Get Geometries and Groups (Universitext) PDF

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

ISBN-10: 3540152814

ISBN-13: 9783540152811

This booklet is dedicated to the idea of geometries that are in the community Euclidean, within the experience that during small areas they're similar to the geometry of the Euclidean airplane or Euclidean 3-space. ranging from the best examples, we continue to strengthen a common thought of such geometries, in accordance with their relation with discrete teams of motions of the Euclidean aircraft or 3-space; we additionally give some thought to the relation among discrete teams of motions and crystallography. the outline of in the neighborhood Euclidean geometries of 1 kind indicates that those geometries are themselves evidently represented because the issues of a brand new geometry. The systematic examine of this new geometry leads us to 2-dimensional Lobachevsky geometry (also referred to as non-Euclidean or hyperbolic geometry) which, following the good judgment of our learn, is developed ranging from the homes of its team of motions. hence during this booklet we wish to introduce the reader to a idea of geometries that are diversified from the standard Euclidean geometry of the airplane and 3-space, when it comes to examples that are obtainable to a concrete and intuitive learn. the fundamental approach to examine 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 faculty geometry course.

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