9780817683825
IR
EN-52490
انگلیسی
IR
A Tale of Two Fractal
[Book]
:[delta
/ by A.A. Kirillov
New York, NY
: Springer New York :Imprint: Birkh?nuser,
, 2013.
XIII, 138 p. 44 illus., 4 illus. in color., online resource.
Electronic
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of researcharticles and books have beenpublished on the topic of fractals. Despite thevolume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use.Written bycelebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals helpsbridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The workis designedto give young, non-specialist mathematiciansa solid foundation in the theory of fractals. As its title suggests, this book focuses primarily on twofractals: theSierpi??skigasket and the Apollonian gasket.Over the course of the book, they are developed and discussed in various contexts. Along with fundamentaldefinitions and properties, some of the keyconcepts and approachescovered include * the Laplace operator * harmonic functions * generalized numerical systems * Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of providing undergraduate and graduate students with a sound foundation in fractal theory, A Tale of Two Fractalsserves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a unique opportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but also for any survey course with an aim of honing creative-problem-solving skills.
Introduction -- Part 1. The Sierpi??ski Gasket -- Definition and General Properties -- The Laplace Operator on the Sierpi??ski Gasket.-Harmonic Functions on the Sierpi??ski Gasket -- Part 2. The Apollonian Gasket -- Introduction -- Circles and Disks on Spheres -- Definition of the Apollonian Gasket -- Arithmetic Properties of Apollonian Gaskets -- Geometric and Group-Theoretic Approach -- Many-Dimensional Apollonian Gaskets -- Bibliography.?╗╣
Mathematics
Algebra
Global analysis (Mathematics)
Functions, special
Visualization
Geometry
Electronic books
E-BOOK
Kirillov, A.A.
SpringerLink (Online service)
ایران
9780817683818.pdf
عادی
عادی
9780817683818.pdf
متن
old catalog
e
BL
1
a
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