2009;
325 pp;
Softcover

MSC: Primary 00; 97; 01; 05; 11; 51; 52;

**Print ISBN: 978-0-8218-4814-2
Product Code: MBK/63**

List Price: $41.00

AMS Member Price: $32.80

MAA Member Price: $36.90

**Electronic ISBN: 978-1-4704-1599-0
Product Code: MBK/63.E**

List Price: $38.00

AMS Member Price: $30.40

MAA Member Price: $34.20

#### Supplemental Materials

# Famous Puzzles of Great Mathematicians

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*Miodrag S. Petković*

This entertaining book presents a collection
of 180 famous mathematical puzzles and intriguing elementary problems
that great mathematicians have posed, discussed, and/or solved. The
selected problems do not require advanced mathematics, making this
book accessible to a variety of readers.

Mathematical recreations offer a rich playground for both amateur and
professional mathematicians. Believing that creative stimuli and aesthetic
considerations are closely related, great mathematicians from ancient
times to the present have always taken an interest in puzzles and
diversions. The goal of this book is to show that famous mathematicians
have all communicated brilliant ideas, methodological approaches, and
absolute genius in mathematical thoughts by using recreational mathematics
as a framework. Concise biographies of many mathematicians mentioned in
the text are also included.

The majority of the mathematical problems presented in this book
originated in number theory, graph theory, optimization, and probability.
Others are based on combinatorial and chess problems, while still others
are geometrical and arithmetical puzzles.

This book is intended to be both entertaining as well as an introduction
to various intriguing mathematical topics and ideas. Certainly, many
stories and famous puzzles can be very useful to prepare classroom
lectures, to inspire and amuse students, and to instill affection for
mathematics.

#### Readership

General readers and undergraduate students interested in puzzles and recreational mathematics.

#### Reviews & Endorsements

This book reminds us that puzzles are a big part of the history of mathematics.

-- MAA Reviews

The whole book is very well illustrated with diagrams and pictures as well as clear mathematical formulae making it very readable. ... I would fully recommend the book. It does not require advanced mathematics but it would inspire curiosity to look further. There is valuable material for a teacher perhaps at Advanced level to introduce new topics by way of a puzzle or two. The book is also a good read for those interested in the history of mathematics and mathematicians.

-- Mathematics Today

*Famous Puzzles of Great Mathematicians* contains a nice collection
of recreational mathematics problems and puzzles, problems whose solutions
do not rely on knowledge of advanced mathematics. ... Despite its recreational
nature, this book does not give up on being rigorous in its arguments, nor
does it shy away from presenting some difficult problems, albeit solvable by
elementary methods. ... What makes this book especially compelling is
Petković's efforts in putting the problems into context. He makes it clear that
math is a human subject, with its own stories and history. ... [I]
wholeheartedly recommend it to a wide variety of audiences. ... Petković aims
to bring his readers closer to the ideas of brilliant mathematicians, and I
believe he succeeds. This book would be especially appropriate for
undergraduates or even high school students with aptitude in mathematics. They
should find *Famous Puzzles of Great Mathematicians*
both very informative and fun, and might even become inspired to explore a
career in math.

-- Lev Reyzin, ACM SIGACT News

*Famous Puzzles of Great Mathematicians* reminds us that puzzles
are a big part of the history of mathematics. I daresay many mathematicians
were sucked into the field by puzzles, such as those disseminated by the late
Martin Gardner in his "Mathematical Games" column in *Scientific
American*, 1956--1986. ... What is a puzzle, anyway --- in particular, a
mathematical puzzle? To me it is an engaging, self-contained mathematical
question. ... [This book] ... contains (by my debatable count) 180 puzzles of
which 30% are tasks, 25% historical, 20% natural, 10% examplars, 10% riddles,
4% obstacles, and 1% paradoxes. To these the book adds some entertaining and
enlightening information about great mathematicians from Archimedes to Knuth.
The puzzles themselves are (mostly) solved with undergraduate-level
mathematics, making the book ideal for leaving within easy reach of current
or potential mathematics majors.

-- Peter Winkler, American Mathematical Monthly

The author has done an admirably accurate and thorough job in presenting his material... The problems are here, their histories are here, the mathematics needed to solve them is here. The book would be the ideal graduation present for a mathematics major, an ideal prize for the winner of an integration contest, an ideal book to have lying around a mathematics department (if properly chained down, that is).

-- MAA Reviews

This book will be accessible to undergraduate students and should also be of interest to faculty looking for interesting problems to use in their teaching.

-- CHOICE Magazine

The selected problems do not require advanced mathematics, making this book accessible to a variety of readers.

-- SciTech Book News

#### Table of Contents

# Table of Contents

## Famous Puzzles of Great Mathematicians

- Cover Cover11 free
- Title page i2 free
- Dedication iii4
- Contents v6 free
- Preface xiii14 free
- Art and photo credits xvii18 free
- 1. Recreational mathematics 120 free
- 2. Arithmetics 928
- 3. Number theory 3756
- 4. Geometry 6786
- 5. Tiling and packing 119138
- 6. Physics 151170
- 7. Combinatorics 171190
- 8. Probability 209228
- 9. Graphs 229248
- 10. Chess 257276
- 11. Miscellany 283302
- Appendix A. Method of continued fractions for solving Pell’s equation 289308
- Appendix B. Geometrical inversion 289308
- Appendix C. Some basic facts from graph theory 289308
- Appendix D. Linear difference equations with constant coefficients 289308
- Biographies – a chronological order 299318
- Bibliography 311330
- Name index 319338
- Back Cover Back Cover1346