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Indra's Pearls
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  • Cited by 61
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    El Naschie, M.S. 2003. Complex vacuum fluctuation as a chaotic “limit” set of any Kleinian group transformation and the mass spectrum of high energy particle physics via spontaneous self-organization. Chaos, Solitons & Fractals, Vol. 17, Issue. 4, p. 631.

    Sinclair, Nathalie 2004. The Roles of the Aesthetic in Mathematical Inquiry. Mathematical Thinking and Learning, Vol. 6, Issue. 3, p. 261.

    Crowdy, Darren and Marshall, Jonathan 2004. Constructing Multiply Connected Quadrature Domains. SIAM Journal on Applied Mathematics, Vol. 64, Issue. 4, p. 1334.

    Crowdy, Darren 2005. Genus-Nalgebraic reductions of the Benney hierarchy within a Schottky model. Journal of Physics A: Mathematical and General, Vol. 38, Issue. 50, p. 10917.

    Crowdy, Darren 2005. The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, Issue. 2061, p. 2653.

    Crowdy, Darren 2005. Quadrature Domains and Their Applications. Vol. 156, Issue. , p. 113.

    Zun-Tao, Fu Shi-Da, Liu Shi-Kuo, Liu Fu-Ming, Liang and Guo-Jun, Xin 2005. Homoclinic (Heteroclinic) Orbit of Complex Dynamical System and Spiral Structure. Communications in Theoretical Physics, Vol. 43, Issue. 4, p. 601.

    Crowdy, Darren and Marshall, Jonathan 2005. Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, Issue. 2060, p. 2477.

    DeLillo, Thomas K. 2006. Schwarz-Christoffel Mapping of Bounded, Multiply Connected Domains. Computational Methods and Function Theory, Vol. 6, Issue. 2, p. 275.

    Crowdy, Darren and Marshall, Jonathan 2006. Conformal Mappings between Canonical Multiply Connected Domains. Computational Methods and Function Theory, Vol. 6, Issue. 1, p. 59.

    Debnath *, Lokenath 2006. A brief historical introduction to fractals and fractal geometry. International Journal of Mathematical Education in Science and Technology, Vol. 37, Issue. 1, p. 29.

    Brown, Tony 2007. The Art of Mathematics: Bedding down for a new era. Educational Philosophy and Theory, Vol. 39, Issue. 7, p. 755.

    HINOJOSA, GABRIELA 2007. A WILD KNOT 𝕊2↪ 𝕊4AS LIMIT SET OF A KLEINIAN GROUP: INDRA'S PEARLS IN FOUR DIMENSIONS. Journal of Knot Theory and Its Ramifications, Vol. 16, Issue. 08, p. 1083.

    Ungar, Abraham A. 2008. From Möbius to Gyrogroups. The American Mathematical Monthly, Vol. 115, Issue. 2, p. 138.

    Crowdy, Darren 2008. Geometric function theory: a modern view of a classical subject. Nonlinearity, Vol. 21, Issue. 10, p. T205.

    Lenz, Reiner 2008. Lie methods for color robot vision. Robotica, Vol. 26, Issue. 04,

    Field, Michael 2008. Book review. Journal of Mathematics and the Arts, Vol. 2, Issue. 4, p. 208.

    Velleman, Daniel J. 2008. Editor's Endnotes. The American Mathematical Monthly, Vol. 115, Issue. 8, p. 769.

    Burns, Anne M. 2008. Iterated Möbius transformations. Journal of Mathematics and the Arts, Vol. 2, Issue. 4, p. 171.

    Ungar, Abraham Albert 2008. A Gyrovector Space Approach to Hyperbolic Geometry. Synthesis Lectures on Mathematics and Statistics, Vol. 1, Issue. 1, p. 1.

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Book description

Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.


‘[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.'

John H. Hubbard Source: The American Mathematical Monthly

‘It has been a great pleasure to read such a gracefully written, original book of mathematics … it is a flowing narrative, leavened with wit, whimsy, and lively cartoons by Larry Gonick. The three authors, with the support of Cambridge University Press, have produced a book that is as handsome in physical appearance as its content is stimulating and accessible. The book is an exemplar of its genre and a singular contribution to the contemporary mathematics literature.'

Albert Marden Source: Notices (journal of the American Mathematical Society)

‘The production of the book leaves nothing to be desired. It is splendid. Printed entirely on glossy paper, with practically all of the many figures in glorious color, the book has a number of admirable design features: large type and wide margins wherein references are given and occasional comments (often quite talky) are made. Cambridge University Press has done a beautiful job, and David Tranah of the Press deserves special commendation for his role in pulling out all the stops.'

Philip J. Davis Source: SIAM News

‘All of it is patiently explained … By the time you finish, you'll know your way around the complex plane.'

Brian Hayes Source: American Scientist

‘The book itself is a work of art … I am sure that [it] will have a major impact on the way we teach geometry and dynamics … a jewel that will more than repay the persistent reader's efforts.'

Michael Field Source: Science

‘I rarely feel a certain kind of euphoria by just looking at the cover of a mathematics book. But that happened with Indra's Pearls: The Vision of Felix Klein … [contains] fantastic illustrations together with apparently well-founded mathematical explanations … [it is] presented in an accessible way which dares to prioritize general comprehension above a strict theoretical approach … As far as I know, this book is one of the most beautiful examples of the illustration of the inherent aesthetic beauty (which exists) within mathematics … the images are of the highest quality obtainable at present for mathematical structures. Everyone, who ever tried to create something comparable, knows how difficult it is.'

Jürgen Richter-Gebert - Technische Universität München

‘This unique book can serve as a pedagogical and visual introduction to group theory for schoolchildren, and yet is just as suitable for professional mathematicians: I believe that both of them would read the book from the beginning to the end. Finally, it can be used as a book for popularising science, but is very different from most fashionable books on strings, black holes, etc: it gives you the joy of seeing, thinking and understanding.'

Source: European Mathematical Society

‘This is a beautifully presented book, rich in mathematical gems.'

Source: The Mathematical Gazette

‘One can browse through the numerous beautiful and fascinating pictures and marvel at them … Readers with widely different backgrounds will find something enjoyable in this unique book.'

Source: Acta Scientiarum Mathematicarum

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