The Mathematics of Various Entertaining Subjects

Research in Games, Graphs, Counting, and Complexity, Volume 2

Jennifer Beineke, Jason Rosenhouse (Herausgeber)

Buch | Hardcover

408 Seiten

2017
Princeton University Press (Verlag)
978-0-691-17192-0 (ISBN)

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The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic's background, providing a framework for understanding the relationship between serious mathematics and recreational games.
Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

Jennifer Beineke is professor of mathematics at Western New England University. Jason Rosenhouse is professor of mathematics at James Madison University. Beineke and Rosenhouse are the coeditors of The Mathematics of Various Entertaining Subjects: Research in Recreational Math (Princeton).

Foreword by Ron Graham vii

Preface and Acknowledgments xi

I PUZZLES AND BRAINTEASERS

1 The Cyclic Prisoners 3

Peter Winkler

2 Dragons and Kasha 11

Tanya Khovanova

3 The History and Future of Logic Puzzles 23

Jason Rosenhouse

4 The Tower of Hanoi for Humans 52

Paul K. Stockmeyer

5 Frenicle's 880 Magic Squares 71

John Conway, Simon Norton, and Alex Ryba

II GEOMETRY AND TOPOLOGY

6 A Triangle Has Eight Vertices But Only One Center 85

Richard K. Guy

7 Enumeration of Solutions to Gardner's Paper Cutting and Folding Problem 108

Jill Bigley Dunham and Gwyneth R. Whieldon

8 The Color Cubes Puzzle with Two and Three Colors 125

Ethan Berkove, David Cervantes-Nava, Daniel Condon, Andrew Eickemeyer, Rachel Katz, and Michael J. Schulman

9 Tangled Tangles 141

Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Quanauan Liu, Ron Taylor, and Ryuhei Uehara

III GRAPH THEORY

10 Making Walks Count: From Silent Circles to Hamiltonian Cycles 157

Max A. Alekseyev and Gerard P. Michon

11 Duels, Truels, Gruels, and Survival of the Unfittest 169

Dominic Lanphier

12 Trees, Trees, So Many Trees 195

Allen J. Schwenk

13 Crossing Numbers of Complete Graphs 218

Noam D. Elkies

IV GAMES OF CHANCE

14 Numerically Balanced Dice 253

Robert Bosch, Robert Fathauer, and Henry Segerman

15 A TROUBLE-some Simulation 269

Geoffrey D. Dietz

16 A Sequence Game on a Roulette Wheel 286

Robert W. Vallin

V COMPUTATIONAL COMPLEXITY

17 Multinational War Is Hard 301

Jonathan Weed

18 Clickomania Is Hard, Even with Two Colors and Columns 325

Aviv Adler, Erik D. Demaine, Adam Hesterberg, Quanquan Liu, and Mikhail Rudoy

19 Computational Complexity of Arranging Music 364

Erik D. Demaine and William S. Moses

About the Editors 379

About the Contributors 381

Index 387

Erscheinungsdatum	15.03.2018
Zusatzinfo	71 color illus. 1 halftone. 76 line illus. 47 tables.
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 235 mm
Gewicht	794 g
Themenwelt	Sachbuch/Ratgeber ► Freizeit / Hobby
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
ISBN-10	0-691-17192-0 / 0691171920
ISBN-13	978-0-691-17192-0 / 9780691171920
Zustand	Neuware