Skip to content
Register Sign in Wishlist
Introduction to Circle Packing

Introduction to Circle Packing
The Theory of Discrete Analytic Functions

$103.00 (C)

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

$ 103.00 (C)

Add to cart Add to wishlist

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
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
    Read more

    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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: April 2005
    • format: Hardback
    • isbn: 9780521823562
    • length: 370 pages
    • dimensions: 260 x 185 x 25 mm
    • weight: 0.929kg
    • 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

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact

  • 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.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.