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Geometries and Groups
Viacheslav V. Nikulin, Igor R. Shafarevich (Taschenbuch, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.11.1987
Sprache
Englisch
EAN
9783540152811
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Universitext
Sonderedition
Nein
Autor
Viacheslav V. Nikulin, Igor R. Shafarevich
Seitenanzahl
254
Einbandart
Taschenbuch
Übersetzt von
M. Reid
Schlagwörter
Lattice, Mathematica, Non-Euclidean Geometry, Symmetry group, addition, algebra, boundary element method, field, form, mathematics, philosophy, set, similarity, story, symmetry
Thema-Inhalt
PBM - Geometrie
PBG - Gruppen und Gruppentheorie
PBP - Topologie
Höhe
233 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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