Introduction to Circle Packing : The Theory of Discrete Analytic Functions
Editorial Reviews
Review
'This book lays out the study of circle packing, 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. ... The author uses both discrete functions and discrete conformal structures in several settings of active research interest, ranging from number theory to conformal tilings to (of all things!) human 'brain mapping'. These are all settings involving classically defined structures for which no numerical approximation methods were available until circle packing arrived on the scene. There are intriguing, often very accessible, open problems throughout the book and nine Appendices on subtopics of independent interest: Primer on classical complex analysis, The ring lemma, Doyle spirals, The Brooks parameter, Inversive distance packings, Graph embedding, Square grid packings, Schwarz and buckyballs, Circle packings.' Zentralblatt MATH
Book Description
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.
Introduction to Circle Packing : The Theory of Discrete Analytic Functions
Introduction to Circle Packing: The Theory of Discrete Analytic Functions,Kenneth Stephenson,Cambridge University Press,0521823560,Analytic functions,Circle packing,Discrete geometry,Geometry - General,Mathematical Analysis,Mathematics,Science/Mathematics,Mathematics / Applied,Probability & statistics
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