Yaglom / Booker / Bromley Complex Numbers in Geometry

1. Auflage 2014
ISBN: 978-1-4832-6663-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 256 Seiten, Web PDF

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

Autoren/Hrsg.

Yaglom, I. M.

Booker, Henry

Bromley, D. Allan

Declaris, Nicholas

Inhaltsverzeichnis

1;Front Cover;1
2;Complex Numbers in Geometry;4
3;Copyright Page;5
4;Table of Contents;12
5;Translator's Note;6
6;Preface;8
7;Chapter I. Three Types of Complex Numbers;14
7.1;1. Ordinary Complex Numbers;14
7.2;2. Generalized Complex Numbers;20
7.3;3. The Most General Complex Numbers;23
7.4;4. Dual Numbers;27
7.5;5.
Double Numbers;31
7.6;6.
Hypercomplex Numbers;35
8;Chapter II. Geometrical Interpretation of Complex Numbers;39
8.1;7. Ordinary Complex Numbers as Points of a Plane;39
8.2;8.
Applications and Examples;47
8.3;9. Dual Numbers as Oriented Lines of a Plane;93
8.4;10.
Applications and Examples;108
8.5;11.
interpretation of Ordinary Complex Numbers in the Lobachevskii Plane;121
8.6;12.
Double Numbers as Oriented Lines of the Lobachevskii Plane;131
9;Chapter III. Circular Transformations and Circular Geometry;143
9.1;13. Ordinary Circular Transformations;143
9.2;14.
Applications and Examples;158
9.3;15. Axial Circular Transformations;170
9.4;16.
Applications and Examples;184
9.5;17.
Circular Transformations of the Lobachevskii Plane;192
9.6;18.
Axial Circular Transformations of the Lobachevskii Plane;201
10;Appendix: Non-Euclidean Geometries in the Plane and Complex Numbers;208
10.1;Al. Non-Euclidean Geometries in the Plane;208
10.2;A2. Complex Coordinates of Points and Lines of the Plane Non-Euclidean Geometries;218
10.3;A3. Cycles and Circular Transformations;225
11;Addenda;233
12;Index;254