The Tower of Hanoi-- myths and maths Andreas M. Hinz [and others] ; foreword by Ian Stewart

Format:

Book

Contributor:

Hinz, Andreas M.

Language:

English

Subjects (All):

Mathematical recreations.

Mathematical recreations--History.

Genre:

History

Software

Physical Description:

1 online resource

Place of Publication:

Basel New York Birkhäuser ©2013

System Details:

text file PDF

Summary:

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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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 Sierpiński 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

Contents:

The Beginning of the World The Chinese Rings The Classical Tower of Hanoi Lucas's Second Problem Sierpinski Graphs The Tower of Hanoi with More Pegs Variations of the Puzzle The Tower of London Tower of Hanoi Variants with Oriented Disc Moves The End of the World

Notes:

Includes bibliographical references and indexes

Other Format:

Tower of Hanoi

ISBN:

9783034802376

3034802374

3034802366

9783034802369

OCLC:

827002131

Access Restriction:

Restricted for use by site license