The Tower of Hanoi - Myths and Maths
(Sprache: Englisch)
This book offers a comprehensive review of the mathematical theory of the solitaire game The Tower of Hanoi, from its invention in 1883 by the number theorist Édouard Lucas to current research in mathematics and applications in computer science and psychology.
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This book offers a comprehensive review of the mathematical theory of the solitaire game The Tower of Hanoi, from its invention in 1883 by the number theorist Édouard Lucas to current research in mathematics and applications in computer science and psychology.
Klappentext zu „The Tower of Hanoi - Myths and Maths “
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 Édouard 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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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 structuresand 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.
Inhaltsverzeichnis zu „The Tower of Hanoi - Myths and Maths “
- Foreword by Ian N. Stewart- Preface
0 The Beginning of the World
1 The Chinese Rings
2 The Classical Tower of Hanoi
3 Lucas's Second Problem
4 Sierpinski Graphs
5 The Tower of Hanoi with More Pegs
6 Variations of the Puzzle
7 The Tower of London
8 Tower of Hanoi Variants with Oriented Disc Moves
9 The End of the World
- Solutions to Exercises
- Glossary
- Bibliography
- Name Index
- Subject Index
Autoren-Porträt
Andreas M. Hinz is Professor at the Institute for Mathematics, University of Munich (LMU), Germany.Sandi Klavzar is Professor at the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia.
Uros Milutinovi? is Professor at the Department of Mathematics and Computer Science, University of Maribor, Slovenia.
Ciril Petr is a researcher at the Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia.
Bibliographische Angaben
- 2013, 335 Seiten, Maße: 23,5 cm, Gebunden, Englisch
- By Andreas M. Hinz, Sandi Klavzar, Uro Milutinovic et al.
- Verlag: Springer
- ISBN-10: 3034802366
- ISBN-13: 9783034802369
Sprache:
Englisch
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