Symmetries / D. L. JohnsonType de document : MonographieCollection : Springer undergraduate mathematics seriesLangue : anglais.Pays : Grande Bretagne.Mention d'édition: 2nd printingÉditeur : London : Springer, 2003Description : 1 vol. (XI-198 p.) ; 24 cmISBN : 1852332700.ISSN : 1615-2085.Bibliographie : Bibliogr. p. 189-190. Index.Sujet MSC : 51F15, Metric geometry, Reflection groups, reflection geometries
52C15, Discrete geometry, Packing and covering in 2 dimensions
20H10, Group theory - Other groups of matrices, Fuchsian groups and their generalizations (group-theoretic aspects)
20H15, Group theory - Other groups of matrices, Other geometric groups, including crystallographic groupsEn-ligne : Springerlink | Zentralblatt | MathSciNet
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Bibliogr. p. 189-190. Index
he book studies geometry via group theory to express geometric ideas. It is divided into the following major chapters. 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, Tessellations of the Plane/of the Sphere, Triangle Groups, Regular Polytopes.
It offers complete derivation and clsssification of the 17 plane crystallographic groups and guide for suggestion to further reading. Each chapter contains a number of exercises, most with solutions.
This book is suitable for all undergraduate geometry courses and for architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry. (Zentralblatt)