Introduction to Circle Packing: The Theory of Discrete Analytic Functions (Hardback)
Introduction to Circle Packing: The Theory of Discrete Analytic Functions (Hardback)
Regular price
$54.15 USD
Regular price
Sale price
$54.15 USD
Unit price
/
per
Condition
LIKE NEW: This book and its dust jacket are in excellent, like-new condition. There is a remainder mark on the top page edge.Product Details
From the dust jacket: "A circle packing is a configuration of circles having specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to the 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 that is unique in pure mathematics, and the book exploits that character 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."BRIEF CONTENTS
- Preface
- I. An Overview of Circle Packing
- A Circle Packing Menagerie
- Circle Packings in the Wild
- II. Rigidity: Maximal Packings
- Preliminaries: Topology, Combinatorics, and Geometry
- Statement of the Fundamental Result
- Bookkeeping and Monodromy
- Proof for Combinatorial Closed Discs
- Proof for Combinatorial Spheres
- Proof for Combinatorial Open Discs
- Proof for Combinatorial Surfaces
- III. Flexibility: Analytic Functions
- The Intuitive Landscape
- Discrete Analytic Functions
- Construction Tools
- Discrete Analytic Functions on the Disc
- Discrete Entire Functions
- Discrete Rational Functions
- Discrete Analytic Functions on Riemann Surfaces
- Discrete Conformal Structure
- Random Walks on Circle Packings
- IV. Resolution: Approximation
- Thurston's Conjecture
- Extending the Rodin-Sullivan Theorem
- Approximation of Analytic Functions
- Approximation of Conformal Structures
- Applications
- Appendices
- Primer on Classical Complex Analysis
- The Ring Lemma
- The Brooks Parameter
- Inversive Distance Packings
- Graph Embedding
- Square Grid Packings
- Schwartz and Buckyballs
- CirclePack
- Bibliography
- Index
Share
PUBLISHER: Cambridge University Press
ISBN-13: 9780521823562
ISBN-10: 0521823560