Symmetries

D.L. Johnson

210 pages, parution le 15/07/2001

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Résumé

Written by the author of Elements of Logic via Numbers and Sets the main object of study for this book is geometry, with group theory providing an appropriate language in which to express geometrical ideas.
Key features include: -An overview of the preliminaries from group theory and geometry -Coverage of the discrete subgroups of the Euclidean group -A clear and complete derivation and classification of the 17 plane crystallographic groups -Tessellations of various spaces (they are constructed, described and classified) -A brief introduction to hyperbolic geometry. Each chapter contains a number of exercises, most with solutions, and suggestions for background, alternative and further reading. The author accessible and down-to-earth approach make this an ideal introduction for readers in the second or third year of a mathematics undergraduate course. It is also recommended for mechanical engineers, architects, physicists and crystallographers needing an understanding of 3-dimensional geometry, symmetry and trigonometry.

Contents

Preface
Metric Spaces and their Groups
Isometries of the Plane
Some Basic Group Theory
Products of Reflections
Generators and Reflections
Discrete Subgroups of the Euclidean Group
Plane Crystallographic Groups: OP Case
Tessellations of the Plane
Tessellations of the Sphere
Triangle Groups
Regular Polytopes
Solutions to Exercises
Guide to the Literature
Index of Notation
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	D.L. Johnson
Parution	15/07/2001
Nb. de pages	210
Format	17 x 23
Couverture	Broché
Poids	360g
Intérieur	Noir et Blanc
EAN13	9781852332709
ISBN13	978-1-85233-270-9