The topic of circle packing was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven appendices on subtopics of independent interest. This book lays the foundation for a topic with wide appeal and a bright future.Read more
- Foundational: this is the first book on a fascinating new topic and it lays out a clear formulation from definitions to applications
- Accessible: it has four parts with increasing sophistication, accompanied by numerous illustrations
- There are seven appendices on stand-alone topics which are widely accessible and suitable for independent projects
Reviews & endorsements
"Stephenson is one of a new breed of pure mathematicians, growing in number, who love to combine experiment with theory. This means he has computer code to carry out these packings and investigate their properties. And the book is interlaced with experimentssome successful, some not, some which worked one day but not the next when pushed further. His immense enthusiasm for this subject comes through on every page."
American ScientistSee more reviews
"Ken Stephenson has produced this textbook an effective and enjoyable tour of both the basic theory of circle parking and its use in deriving an intricate theory of discrete analytic functions. All this from the humble circle! I expect Introduction to Circle Parking: the Theory of Discrete Analytic Functions to be the source for student and researcher for many years to come."
Bulletin of the AMS
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- Date Published: April 2005
- format: Hardback
- isbn: 9780521823562
- length: 370 pages
- dimensions: 254 x 178 x 22 mm
- weight: 0.86kg
- contains: 190 b/w illus. 10 colour illus.
- availability: Available
Table of Contents
Part I. An Overview of Circle Packing:
1. A circle packing menagerie
2. Circle packings in the wild
Part II. Rigidity: Maximal Packings:
3. Preliminaries: topology, combinatorics, and geometry
4. Statement of the fundamental result
5. Bookkeeping and monodromy
6. Proof for combinatorial closed discs
7. Proof for combinatorial spheres
8. Proof for combinatorial open discs
9. Proof for combinatorial surfaces
Part III. Flexibility: Analytic Functions:
10. The intuitive landscape
11. Discrete analytic functions
12. Construction tools
13. Discrete analytic functions on the disc
14. Discrete entire functions
15. Discrete rational functions
16. Discrete analytic functions on Riemann surfaces
17. Discrete conformal structure
18. Random walks on circle packings
19. Thurston's Conjecture
20. Extending the Rodin/Sullivan theorem
21. Approximation of analytic functions
22. Approximation of conformal structures
Appendix A. Primer on classical complex analysis
Appendix B. The ring lemma
Appendix C. Doyle spirals
Appendix D. The brooks parameter
Appendix E. Schwarz and buckyballs
Appendix F. Inversive distance packings
Appendix G. Graph embedding
Appendix H. Square grid packings
Appendix I. Experimenting with circle packings.
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