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Introduction to Circle Packing The Theory of Discrete Analytic Functions 1st Edition by Kenneth Stephenson 9780521823562 0521823560

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Introduction to Circle Packing The Theory of Discrete Analytic Functions 1st Edition Kenneth Stephenson Digital Instant Download

Author(s): Kenneth Stephenson
ISBN(s): 9780521823562, 0521823560
Edition: 1
File Details: PDF, 89.97 MB
Year: 2005
Language: english
SKU: EB-5895154 Category: Tag:

Introduction to Circle Packing The Theory of Discrete Analytic Functions 1st Edition by Kenneth Stephenson – Ebook PDF Instant Download/Delivery: 9780521823562, 0521823560

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Product details:

ISBN 10: 0521823560

ISBN 13: 9780521823562

Author: Kenneth Stephenson

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.

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

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Tags: Kenneth Stephenson, Circle, Packing, Theory