Introduction To Circle Packing: The Theory Of Discrete Analytic Functions. - Tapa dura

'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

'this beautifully produced book is an inviting introduction to an emerging area of mathematics that hs both an immediate visual appeal, with plenty of opportunities for computer-driven experimentation, and a rapidly developing clean line of theory ... Stephenson is one of the leading pioneers in this exciting development and his stimulating book, written in an enthusiastic, almost conversational, style, will surely attract new workers into this new field. For, as he aptly remarks in the Preface, 'Circle packing has opened a discrete world that both parallels and approximates the classical world of conformal geometry - a 'quantum' classical analysis that is classical in the limit.' The Mathematical Gazette

'... a splendid work of academic art. ... The overall effect is that of a stunning menagerie of images complementing beautifully scripted text. ... Ken Stephenson has produced in this textbook an effective and enjoyable tour of both the basic theory of circle packing and its use in deriving an intricate theory of discrete analytic functions. ... I expect Introduction to Circle Packing: the Theory of Discrete Analytic Functions to be the source for student and researcher for many years to come.' Bulletin of the American Mathematical Society

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. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest.