Famous Puzzles of Great MathematiciansAmerican Mathematical Soc., 2 sept 2009 - 325 páginas 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. |
Índice
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 |
311 | |
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algebra angle arbelos Archimedes arithmetic arrangement Bachet Bernoulli binary Born Brahmagupta Cardano chapter chess chessboard circle combinatorial considered Conway Coxeter crossing cube denote difierent digits Diophantine equation Diophantus disks distance eight queens problem equal Euler example famous Fermat Fibonacci field figure find first five fixed flavors formula French mathematician gambler Gardner Gauss geometry Gerolamo Cardano given graph theory Gray-code Hamiltonian cycle Huygens infinite integer John Horton Conway Josephus problem Kepler Kirkman knight’s tour known Knuth Leonhard Euler math mathematician maximum number natural numbers number of moves number theory obtain packing pair Pascal path pentaminoes plane player probability proof radius re-entrant recreational mathematics reflection relation rings puzzle river Scientific American sequence shown in Figure solution solved sphere square straight line Sylvester Tartaglia task tessellations theorem tiling total number Tower of Hanoi triangle vertex vertices