Academic journal article The Mathematics Enthusiast

Book Review of the Tower of Hanoi - Myths and Maths (Birkhäuser)*

Academic journal article The Mathematics Enthusiast

Book Review of the Tower of Hanoi - Myths and Maths (Birkhäuser)*

Article excerpt

Book review of The Tower of Hanoi - Myths and Maths (Birkhäuser)* ISBN 978-3-0348-0236-9, $44.95

As the title of the book suggests, the central topic of "The Tower of Hanoi - Myths and Maths" by Hinz, Klavzar, Milutinovic, and Petr is the famous puzzle of the same name. The classic Tower of Hanoi puzzle along with a number of its variations and related puzzles are examined in a rigorous mathematical framework.

Chapter 0 of the book gives a detailed historical account of the Tower of Hanoi puzzle and its variants as well as an introduction to some of the mathematical results concerning them. The later chapters of the book tend to be dedicated to a particular puzzle or variant and a number of theorems and proofs concerning it.

Despite its somewhat playful title, this book is not for a casual reader. It really should be thought of as a mathematical textbook. It is probably best suited for a graduate student or someone with a strong background in mathematics; particularly combinatorics. Throughout the book, the authors assume the reader has some familiarity with, for example, recurrence relations, graph theory, and group theory. In examining the Tower puzzle and its variants, the authors present many theorems and proofs. Despite the simplicity of these puzzles, many of the results in the book are difficult.

I think the book would be ideal for a topics course for graduate students and advanced undergraduates. The book includes a nice selection of exercises of varying levels of difficulty (hints and complete solutions for most problems appear at the end). In addition, the text contains a number of interesting conjectures and open problems (Chapter 9 has a nice list). This book would also serve as a good base for thesis or dissertation topics for different levels of students of mathematics.

One particularly unique and appealing part of the book is its dedication to telling the history of the Tower of Hanoi puzzle and related puzzles. Along the way they dispel several persistent myths in the history of mathematics. Most textbooks either have no historical perspective or include just a few footnotes. …

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