LEADER 03835nam 2200565Ia 450 001 9910437866103321 005 20200520144314.0 010 $a3-0348-0237-4 024 7 $a10.1007/978-3-0348-0237-6 035 $a(CKB)2670000000342860 035 $a(EBL)1156184 035 $a(OCoLC)831115880 035 $a(SSID)ssj0000870789 035 $a(PQKBManifestationID)11957710 035 $a(PQKBTitleCode)TC0000870789 035 $a(PQKBWorkID)10820717 035 $a(PQKB)10366963 035 $a(DE-He213)978-3-0348-0237-6 035 $a(MiAaPQ)EBC1156184 035 $a(PPN)168306972 035 $a(EXLCZ)992670000000342860 100 $a20130208d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 04$aThe Tower of Hanoi-- myths and maths /$fAndreas M. Hinz ...[et al.] ; foreword by Ian Stewart 205 $a1st ed. 2013. 210 $aBasel ;$aNew York $cBirkhuser$dc2013 215 $a1 online resource (339 p.) 300 $aDescription based upon print version of record. 311 $a3-0348-0769-4 311 $a3-0348-0236-6 320 $aIncludes bibliographical references and indexes. 327 $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. 330 $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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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 Sierpi?ski 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. 606 $aMathematical recreations 606 $aMathematical recreations$xHistory 615 0$aMathematical recreations. 615 0$aMathematical recreations$xHistory. 676 $a793.74 701 $aHinz$b Andreas M$0767927 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437866103321 996 $aThe Tower of Hanoi ? Myths and Maths$92047139 997 $aUNINA