000 03972nam a22005295i 4500
001 978-3-0348-0237-6
003 DE-He213
005 20140220082836.0
007 cr nn 008mamaa
008 130130s2013 sz | s |||| 0|eng d
020 _a9783034802376
_9978-3-0348-0237-6
024 7 _a10.1007/978-3-0348-0237-6
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
082 0 4 _a510
_223
100 1 _aHinz, Andreas M.
_eauthor.
245 1 4 _aThe Tower of Hanoi – Myths and Maths
_h[electronic resource] /
_cby Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aXV, 335 p. 133 illus., 60 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aForeword by Ian 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 -- A Hints and Solutions to Exercises -- Glossary -- Bibliography -- Name Index -- Subject Index -- Symbol Index.
520 _aThis 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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.
650 0 _aMathematics.
650 0 _aComputer software.
650 0 _aSequences (Mathematics).
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aMathematics, general.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aSequences, Series, Summability.
650 2 4 _aCombinatorics.
650 2 4 _aGame Theory, Economics, Social and Behav. Sciences.
650 2 4 _aAlgorithm Analysis and Problem Complexity.
700 1 _aKlavžar, Sandi.
_eauthor.
700 1 _aMilutinović, Uroš.
_eauthor.
700 1 _aPetr, Ciril.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034802369
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0237-6
912 _aZDB-2-SMA
999 _c96282
_d96282