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Geometry of Complex Numbers (Paperback or Softback)
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Located in: Grand Rapids, Michigan, United States
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eBay item number:386299189353
Item specifics
- Condition
- ISBN
- 0486638308
- EAN
- 9780486638300
- UPC
- 00800759638307
- Binding
- TP
- Book Title
- Geometry of Complex Numbers
- Publication Name
- Geometry of Complex Numbers
- Item Length
- 8.2in
- Publisher
- Dover Publications, Incorporated
- Series
- Dover Books on Mathematics Ser.
- Publication Year
- 1980
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Height
- 0.4in
- Features
- New Edition
- Item Width
- 5.6in
- Item Weight
- 8.5 Oz
- Number of Pages
- 224 Pages
About this product
Product Information
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book." -- Mathematical Review.
Product Identifiers
Publisher
Dover Publications, Incorporated
ISBN-10
0486638308
ISBN-13
9780486638300
eBay Product ID (ePID)
127407867
Product Key Features
Publication Name
Geometry of Complex Numbers
Format
Trade Paperback
Language
English
Features
New Edition
Series
Dover Books on Mathematics Ser.
Publication Year
1980
Type
Textbook
Number of Pages
224 Pages
Dimensions
Item Length
8.2in
Item Height
0.4in
Item Width
5.6in
Item Weight
8.5 Oz
Additional Product Features
Lc Classification Number
Qa255.S36
Edition Description
New Edition
Table of Content
INTRODUCTION: NOTE ON TERMINOLOGY AND NOTATIONSCHAPTER I. ANALYTIC GEOMETRY OF CIRCLES§ 1. Representation of Circles by Hermitian Matrices a. One circle b. Two circles c. Pencils of circles Examples§ 2. The Inversion a. Definition b. Simple properties of the inversion Examples§ 3. Stereographic Projection a. Definition b. Simple properties of the stereographic projection c. Stereographic projection and polarity Examples§ 4. Pencils and Bundles of Circles a. Pencils of circles b. Bundles of circles Examples§ 5. The Cross Ratio a. The simple ratio b. The double ratio or cross ratio c. The cross ratio in circle geometry ExamplesCHAPTER II. THE MOEBIUS TRANSFORMATION§ 6. Definition: Elementary Properties a. Definition and notation b. The group of all Moebius transformations c. Simple types of Moebius transformations d. Mapping properties of the Moebius transformations e. Transformation of a circle f. Involutions Examples§ 7. Real One-dimensional Projectivities a. Perpectivities b. Projectivities c. Line-circle perspectivity Examples§ 8. Similarity and Classification of Moebius Transformations a. Introduction of a new variable b. Normal forms of Moebius transformations c. "Hyperbolic, elliptic, loxodromic transformations" d. The subgroup of the real Moebius transformations e. The characteristic parallelogram Examples§ 9. Classification of Anti-homographies a. Anti-homographies b. Anti-involutions c. Normal forms of non-involutory anti-homographies d. Normal forms of circle matrices and anti-involutions e. Moebius transformations and anti-homographies as products of inversions f. The groups of a pencil Examples§ 10. Iteration of a Moebius Transformation a. General remarks on iteration b. Iteration of a Moebius transformation c. Periodic sequences of Moebius transformations d. Moebius transformations with periodic iteration e. Continuous iteration f. Continuous iteration of a Moebius transformation Examples§ 11. Geometrical Characterization of the Moebius Transformation a. The fundamental theorem b. Complex projective transformations c. Representation in space ExamplesCHAPTER III. TWO-DIMENSIONAL NON-EUCLIDEAN GEOMETRIES§ 12. Subgroups of Moebius Transformations a. The group U of the unit circle b. The group R of rotational Moebius transformations c. Normal forms of bundles of circles d. The bundle groups e. Transitivity of the bundle groups Examples§ 13. The Geometry of a Transformation Group a. Euclidean geometry b. G-geometry c. Distance function d. G-circles Examples§ 14. Hyperbolic Geometry a. Hyperbolic straight lines and distance b. The triangle inequality c. Hyperbolic circles and cycles d. Hyperbolic trigonometry e. Applications Examples§ 15. Spherical and Elliptic Geometry a. Spherical straight lines and distance b. Additivity and triangle inequality c. Spherical circles d. Elliptic geometry e. Spherical trigonometry ExamplesAPPENDICES1. Uniqueness of the cross ratio2. A theorem of H. Haruki3. Applications of the characteristic parallelogram4. Complex Numbers in Geometry by I. M. YaglomBIBLIOGRAPHYSUPPLEMENTARY BIBLIOGRAPHYINDEX
Copyright Date
1979
Target Audience
College Audience
Topic
Geometry / General, Earth Sciences / Geology
Lccn
79-052529
Dewey Decimal
516
Dewey Edition
18
Illustrated
Yes
Genre
Science, Mathematics
Item description from the seller
Seller assumes all responsibility for this listing.
eBay item number:386299189353
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