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Geometric Transformations, Volume 1: Euclidean and Affine Transformations

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Author(s): P. S. Modenov, A. S. Parkhomenko
Series: Geometric Transformations 01
Publisher: Mir Publishers
Year: 1965

Language: English
City: Moscow

Front Cover
Title Page
Preface to Volume 1 of the English Edition
Translator’s Note
Preface to the Russian Edition
Contents
Introduction
1. General Definitions
1. Sets and Functions
2. Mappings
3. Groups of Transformations
4. Orthogonal Mappings
2. Orthogonal Transformations
5. Properties of Orthogonal Mappings
6. Orientation
7. Orthogonal Transformations of the First and Second Kinds
8. The Fundamental Types of Orthogonal Transformation (Translation, Reflection, Rotation)
9. Representations of Orthogonal Transformations as Products of the Fundamental Orthogonal Transformations: Translations, Reflections, and Rotations
10. Orthogonal Transformations of the Plane in Coordinates
II. Orthogonal Transformations in Space
12. Representation of an Orthogonal Transformation of Space as a Product of Fundamental Orthogonal Transformations
13. Orthogonal Transformations of Space in Coordinates
3. Similarity Transformations
14. Similarity Mappings
15. Properties of Similarity Transformations
16. Homothetic Transformations
17. Representation of a Similarity Transformation as the Product of a Homothetic Transformation and an Orthogonal Transformation
18. Similarity Transformations of the Plane in Coordinates
19. Similarity Transformations in Space
4. Affine Transformations
21. Examples of Affine Transformations and Mappings of a Plane
22. Properties of Affine Mappings
23. Darboux’s Lemma and its Consequences
24. Invariance of Length Ratios Under Affine Mappings
25. Further Properties of Affine Mappings
26. Representation of any Affine Transformation as a Product of Affine Transformations of the Simplest Types
27. Noninvariance of Lengths of Segments under Affine Mappings
28. The Change in Area under an Affine Mapping of One Plane onto Another
29. An Application of Affine Transformations to the Investigation of Properties of the Ellipse
30. Affine Transformations in Coordinates
31. Affine Classification of Quadratic Curves
32. Affine Transformations of Space
APPENDIX TO CHAPTER II Length-Preserving Mappings
Subject Index