LDR 03137 a2200301 4500 010 _a9780521823562 _brel. 090 _a16468 101 _aeng 102 _aGB 100 _a20180711 frey50 200 _bM _aIntroduction to circle packing _fKenneth Stephenson _ethe theory of discrete analytic functions 210 _cCambridge University Press _aCambridge _dcop. 2005 215 _a1 vol. (XII-356 p.) _cill. _d26 320 _aBibliogr. p. 347-353. Index 330 _aA circle packing is a configuration of circles having a special pattern of tangencies. In 1985, W. Thurston linked this topic to analytic functions and conjectured how discrete analytic functions built with circle packings should approximate the Riemann uniformization mapping of a simply connected bounded open set in the plane. This conjecture and the (positive) answer given by B. Rodin and D. Sullivan in 1987 were the starting point for a great amount of research in the past 20 years. This book is an overview of this topic. It lays out the study of circle packings, from first definitions to the latest theory, computations and applications. The experimental and visual character of circle packings is exploited to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. The questions of existence, uniqueness, convergence are addressed, widely using manipulations and displays. Let us briefly outline the way this book is structured. Part I is devoted to an informal and largely visual tour of the topic. Part II contains a complete and essentially self-contained proof of the fundamental result of existence and uniqueness of a circle packing with prescribed combinatorics. Removing topological conditions in the latter result gives a wealth of flexibility which is studied in Part III. Part IV deals with approximation of classical analytic functions by their discrete counterparts. This text is both mathematically rigorous and accessible to the novice mathematician, enabling him to penetrate deeply into the subject. The reading is pleasant, the style is lively and the enthusiasm of the author is quite communicative (MSN) 676 _a2010 686 _20 _9164860 _a52C26 _bConvex and discrete geometry -- Discrete geometry _xCircle packings and discrete conformal geometry 686 _20 _9164811 _a52-02 _bConvex and discrete geometry _xResearch exposition (monographs, survey articles) 686 _20 _9164855 _a52C17 _bConvex and discrete geometry -- Discrete geometry _xPacking and covering in n dimensions 686 _20 _9164854 _a52C15 _bConvex and discrete geometry -- Discrete geometry _xPacking and covering in 2 dimensions 686 _20 _9162979 _a30G25 _bFunctions of a complex variable -- Generalized function theory _xDiscrete analytic functions 700 _4070 _aStephenson _bKenneth _f1945- _9183237 856 _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=2131318 _zMSN 856 _uhttps://zbmath.org/?q=an%3A1074.52008 _zzbMath 905 _aaw _b2018 906 _aaw _b2018-08-30 001 16468 995 _f12505-01 _xachat Ebsco _918664 _cCMI _20 _k52 STE _o0 _eSalle R _z71 _bCMI