Introduction to Circle Packing The Theory of Discrete Analytic Functions [Hardcover]

This book, first published in 2005, introduces a new mathematical topic known as 'circle packing', taking the reader from first definitions to late-breaking results.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.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.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 lC0