Introduction to Circle Packing: The Theory of Discrete Analytic Functions

Hardcover

ISBN 10: 0521823560 ISBN 13: 9780521823562

Publisher: Cambridge University Press, 2005

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.

Book Description:

This book introduces a new mathematical topic known as "circle packing", taking the reader from first definitions to late-breaking results. It can be enjoyed for visual appeal, the elegance of circle geometry, the clean theory, classical connections, or applications. The book ramps up from intuitive notions to links with core areas of complex analysis and Riemann surfaces. However, it is firmly grounded in a computational, experimental and visual approach, which can carry the reader deeply into these topics, and which provides many enticing and accessible open problems. This book lays the foundation for a topic with wide appeal and a bright future.

About the Author:

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.