Famous Puzzles of Great Mathematicians

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American Mathematical Soc., 2 sep. 2009 - 325 páginas
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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.
 

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Índice

RECREATIONAL MATHEMATICS
1
ARITHMETICS
9
Square numbers problem Fibonacci
15
Wine and water T aitaglia
25
Gathering an army Alcum of York
29
NUMBER THEORY
37
Dividing the square Diophantus
44
Horses and bulls a Diophantine equation Euler
50
Counting problem Cayley 193
172
The problem of the misaddressed letters N H Bernoulli Euler
184
The Tower of Hanoi Lucas
196
The tree planting problem Sylvester
202
PROBABILITY
209
Gambling game with dice Huygens
215
Matchbox problem Banach
224
The problem of Konigsbergs bridges Euler
230

Unknown address Ramanujan
57
Answers to Problems
64
The same distance of traversed paths Brahmagupta
77
Dissection of four triangles Abul Wafa
83
Division of space by planes Steiner
98
Answers to Problems
112
Nonperiodic tiling Penrose Conway
126
Cubepacking puzzles Conway
142
Meeting of ships Lucas p 155
155
COMBINATORICS
171
A man a wolf a goat and a cabbage Alcuin of York
240
Milk puzzle Poisson
247
CHESS
257
Nonattacking rooks Euler
265
The longest uncrossed knights tour Knuth
273
Answers to Problems
276
Method of continued fractions for solving
289
Bibliography
311
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