Symmetries / D. L. Johnson

Auteur: Johnson, David Lawrence (1943-) - AuteurType de document: Monographie Collection: Springer undergraduate mathematics series Langue: anglaisPays: Grande BretagneÉditeur: London : Springer, 2003Edition: 2nd printingDescription: 1 vol. (XI-198 p.) ; 24 cm ISBN: 1852332700 ; br. Résumé: 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).Bibliographie: Bibliogr. p. 189-190. Index. Sujets MSC: 51F15 Geometry -- Metric geometry -- Reflection groups, reflection geometries
52C15 Convex and discrete geometry -- Discrete geometry -- Packing and covering in 2 dimensions
20H10 Group theory and generalizations -- Other groups of matrices -- Fuchsian groups and their generalizations
20H15 Group theory and generalizations -- Other groups of matrices -- Other geometric groups, including crystallographic groups
En-ligne: Springerlink | Zentralblatt | MathSciNet
Location Call Number Status Date Due
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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)

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