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AuthorHinz, Andreas M., 1954-
Klavžar, Sandi
Milutinović, Uroš
Petr, Ciril
Title The Tower of Hanoi - Myths and Maths / Andreas M. Hinz ... [et al.] ; foreword by Ian Stewart
Other titlesThe tower of Hanoi
Hanojski stolpi - miti in matematika
Type/contenttype of material scientific monograph
Publication date2013
Publication and manufactureBasel [etc.] : Birkhäuser, cop. 2013
Other authorsStewart, Ian, 1945-
Physical descriptionXV, 335 str. : ilustr. ; 25 cm
NotesBibliografija: str. 297-317 (352 enot)
ISBNISBN 978-3-0348-0236-9
ISBN 978-3-0348-0237-6 (el. knjiga)
Subject termsMatematika - Kombinatorika - Teorija grafov - Matematične igre
Uncontrolled subject headingskitajski obroči / Frame-Stewartova domneva / Grayjeva koda / zgodovina iger / trikotnik Sierpińskega / grafi Sierpińskega / hanojski stolp / londonski stolp / algoritmi / kognitivni testi / končni avtomati / celoštevilska zaporedja / graf stanj / mathematics / combinatorics / Chinese rings / Frame-Stewart conjecture / Gray code / history of puzzles / Sierpiński triangle / Sierpiński graphs / Tower of Hanoi / Tower of London / algorithms / cognitive tests / finite automata / integer sequences / state graph
Other class numbers
97A20 (MSC 2010)
SummaryThis 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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.

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FMF and IMFM, Mathematical Library, Ljubljana Ljubljana MAKLJ 001availability outside loan: 3 Cop. FMF and IMFM, Mathematical Library, Ljubljana
University of Maribor Library Maribor UKM 002availability outside loan: 2 Cop. availability loan not possible: 1 Cop. University of Maribor Library
Miklošič Library FPNM, Maribor Maribor PEFMB 003availability outside loan: 2 Cop.
availability reading room: 1 Cop.
Miklošič Library FPNM, Maribor
Faculty of Mechanical Engineering, Ljubljana Ljubljana FSLJ 004availability outside loan: 1 Cop. Faculty of Mechanical Engineering, Ljubljana
UP University Library Koper - Capodistria UPUK 005availability outside loan: 1 Cop. UP University Library
National and University Library, Ljubljana Ljubljana NUK 006availability reading room: 1 Cop. National and University Library, Ljubljana
Grammar School Bežigrad, Ljubljana Ljubljana GBEZ 007availability reading room: 1 Cop. Grammar School Bežigrad, Ljubljana