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Geometric transformations. Volume 1, Euclidean and affine transformations.
Euclidean and Affine Transformations.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
New York :
Academic Press,
1965.
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| Colección: | Academic paperbacks.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Euclidean and Affine Transformations; Copyright Page; Preface to Volume 1 of the English Edition; Translator's Note; Preface to the Russian Edition; Table of Contents; Introduction; CHAPTER I. General Definitions; 1. Sets and Functions; 2. Mappings; 3. Groups of Transformations; CHAPTER II. Orthogonal Transformations; 4. Orthogonal Mappings; 5. Properties of Orthogonal Mappings; 6. Orientation; 7. Orthogonal Transformations of the First and SecondKinds; 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 Rotations10. Orthogonal Transformations of the Plane inCoordinates; 11. Orthogonal Transformations in Space; 12. Representation of an Orthogonal Transformation of Space as a Product of FundamentalOrthogonal Transformations; 13. Orthogonal Transformations ofSpace in Coordinates; CHAPTER III. 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 Transformation18. Similarity Transformations of the Plane in Coordinates; 19. Similarity Transformations in Space; CHAPTER IV. Affine Transformations; 20. Definition of Affine Mappings and Transformations of the Plane; 21. Examples of Affine Transformations andMappings of a Plane; 22. Properties of Affine Mappings; 23. Darboux's Lemma and its Consequences; 25. Further Properties of Affine Mappings.
- 26. Representation of any Affine Transformation as a Product of Affine Transformations of the Simplest Types27. Noninvariance of Lengths of Segments under Affine Mappings; 28. The Change in Area under an Affine Mapping of One Plane on to 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.