Complex Numbers in Geometry

Complex Numbers in Geometry

1st Edition - January 1, 1968

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  • Author: I. M. Yaglom
  • eBook ISBN: 9781483266633

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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


    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



Product details

  • No. of pages: 256
  • Language: English
  • Copyright: © Academic Press 1968
  • Published: January 1, 1968
  • Imprint: Academic Press
  • eBook ISBN: 9781483266633

About the Author

I. M. Yaglom

About the Editors

Henry Booker

D. Allan Bromley

Nicholas DeClaris

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