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Introduction to Circle Packing

Introduction to Circle Packing
The Theory of Discrete Analytic Functions

$105.00 (P)

  • Date Published: April 2005
  • availability: Available
  • format: Hardback
  • isbn: 9780521823562

$ 105.00 (P)
Hardback

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About the Authors
  • 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.

    • 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
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    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 experiments—some 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 Scientist

    "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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    Product details

    • 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
    Part IV:
    19. Thurston's Conjecture
    20. Extending the Rodin/Sullivan theorem
    21. Approximation of analytic functions
    22. Approximation of conformal structures
    23. Applications
    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.

  • Resources for

    Introduction to Circle Packing

    Kenneth Stephenson

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  • Author

    Kenneth Stephenson, University of Tennessee
    Kenneth Stephenson is Professor of Mathematics at the University of Tennessee in Knoxville, where he has established an active research program in complex function theory. He has had visiting positions at the University of Hawaii and Florida State University, and sabbatical appointments at the Open University and the University of Cambridge. Over the last fifteen years he has centered his research on circle packing. In this book he formulates circle packing as a discrete incarnation of classical analytic function theory.

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