Viacheslav V. Nikulin,Igor R. Shafarevich,M. Reid's Geometries and Groups (Universitext) PDF

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

This e-book is dedicated to the speculation of geometries that are in the community Euclidean, within the feel that during small areas they're similar to the geometry of the Euclidean aircraft or Euclidean 3-space. ranging from the easiest examples, we continue to increase a common concept of such geometries, in line with their relation with discrete teams of motions of the Euclidean airplane or 3-space; we additionally reflect on the relation among discrete teams of motions and crystallography. the outline of in the community Euclidean geometries of 1 variety exhibits that those geometries are themselves evidently represented because the issues of a brand new geometry. The systematic research of this new geometry leads us to 2-dimensional Lobachevsky geometry (also known as non-Euclidean or hyperbolic geometry) which, following the good judgment of our research, is developed ranging from the homes of its crew of motions. hence during this publication we wish to introduce the reader to a idea of geometries that are assorted from the standard Euclidean geometry of the airplane and 3-space, by way of examples that are available to a concrete and intuitive research. the fundamental approach to research is using teams of motions, either discrete teams and the teams of motions of geometries. The ebook doesn't presuppose at the a part of the reader any initial wisdom outdoor the boundaries of a college geometry course.

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Geometries and Groups (Universitext) by Viacheslav V. Nikulin,Igor R. Shafarevich,M. Reid

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