Complex Numbers in Geometry - 1st Edition - ISBN: 9781483256634, 9781483266633

Complex Numbers in Geometry

1st Edition

Authors: I. M. Yaglom
Editors: Henry Booker D. Allan Bromley Nicholas DeClaris
eBook ISBN: 9781483266633
Imprint: Academic Press
Published Date: 1st January 1968
Page Count: 256
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Description

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.

Table of Contents


Translator's Note

Preface

Chapter I: Three Types of Complex Numbers

1. Ordinary Complex Numbers

2. Generalized Complex Numbers

3. The Most General Complex Numbers

4. Dual Numbers

5. Double Numbers

6.
Hypercomplex Numbers

Chapter II: Geometrical Interpretation of Complex Numbers

7. Ordinary Complex Numbers as Points of a Plane

8. Applications and Examples

9. Dual Numbers as Oriented Lines of a Plane

10.
Applications and Examples

11. Interpretation of Ordinary Complex Numbers in the Lobachevskii Plane

12.
Double Numbers as Oriented Lines of the Lobachevskii Plane

Chapter III: Circular Transformations and Circular Geometry

13. Ordinary Circular Transformations (Möbius Transformations)

14. Applications and Examples

15. Axial Circular Transformations (Laguerre Transformations)

16.
Applications and Examples

17. Circular Transformations of the Lobachevskii Plane

18.
Axial Circular Transformations of the Lobachevskii Plane

Appendix: Non-Euclidean Geometries in the Plane and Complex Numbers

A1. Non-Euclidean Geometries in the Plane

A2. Complex Coordinates of Points and Lines of the Plane Non-Euclidean Geometries

A3. Cycles and Circular Transformations

Addenda

Index

Details

No. of pages:
256
Language:
English
Copyright:
© Academic Press 1968
Published:
Imprint:
Academic Press
eBook ISBN:
9781483266633

About the Author

I. M. Yaglom

About the Editor

Henry Booker

D. Allan Bromley

Nicholas DeClaris

Ratings and Reviews