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**Geometry of Complex Numbers ** written by
** Hans Schwerdtfeger **.

This book some twenty years ago while trying to improve my knowledge of plane geometry; I used it especially to work on circle pencils: a part of geometry I had already encountered time and again; setting up circles through two-rowed hermitian matrices and linear transforms {z->(az+b)/(cz+d) }as done in the book is both very pretty and efficient. The appendix (numbered 3) describing the use and applications of the characteristic parallelogram really appealed to me. I was also quite impressed by the way the cross ratio of 4 complex numbers is dealt with in the book; to put icing on the cake, one can find within those 200 pages some knowledge of non euclidian plane geometry plan...and dynamical systems associated with linear transforms in the complex plane; very informative and quite refreshing.

**Book Detail :- **
** Title: ** Geometry of Complex Numbers
** Edition: **
** Author(s): ** Hans Schwerdtfeger
** Publisher: ** Dover
** Series: **
** Year: ** 1979
** Pages: ** 215
** Type: ** PDF
** Language: ** English
** ISBN: ** 0-486-63830-8, 79-52529
** Country: ** Canada

** Download from Amazon : **

**About Author :- **

Author ** Hans Schwerdtfeger ** Hans Schwerdtfeger (1902 – 1990) was a German-born mathematician. He was born in German but most of his career and life was spend in Australian and Canada.
He was appointed as a lecturer at the University of Adelaide in 1940, moving to the position of Senior Lecturer at the University of Melbourne.
He was joined as an Associate Professor of Mathematics at McGill University in Canada in 1957, and he was promoted to full Professor in 1960. He remained at McGill University until he retired in 1983.
He was famous because of his work in Galois theory, matrix theory, group theory, and complex analysis.

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**Geometry of Complex Numbers ** written by
** Hans Schwerdtfeger **
cover the following topics.
**Chapter-I. Analytic Geometry Of Circles**

1. Representation of Circles by Hermitian Matrices

2. The Inversion

3. Stereographic Projection

4. Pencils and Bundles of Circles

5. The Cross Ratio
**Chapter-II. The Moebius Transformation**

6. Definition

7. Real One-dimensional Projectivities

8. Similarity and Classification of Moebius Transformations

9. Classification of Anti-homographies

10. Iteration of a Moebius Transformation

11. Geometrical Characterization of the Moebius Transformation
**Chapter-III. Two-Dimensional Non-Euclidean Geometries**

12. Subgroups of Moebius Transformations

13. The Geometry of a Transformation Group

14. Hyperbolic Geometry

15. Spherical and Elliptic Geometry

Appendices

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