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
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