The Mathematics of Various Entertaining Subjects: Volume 3: The Magic of Mathematics

Presented to you through Paradigm Publishing Services

Princeton University Press

Visit our Partner Page See all our books

Book

The Mathematics of Various Entertaining Subjects

Volume 3: The Magic of Mathematics

Edited by: and

Language: English

Published/Copyright: 2019

About this book

The history of mathematics is replete with examples of major breakthroughs resulting from solutions to recreational problems. The modern theory of probability arose out of problems of concern to gamblers, for example, and modern combinatorics grew out of various games and puzzles. Despite this track record and a wealth of popular-level books, there remain few conduits for research in recreational mathematics. The Mathematics of Various Entertaining Subjects now returns with an all-new third volume, presenting new research in diverse areas of recreational mathematics.

This volume focuses on four areas: puzzles and brainteasers, games, algebra and number theory, and geometry and topology. Readers will create Spiral Galaxies, Japanese symmetric grid puzzles consisting of squares and circles whose solutions are letters and numbers; delve into a paradox in the game of Bingo; examine the card tricks of mathematician-philosopher Charles Sanders Peirce; learn about the mathematics behind Legos; and much more.

Elucidating the many connections between mathematics and games, The Mathematics of Various Entertaining Subjects is sure to challenge and inspire mathematicians and math enthusiasts.

Author / Editor information

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, Volumes 1 and 2 (Princeton).

Reviews

"This is a fantastic (and entertaining) book on various aspects of recreational mathematics which are also at the forefront of research level mathematics."---Manjil Pratim Saikia, Zentralblatt MATH

Topics

Publicly Available

Frontmatter
i

Download PDF
Publicly Available

Contents
v

Download PDF
Publicly Available

Foreword
vii
Manjul Bhargava

Download PDF
Publicly Available

Preface and Acknowledgments
xv

Download PDF
PART I. Puzzles and Brainteasers
Requires Authentication Unlicensed

Licensed

1. Probability in Your Head
3
Peter Winkler

Download PDF
Requires Authentication Unlicensed

Licensed

2. Solving Puzzles Backward
11
Anany Levitin and Jason Rosenhouse

Download PDF
Requires Authentication Unlicensed

Licensed

3. Spiral Galaxies Font
24
Walker Anderson, Erik D. Demaine and Martin L. Demaine

Download PDF
Requires Authentication Unlicensed

Licensed

4. Kings, Sages, Hats, and Codes
31
Steven T. Dougherty and Yusra Naqvi

Download PDF
Requires Authentication Unlicensed

Licensed

5. How to Predict the Flip of a Coin
42
James D. Stein and Leonard M. Wapner

Download PDF
Requires Authentication Unlicensed

Licensed

6. Coins and Logic
55
Tanya Khovanova

Download PDF
PART II. Games
Requires Authentication Unlicensed

Licensed

7. Bingo Paradoxes
77
Barry A. Balof, Arthur T. Benjamin, Jay Cordes and Joseph Kisenwether

Download PDF
Requires Authentication Unlicensed

Licensed

8. Wiggly Games and Burnside’s Lemma
91
David Molnar

Download PDF
Requires Authentication Unlicensed

Licensed

9. Losing at Checkers Is Hard
103
Jeffrey Bosboom, Spencer Congero, Erik D. Demaine, Martin L. Demaine and Jayson Lynch

Download PDF
Requires Authentication Unlicensed

Licensed

10. Chutes and Ladders without Chutes or Ladders
119
Darren B. Glass, Stephen K. Lucas and Jonathan S. Needleman

Download PDF
Requires Authentication Unlicensed

Licensed

11. Bugs, Braids, and Batching
139
Michael P. Allocca, Steven T. Dougherty and Jennifer F. Vasquez

Download PDF
PART III. Algebra and Number Theory
Requires Authentication Unlicensed

Licensed

12. The Magic of Charles Sanders Peirce
161
Persi Diaconis and Ron Graham

Download PDF
Requires Authentication Unlicensed

Licensed

13. Can You Win Khalou in Five Moves?
204
Brian Hopkins

Download PDF
Requires Authentication Unlicensed

Licensed

14. On Partitions into Squares of Distinct Integers Whose Reciprocals Sum to 1
213
Max A. Alekseyev

Download PDF
Requires Authentication Unlicensed

Licensed

15. Puzzles, Parity Maps, and Plenty of Solutions
222
David Nacin

Download PDF
PART IV. Geometry and Topology
Requires Authentication Unlicensed

Licensed

16. Should We Call Them Flexa-Bands?
249
Yossi Elran and Ann Schwartz

Download PDF
Requires Authentication Unlicensed

Licensed

17. The Shortest Connection Problem on Triangular Grids
262
Jie Mei and Edmund A. Lamagna

Download PDF
Requires Authentication Unlicensed

Licensed

18. Entropy of Lego Jumper Plates
287
David M. McClendon and Jonathon Wilson

Download PDF
Requires Authentication Unlicensed

Licensed

About the Editors
313

Download PDF
Requires Authentication Unlicensed

Licensed

About the Contributors
315

Download PDF
Requires Authentication Unlicensed

Licensed

Index
323

Download PDF

Publishing information

Pages and Images/Illustrations in book

eBook published on:

September 23, 2019

eBook ISBN:

9780691194417

Pages and Images/Illustrations in book

https://doi.org/10.1515/9780691194417

eBook ISBN: 9780691194417

Keywords for this book

Probability; Mathematics; Flexagon; Popular mathematics; Recreational mathematics; Parity (mathematics); Mathematician; Variable (mathematics); Theorem; Pure mathematics; Set (mathematics); Mathematical optimization; Permutation; Sign (mathematics); Mathematical problem; Number theory; Mathematical induction; Dynamic programming; Result; Mathematical proof; Discrete mathematics; On Numbers and Games; Fair coin; Lucky number; Calculation; Combinatorial proof; Optimization problem; Algorithm; Analytic number theory; Mathematical analysis; Potential game; Geometry; Applied mathematics; Computational problem; Interval (mathematics); Complex number; Abstract algebra; Fermat's little theorem; Arithmetic; Open problem; Friendly number; Significant figures; Computational geometry; The College Mathematics Journal; Computation; Expected value; NP-hardness; Computational complexity theory; Mathematical Association; Binary tree; Instance (computer science); Arithmetic mean; Scientific notation; Inequality (mathematics); Translational symmetry; Latin square; Mathematical notation; Mathematical logic; Prime number; Mathematical structure; Summation; Magic square; Coprime integers; Mental calculation; Equiprobability; Train track (mathematics); Algebraic geometry; Elementary proof; NP-completeness; Geometry and topology

Audience(s) for this book

For a non-specialist adult audience

Princeton University Press

The Mathematics of Various Entertaining Subjects

Overview

About this book

Author / Editor information

Reviews

Topics

Table of contents

Frontmatter

Contents

Foreword

Preface and Acknowledgments

1. Probability in Your Head

2. Solving Puzzles Backward

3. Spiral Galaxies Font

4. Kings, Sages, Hats, and Codes

5. How to Predict the Flip of a Coin

6. Coins and Logic

7. Bingo Paradoxes

8. Wiggly Games and Burnside’s Lemma

9. Losing at Checkers Is Hard

10. Chutes and Ladders without Chutes or Ladders

11. Bugs, Braids, and Batching

12. The Magic of Charles Sanders Peirce

13. Can You Win Khalou in Five Moves?

14. On Partitions into Squares of Distinct Integers Whose Reciprocals Sum to 1

15. Puzzles, Parity Maps, and Plenty of Solutions

16. Should We Call Them Flexa-Bands?

17. The Shortest Connection Problem on Triangular Grids

18. Entropy of Lego Jumper Plates

About the Editors

About the Contributors

Index

Bibliographic data