Geometry

Author(s)

• Prasolov, V. V.
• Tikhomirov, Vladimir M. (Vladimir Mikhaĭlovich)
• Sipacheva, O. V.
• Sossinski, A. B.

Bibliographic Information

Geometry

V.V. Prasolov, V.M. Tikhomirov ; [traslated from the Russian by O.V. Sipacheva ; translation edited by A.B. Sossinski]

（Translations of mathematical monographs, v. 200）

American Mathematical Society, c2001

Other Title

Геометрия

Note

Includes bibliography (p. 251) and indexes

Description and Table of Contents

Description

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.

Table of Contents

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 Bibliography Author index Subject index.

by "Nielsen BookData"

Details

• NCID: BA52662103
• ISBN:
  • 0821820389
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Providence, R.I.
• Pages/Volumes: xi, 257 p.
• Size: 27 cm
• Classification:
  • DC21 : 516
• Subject Headings:
  • LCSH : Geometry
• Parent Bibliography ID:
  • BA00080309