Author | Martin, George E. author |
---|---|
Title | Transformation Geometry [electronic resource] : An Introduction to Symmetry / by George E. Martin |
Imprint | New York, NY : Springer New York, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5680-9 |
Descript | XII, 240 p. online resource |
1 Introduction -- 1.1 Transformations and Collineations -- 1.2 Geometric Notation -- 1.3 Exercises -- 2 Properties of Transformations -- 2.1 Groups of Transformations -- 2.2 Involutions -- 2.3 Exercises -- 3 Translations and Halfturns -- 3.1 Translations -- 3.2 Halfturns -- 3.3 Exercises -- 4 Reflections -- 4.1 Equations for a Reflection -- 4.2 Properties of a Reflection -- 4.3 Exercises -- 5 Congruence -- 5.1 Isometries as Products of Reflections -- 5.2 Paper Folding Experiments and Rotations -- 5.3 Exercises -- 6 The Product of Two Reflections -- 6.1 Translations and Rotations -- 6.2 Fixed Points and Involutions -- 6.3 Exercises -- 7 Even Isometries -- 7.1 Parity -- 7.2 The Dihedral Groups -- 7.3 Exercises -- 8 Classification of Plane Isometries -- 8.1 Glide Reflections -- 8.2 Leonardoโs Theorem -- 8.3 Exercises -- 9 Equations for Isometries -- 9.1 Equations -- 9.2 Supplementary Exercises (Chapter 1โ8) -- 9.3 Exercises -- 10 The Seven Frieze Groups -- 10.1 Frieze Groups -- 10.2 Frieze Patterns -- 10.3 Exercises -- 11 The Seventeen Wallpaper Groups -- 11.1 The Crystallographic Restriction -- 11.2 Wallpaper Groups and Patterns -- 11.3 Exercises -- 12 Tessellations -- 12.1 Tiles -- 12.2 Reptiles -- 12.3 Exercises -- 13 Similarities on the Plane -- 13.1 Classification of Similarities -- 13.2 Equations for Similarities -- 13.3 Exercises -- 14 Classical Theorems -- 14.1 Menelaus, Ceva, Desargues, Pappus, Pascal -- 14.2 Euler, Brianchon, Poncelet, Feuerbach -- 14.3 Exercises -- 15 Affine Transformations -- 15.1 Collineations -- 15.2 Linear Transformations -- 15.3 Exercises -- 16 Transformations on Three-space -- 16.1 Isometries on Space -- 16.2 Similarities on Space -- 16.3 Exercises -- 17 Space and Symmetry -- 17.1 The Platonic Solids -- 17.2 Finite Symmetry Groups on Space -- 17.3 Exercises -- Hints and Answers -- Notation Index