Complex Numbers in Geometry (eBook)

I. M. Yaglom (Autor)

Henry Booker, D. Allan Bromley, Nicholas Declaris (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
256 Seiten
Elsevier Reference Monographs (Verlag)
978-1-4832-6663-3 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Complex Numbers in Geometry 4
Copyright Page 5
Table of Contents 12
Translator's Note 6
Preface 8
Chapter I. Three Types of Complex Numbers 14
1. Ordinary Complex Numbers 14
2. Generalized Complex Numbers 20
3. The Most General Complex Numbers 23
4. Dual Numbers 27
5. 
31 
6. 
35 
Chapter II. Geometrical Interpretation of Complex Numbers 39
7. Ordinary Complex Numbers as Points of a Plane 39
8. 
47 
9. Dual Numbers as Oriented Lines of a Plane 93
10. 
108 
11. 
121 
12. 
131 
Chapter III. Circular Transformations and Circular Geometry 143
13. Ordinary Circular Transformations 143
14. 
158 
15. Axial Circular Transformations 170
16. 
184 
17. 
192 
18. 
201 
Appendix: Non-Euclidean Geometries in the Plane and Complex Numbers 208
Al. Non-Euclidean Geometries in the Plane 208
A2. Complex Coordinates of Points and Lines of the Plane Non-Euclidean Geometries 218
A3. Cycles and Circular Transformations 225
Addenda 233
Index 254

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• ISBN-10: 1-4832-6663-X / 148326663X
• ISBN-13: 978-1-4832-6663-3 / 9781483266633