2nd printing. — Springer, 2003. — 209 p. — (SUMS) —ISBN 1852332700.In many of the physical sciences a fundamental role is played by the concept of length: units of length are used to measure the distance between two points. In mathematics the idea of distance, as a function that assigns a real number to a given pair of points in some space, is formalised in terms of a few reasonablelooking properties, or axioms, and the result is called a metric on that space. Having defined a structure such as this on a set, it is natural to study those transformations, or maps, of such sets which preserve that structure. The requirement that these maps be invertible then leads naturally into the theory of groups. Many types of groups arise in this way. Important examples are permutation groups, linear groups, Galois groups and symmetry groups. The story of the last of these begins as follows. Contents Metric Spaces and their Groups Isometries of the Plane Some Basic Group Theory Products of Reflections Generators and Relations Discrete Subgroups of the Euclidean Group Plane Crystallographic Groups: OP Case Plane Crystallographic Groups: OR Case Tessellations of the Plane Tessellations of the Sphere Triangle Groups Regular Polytopes
Чтобы скачать этот файл зарегистрируйтесь и/или войдите на сайт используя форму сверху.