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Geometries and groups

Author: Никулин, В. В. Шафаревич, И. Р. ; V V Nikulin; I R Shafarevich
Publisher: Berlin ; New York : Springer-Verlag, ©1987.
Series: Universitext; Springer series in Soviet mathematics.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general  Read more...
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Additional Physical Format: Online version:
Nikulin, V.V. (Vi︠a︡cheslav Valentinovich).
Geometries and groups.
Berlin ; New York : Springer-Verlag, ©1987
(OCoLC)622375654
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Никулин, В. В. Шафаревич, И. Р. ; V V Nikulin; I R Shafarevich
ISBN: 0387152814 9780387152813 3540152814 9783540152811
OCLC Number: 15696376
Language Note: Translation of: Geometrii i gruppy.
Notes: Translation of: Geometrii i gruppy.
Includes index.
Description: viii, 251 pages : illustrations ; 24 cm.
Contents: Forming geometrical intuition; statement of the main problem --
The theory of 2-dimensional locally Euclidean geometries --
Generalisations and applications --
Geometries on the torus, complex numbers and Lobachevsky geometry.
Series Title: Universitext; Springer series in Soviet mathematics.
Other Titles: Geometrii i gruppy.
Responsibility: V.V. Nikulin, I.R. Shafarevich ; translated from the Russian by M. Reid.
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Abstract:

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry."

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