Introduction to Circle Packing: The Theory of Discrete Analytic Functions by Kenneth Stephenson (PDF)

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, first published in 2005, 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In the preface the author states, “There are no prerequisites for this study; indeed I shamelessly exploit the visual nature of circle packing and our native intuition about circles so that even the novice mathematician can penetrate deeply into the subject”. I say that’s b.s. He tries to breezy and informal and then proceeds to drop many terms, theorems and names without bothering to define them. I’ve put this book away several times and worked through several of the references on Complex Analysis from his bibliography. I’ve been motivated to learn this topic but find the presentation here to be slippery at best.

⭐A BEAUTIFUL EXPLORATION OF COMPLEX FUNCTION THEORY AND PRACTICE AND REVALENCE TO OUR EXPERIENCE : FROM GRAPHICS to MEDICAL UNDERSTANDING OF MRI’S.

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