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- catalog abstract "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's 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.".
- catalog contributor b12304705.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description "Includes bibliographical references (p. 189-190) and index.".
- catalog description "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 -- Plane Crystallographic Groups: OR Case -- Tessellations of the Plane -- Tessellations of the Sphere -- Triangle Groups -- Regular Polytopes -- Solutions to Exercises -- Guide to the Literature -- Index of Notation -- Index.".
- catalog description "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's 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.".
- catalog extent "xi, 198 p. :".
- catalog identifier "1852332700 (alk. paper)".
- catalog isPartOf "Springer undergraduate mathematics series, 1615-2085".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "London ; New York : Springer,".
- catalog subject "512/.2 21".
- catalog subject "Algebra.".
- catalog subject "Geometry.".
- catalog subject "Group theory.".
- catalog subject "Mathematics.".
- catalog subject "QA174.2 .J64 2001".
- catalog subject "Symmetry groups.".
- catalog tableOfContents "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 -- Plane Crystallographic Groups: OR Case -- Tessellations of the Plane -- Tessellations of the Sphere -- Triangle Groups -- Regular Polytopes -- Solutions to Exercises -- Guide to the Literature -- Index of Notation -- Index.".
- catalog title "Symmetries / D.L. Johnson.".
- catalog type "text".