The tower of hanoi - myths and maths

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Langue : Anglais
Couverture de l'ouvrage The tower of hanoi - myths and maths

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This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi. It comprises a survey of the historical development from its invention in 1883 by the French number theorist i‰douard Lucas to recent research in mathematics and applications in computer science and psychology. For instance, the so-called Frame-Stewart conjecture is an open problem since almost 70 years and shows the timeliness of the topic. The bookcontains a thorough presentation of the essential mathematical results with complete proofs. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. The latter have been introduced by Sandi Klavžar und UroÅ¡ Milutinovic.Algorithms (with proofs of correctness) will be an essential part of the book, because of the great popularity of the topic in computer science. In view of the most important practical application of The Tower of Hanoi and related puzzles, namely in cognitive (neuro-)psychology, we will also address variants employed in test tools and analyze their mathematical structure.
Foreword by Ian N. Stewart.- Preface.- 0 The Beginning of the World.- 1 The Chinese Rings.- 2 The Classical Tower of Hanoi.- 3 Lucass 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.