Modenov / Parkhomenko / Booker Projective Transformations

Geometric Transformations
1. Auflage 2014
ISBN: 978-1-4832-6149-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 148 Seiten, Web PDF

Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Autoren/Hrsg.

Modenov, P. S.

Parkhomenko, A. S.

Booker, Henry

Bromley, D. Allan

Declaris, Nicholas

Inhaltsverzeichnis

1;Front Cover;1
2;Projective Transformations;4
3;Copyright Page;5
4;Table of Contents;12
5;Preface to Volume 2 of the English Edition;6
6;Translator's Note;8
7;Preface to the Russian Edition;10
8;CHAPTER I. Projective Transformations;14
8.1;1. The Concept of a Projective Plane;14
8.2;2. Definition of a Projective Mapping;33
8.3;3. Two Fundamental Theorems on Projective Transformations;37
8.4;4. Cross Ratio;44
8.5;5. Harmonic Sets;54
8.6;6. Examples of Projective Transformations;64
8.7;7. Projective Transformations in Coordinates;77
8.8;8. Quadratic Curves in the Projective Plane;84
8.9;9. Projective Transformations of Space;92
9;APPENDIX 1 TO CHAPTER I. The Topology of the Projective Plane;106
10;CHAPTER II. Inversion;124
10.1;10. The Power of a Point with Respect to a Circle;124
10.2;11. Definition of Inversion;125
10.3;12. Properties of Inversion;126
10.4;13. Circle Transformations and the Fundamental Theorem;131
11;APPENDIX 2 TO CHAPTER I. Principle of Duality;139
12;Subject Index;146