The Mathematics of Various Entertaining Subjects: Research in Recreational Math

The Mathematics of Various Entertaining Subjects: Research in Recreational Math

The Mathematics of Various Entertaining Subjects: Research in Recreational Math

The Mathematics of Various Entertaining Subjects: Research in Recreational Math

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Overview

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 exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics.

Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more.

Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.


Product Details

ISBN-13: 9780691164038
Publisher: Princeton University Press
Publication date: 12/29/2015
Pages: 296
Sales rank: 804,893
Product dimensions: 6.00(w) x 9.40(h) x 1.00(d)

About the Author

Jennifer Beineke is professor of mathematics at Western New England University. Jason Rosenhouse is professor of mathematics at James Madison University. He is the author of The Monty Hall Problem and the coauthor of Taking Sudoku Seriously.

Table of Contents

Foreword by Raymond Smullyan vii

Preface and Acknowledgments x

PART I VIGNETTES

1 Should You Be Happy? 3

Peter Winkler

2 One-Move Puzzles with Mathematical Content 11

Anany Levitin

3 Minimalist Approaches to Figurative Maze Design 29

Robert Bosch, Tim Chartier, and Michael Rowan

4 Some ABCs of Graphs and Games 43

Jennifer Beineke and Lowell Beineke

PART II PROBLEMS INSPIRED BY CLASSIC PUZZLES

5 Solving the Tower of Hanoi with Random Moves 65

Max A. Alekseyev and Toby Berger

6 Groups Associated to Tetraflexagons 81

Julie Beier and Carolyn Yackel

7 Parallel Weighings of Coins 95

Tanya Khovanova

8 Analysis of Crossword Puzzle Difficulty Using a Random Graph Process 105

John K. McSweeney

9 From the Outside In: Solving Generalizations of the Slothouber-Graatsma-Conway Puzzle 127

Derek Smith

PART III PLAYING CARDS

10 Gallia Est Omnis Divisa in Partes Quattuor 139

Neil Calkin and Colm Mulcahy

11 Heartless Poker 149

Dominic Lanphier and Laura Taalman

12 An Introduction to Gilbreath Numbers 163

Robert W. Vallin

PART IV GAMES

13 Tic-tac-toe on Affine Planes 175

Maureen T. Carroll and Steven T. Dougherty

14 Error Detection and Correction Using SET 199

Gary Gordon and Elizabeth McMahon

15 Connection Games and Sperner’s Lemma 213

David Molnar

PART V FIBONACCI NUMBERS

16 The Cookie Monster Problem 231

Leigh Marie Braswell and Tanya Khovanova

17 Representing Numbers Using Fibonacci Variants 245

Stephen K. Lucas

About the Editors 261

About the Contributors 263

Index 269

What People are Saying About This

From the Publisher

"This book is a fascinating treasure trove of puzzles, brain teasers, and mathematical recreations that will keep your mind busy for months, if not years. A true gem that is destined to become a classic."—Eli Maor, author of e: The Story of a Number

"As enticing as a Rubik's Cube, this rigorous and inviting book is a treat to the eyes and mind. The list of contributors is an all-star lineup ready to welcome you into their mathematical rec rooms. Pull up a chair and grab a friend, it’s time to be entertained with various mathematical subjects."—Tim Chartier, Davidson College

"This entertaining yet rigorous book of recreational mathematical masterpieces presents centuries-old puzzles and new inventions that illustrate the continuing allure of recreational mathematics. The contributions are up-to-date, well illustrated, and startle with unexpected connections. Lay readers and connoisseurs will find imaginative and instructive delights."—Mircea Pitici, editor of The Best Writing on Mathematics

"A pleasure to read, this inviting book spans the broad range of topics in recreational mathematics, and the contributors are well-respected names in the field. Probability calculations, Fibonacci numbers, continued fractions, card tricks, strategies in games, and coin-weighing problems are all included, and in ways that reinforce each other."—Philip Straffin, professor emeritus of mathematics, Beloit College

"The Mathematics of Various Entertaining Subjects provides a plethora of elegant and surprising mathematical results that were originally motivated by, or found applications in, games and puzzles. The diverse questions, engaging work, and novel, often beautiful solutions make this book an excellent survey and introduction to this kind of analysis."—David Neel, Seattle University

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