Geometries and Groups

Language: English

Published by Springer, 1987

3540152814 / 9783540152811

Series: Book 123 of 261 - Universitext

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course.; 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'.…

Seller Inventory # 9783540152811

Title
Geometries and Groups
Author
Viacheslav V. Nikulin
Publisher
Springer
Publication year
1987
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3540152814
ISBN 13
9783540152811
Edition
2nd Edition
Item weight
458 grams
Dimensions
242x170x15 mm
Series
Book 123 of 261: Universitext

AHA-BUCH GmbH

Einbeck, Germany

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