA Member Price: | $26.25 |
| AMS Member Price: | $26.25 |
| eBook ISBN: | 978-0-88385-979-7 |
| Product Code: | SPEC/69.E |
| List Price: | $30.00 |
| MAA Member Price: | $22.50 |
| AMS Member Price: | $22.50 |
| Softcover ISBN: | 978-1-4704-5640-5 |
| eBook: ISBN: | 978-0-88385-979-7 |
| Product Code: | SPEC/69.B |
| List Price: | $65.00 $50.00 |
| MAA Member Price: | $48.75 $37.50 |
| AMS Member Price: | $48.75 $37.50 |
| Softcover ISBN: | 978-1-4704-5640-5 |
| Product Code: | SPEC/69 |
| List Price: | $35.00 |
| MAA Member Price: | $26.25 |
| AMS Member Price: | $26.25 |
| eBook ISBN: | 978-0-88385-979-7 |
| Product Code: | SPEC/69.E |
| List Price: | $30.00 |
| MAA Member Price: | $22.50 |
| AMS Member Price: | $22.50 |
| Softcover ISBN: | 978-1-4704-5640-5 |
| eBook ISBN: | 978-0-88385-979-7 |
| Product Code: | SPEC/69.B |
| List Price: | $65.00 $50.00 |
| MAA Member Price: | $48.75 $37.50 |
| AMS Member Price: | $48.75 $37.50 |
-
Book DetailsSpectrumVolume: 69; 2011; 227 ppRecipient of the Mathematical Association of America's Beckenbach Book Prize in 2015!
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.
-
Table of Contents
-
Chapters
-
Theory of Parallels—Lobachevski’s Introduction
-
Theory of Parallels—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
-
-
Additional Material
-
Reviews
-
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
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
-
Chapters
-
Theory of Parallels—Lobachevski’s Introduction
-
Theory of Parallels—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
-
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
