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Geometries and Groups (Universitext; Springer Series in Soviet Mathematics) (English and Russian Edition) by Viacheslav V. Nikulin, Igor R. Shafarevich, M. Reid is a nonfiction available to read on EtoBox.

What is Geometries and Groups (Universitext; Springer Series in Soviet Mathematics) (English and Russian Edition) about?

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

Who reads Geometries and Groups (Universitext; Springer Series in Soviet Mathematics) (English and Russian Edition)?

Author

Viacheslav V. Nikulin, Igor R. Shafarevich, M. Reid

Publisher

Springer Berlin / Heidelberg

Published

1994

Language

EN

ISBN

9783540152811

Category

nonfiction

Subjects

Mathematics, Science, Stem