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The solitaire game "The Tower of Hanoi" was invented in the 19th
century by the French number theorist Edouard Lucas. The book
presents its mathematical theory and offers a survey of the
historical development from predecessors up to recent research. In
addition to long-standing myths, it provides a detailed overview of
the essential mathematical facts with complete proofs, and also
includes unpublished material, e.g., on some captivating integer
sequences. The main objects of research today are the so-called
Hanoi graphs and the related Sierpinski graphs. Acknowledging the
great popularity of the topic in computer science, algorithms,
together with their correctness proofs, form an essential part of
the book. In view of the most important practical applications,
namely in physics, network theory and cognitive (neuro)psychology,
the book also addresses other structures related to the Tower of
Hanoi and its variants. The updated second edition includes, for
the first time in English, the breakthrough reached with the
solution of the "The Reve's Puzzle" in 2014. This is a special case
of the famed Frame-Stewart conjecture which is still open after
more than 75 years. Enriched with elaborate illustrations,
connections to other puzzles and challenges for the reader in the
form of (solved) exercises as well as problems for further
exploration, this book is enjoyable reading for students,
educators, game enthusiasts and researchers alike. Excerpts from
reviews of the first edition: "The book is an unusual, but very
welcome, form of mathematical writing: recreational mathematics
taken seriously and serious mathematics treated historically. I
don't hesitate to recommend this book to students, professional
research mathematicians, teachers, and to readers of popular
mathematics who enjoy more technical expository detail." Chris
Sangwin, The Mathematical Intelligencer 37(4) (2015) 87f. "The book
demonstrates that the Tower of Hanoi has a very rich mathematical
structure, and as soon as we tweak the parameters we surprisingly
quickly find ourselves in the realm of open problems." Laszlo
Kozma, ACM SIGACT News 45(3) (2014) 34ff. "Each time I open the
book I discover a renewed interest in the Tower of Hanoi. I am sure
that this will be the case for all readers." Jean-Paul Allouche,
Newsletter of the European Mathematical Society 93 (2014) 56.
This is the first comprehensive monograph on the mathematical
theory of the solitaire game "The Tower of Hanoi" which was
invented in the 19th century by the French number theorist Edouard
Lucas. The book comprises a survey of the historical development
from the game's predecessors up to recent research in mathematics
and applications in computer science and psychology. Apart from
long-standing myths it contains a thorough, largely self-contained
presentation of the essential mathematical facts with complete
proofs, including also unpublished material. The main objects of
research today are the so-called Hanoi graphs and the related
Sierpinski graphs. Acknowledging the great popularity of the topic
in computer science, algorithms and their correctness proofs form
an essential part of the book. In view of the most important
practical applications of the Tower of Hanoi and its variants,
namely in physics, network theory, and cognitive (neuro)psychology,
other related structures and puzzles like, e.g., the "Tower of
London", are addressed. Numerous captivating integer sequences
arise along the way, but also many open questions impose
themselves. Central among these is the famed Frame-Stewart
conjecture. Despite many attempts to decide it and large-scale
numerical experiments supporting its truth, it remains unsettled
after more than 70 years and thus demonstrates the timeliness of
the topic. Enriched with elaborate illustrations, connections to
other puzzles and challenges for the reader in the form of (solved)
exercises as well as problems for further exploration, this book is
enjoyable reading for students, educators, game enthusiasts and
researchers alike.
This is the first comprehensive monograph on the mathematical
theory of the solitaire game "The Tower of Hanoi" which was
invented in the 19th century by the French number theorist Edouard
Lucas. The book comprises a survey of the historical development
from the game's predecessors up to recent research in mathematics
and applications in computer science and psychology. Apart from
long-standing myths it contains a thorough, largely self-contained
presentation of the essential mathematical facts with complete
proofs, including also unpublished material. The main objects of
research today are the so-called Hanoi graphs and the related
Sierpinski graphs. Acknowledging the great popularity of the topic
in computer science, algorithms and their correctness proofs form
an essential part of the book. In view of the most important
practical applications of the Tower of Hanoi and its variants,
namely in physics, network theory, and cognitive (neuro)psychology,
other related structures and puzzles like, e.g., the "Tower of
London", are addressed. Numerous captivating integer sequences
arise along the way, but also many open questions impose
themselves. Central among these is the famed Frame-Stewart
conjecture. Despite many attempts to decide it and large-scale
numerical experiments supporting its truth, it remains unsettled
after more than 70 years and thus demonstrates the timeliness of
the topic. Enriched with elaborate illustrations, connections to
other puzzles and challenges for the reader in the form of (solved)
exercises as well as problems for further exploration, this book is
enjoyable reading for students, educators, game enthusiasts and
researchers alike.
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