Geometries and Groups - Universitext
Geometries and Groups - Universitext
paperback
Published:
1 November, 1987
paperback
Published:
1 November, 1987
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Description
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.
More Details
| Type | Book |
|---|---|
| ISBN13 | 9783540152811 |
| ISBN10 | 3540152814 |
| Number Of Pages | 254 |
| Item Weight | 1000 g |
| Publisher / Reseller | Springer-Verlag Berlin and Heidelberg GmbH & Co. KG |
| Format | paperback |
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