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### Geometry of Complex Numbers by Hans Schwerdtfeger

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Complex Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books. Geometry of Complex Numbers writthen by Hans Schwerdtfeger . This is an other great free downloadable mathematics book cover the following topics of complex number.

• Chapter I. Analytic Geometry Of Circles
• 1. Representation of Circles by Hermitian Matrices
One circle, Two circles, Pencils of circles, Examples

• 2. The Inversion
Definition, Simple properties of the inversion

• 3. Stereographic Projection
Simple properties of the stereographic projection, Stereographic projection and polarity

• 4. Pencils and Bundles of Circles
Pencils of circles, Bundles of circles

• 5. The Cross Ratio
The simple ratio, The double ratio or cross ratio, The cross ratio in circle geometry

• Chapter II. The Moebius Transformation
• 6. Definition:
Elementary Properties, Definition and notation, The group of all Moebius transformations, Simple types of Moebius transformations, Mapping properties of the Moebius transformations, Transformation of a circle, Involutions

• 7. Real One-dimensional Projectivities
Perpectivities, Projectivities, Line-circle perspectivity

• 8. Similarity and Classification of Moebius Transformations
Introduction of a new variable, Normal forms of Moebius transformations, "Hyperbolic, elliptic, loxodromic transformations", The subgroup of the real Moebius transformations, The characteristic parallelogram

• 9. Classification of Anti-homographies
Anti-homographies, Anti-involutions, Normal forms of non-involutory anti-homographies, Normal forms of circle matrices and anti-involutions, Moebius transformations and anti-homographies as products of inversions, The groups of a pencil

• 10. Iteration of a Moebius Transformation
General remarks on iteration, Iteration of a Moebius transformation, Periodic sequences of Moebius transformations, Moebius transformations with periodic iteration, Continuous iteration, Continuous iteration of a Moebius transformation

• 11. Geometrical Characterization of the Moebius Transformation
The fundamental theorem, Complex projective transformations, Representation in space

• Chapter III. Two-Dimensional Non-Euclidean Geometries
• 12. Subgroups of Moebius Transformations
The group U of the unit circle, The group R of rotational Moebius transformations, Normal forms of bundles of circles, The bundle groups, Transitivity of the bundle groups

• 13. The Geometry of a Transformation Group
Euclidean geometry, G-geometry, Distance function, G-circles

• 14. Hyperbolic Geometry
Hyperbolic straight lines and distance, The triangle inequality, Hyperbolic circles and cycles, Hyperbolic trigonometry, Applications

• 15. Spherical and Elliptic Geometry
Spherical straight lines and distance, Additivity and triangle inequality, Spherical circles, Elliptic geometry, Spherical trigonometry

• Appendices
Uniqueness of the cross ratio, A theorem of H. Haruki, Applications of the characteristic parallelogram, Complex Numbers in Geometry by I. M. Yaglom

• ##### Math Books of COMPLEX ANALYSIS

Geometry of Complex Numbers by Hans Schwerdtfeger
• Free
• English
• Page 225
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##### Worksheets (Solved)

###### Integration     