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Geometry
 
V. V. Prasolov Independent University of Moscow, Moscow, Russia
V. M. Tikhomirov Moscow State University, Moscow, Russia
Geometry
Softcover ISBN:  978-1-4704-2543-2
Product Code:  MMONO/200.S
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-2897-6
Product Code:  MMONO/200.S.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-1-4704-2543-2
eBook: ISBN:  978-1-4704-2897-6
Product Code:  MMONO/200.S.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Geometry
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Geometry
V. V. Prasolov Independent University of Moscow, Moscow, Russia
V. M. Tikhomirov Moscow State University, Moscow, Russia
Softcover ISBN:  978-1-4704-2543-2
Product Code:  MMONO/200.S
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-2897-6
Product Code:  MMONO/200.S.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-1-4704-2543-2
eBook ISBN:  978-1-4704-2897-6
Product Code:  MMONO/200.S.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 2002001; 257 pp
    MSC: Primary 51

    This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text.

    With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

    Readership

    Advanced undergraduates, graduate students, mathematics teachers and researchers interested in geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • The Euclidean world
    • The affine world
    • The projective world
    • Conics and quadrics
    • The world of non-Euclidean geometries
    • The infinite-dimensional world
    • Addendum
    • Solutions, hints, and answers
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2002001; 257 pp
MSC: Primary 51

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text.

With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Readership

Advanced undergraduates, graduate students, mathematics teachers and researchers interested in geometry.

  • Chapters
  • Introduction
  • The Euclidean world
  • The affine world
  • The projective world
  • Conics and quadrics
  • The world of non-Euclidean geometries
  • The infinite-dimensional world
  • Addendum
  • Solutions, hints, and answers
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.