Transformation Geometry : An Introduction to Symmetry / by George E. Martin
(Undergraduate Texts in Mathematics)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York |
| 出版年 | 1982 |
| 本文言語 | 英語 |
| 大きさ | XII, 240 p : online resource |
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| 内容注記 | 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 Leonardo’s Theorem 8.3 Exercises 9 Equations for Isometries 9.1 Equations 9.2 Supplementary Exercises (Chapter 1–8) 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 |
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| 一般注記 | Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra. The name describes an approach as much as the content. Our subject is Euclidean geometry. Essential to the study of the plane or any mathematical system is an under standing of the transformations on that system that preserve designated features of the system. Our study of the automorphisms of the plane and of space is based on only the most elementary high-school geometry. In particular, group theory is not a prerequisite here. On the contrary, this modern approach to Euclidean geometry gives the concrete examples that are necessary to appreciate an introduction to group theory. Therefore, a course based on this text is an excellent prerequisite to the standard course in abstract algebra taken by every undergraduate mathematics major. An advantage of having nb college mathematics prerequisite to our study is that the text is then useful for graduate mathematics courses designed for secondary teachers. Many of the students in these classes either have never taken linear algebra or else have taken it too long ago to recall even the basic ideas. It turns out that very little is lost here by not assuming linear algebra. A preliminary version of the text was written for and used in two courses-one was a graduate course for teachers and the other a sophomore course designed for the prospective teacher and the general mathematics major taking one course in geometry |
| 著者標目 | *Martin, George E. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Geometry FREE:Mathematics FREE:Geometry |
| 分 類 | DC23:516 |
| 巻冊次 | ISBN:9781461256809 
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| ISBN | 9781461256809 |
| URL | http://dx.doi.org/10.1007/978-1-4612-5680-9 |
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