Preface; Introduction; 1. The language of symmetry; 2. A delightful fiction; 3. Double spirals and Möbius maps; 4. The Schottky dance; 5. Fractal dust and infinite words; 6. Indra's necklace; 7. The glowing gasket; 8. Playing with parameters; 9. Accidents will happen; 10. Between the cracks; 11. Crossing boundaries; 12. Epilogue; Index; Road map.
This book tells the story of the first computer exploration of Klein's vision of infinitely repeated reflections, featuring extraordinary images.
David Mumford has been University Professor in the Division of Applied Mathematics at Brown University since 1996. Before that he was at Harvard University for thirty-five years. He has been a contributor to the Calculus Textbook Project, led by Hughes-Hallett and Gleason. Over his long and distinguished career, Professor Mumford has received many awards and honours, including the Fields Medal in 1974, the Wolf Prize in 1998 and the National Medal of Science in 2010. Caroline Series is Professor of Mathematics at Warwick University where she currently holds an EPSRC Senior Research Fellowship. She was Kennedy Scholar at Harvard University from 1972 to 1974. In addition to technical publications, she has contributed widely to the popularization of mathematics. In 2014, she won the first Senior Anne Bennett Prize of the London Mathematical Society for contributions to mathematics and to the advancement of female mathematicians. She edits the new International Women in Maths website http://www.mathunion.org/wim/. David Wright is Professor at Oklahoma State University. He has held a guest professorship at the University of Göttingen, and was Sloan Fellow at the Institute for Advanced Study in Princeton from 1988 to 1990. From 1997 to 1999 he helped establish the famous William Lowell Putnam Mathematical Competition. In 2009 he received a Distinguished Teaching Award from the Mathematical Association of America.
'[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, 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, 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, SIAM News
'All of it is patiently explained … By the time you finish, you'll
know your way around the complex plane.' Brian Hayes, 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, 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.'
European Mathematical Society
'This is a beautifully presented book, rich in mathematical gems.'
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.'
Acta Scientiarum Mathematicarum
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