The Tower of Hanoi Myths and Maths

The Tower of Hanoi     Myths and Maths

This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years.

Author: Andreas M. Hinz

Publisher: Birkhäuser

ISBN: 9783319737799

Category: Mathematics

Page: 452

View: 741

The solitaire game “The Tower of Hanoi" was invented in the 19th century by the French number theorist Édouard Lucas. The book presents its mathematical theory and offers a survey of the historical development from predecessors up to recent research. In addition to long-standing myths, it provides a detailed overview of the essential mathematical facts with complete proofs, and also includes unpublished material, e.g., on some captivating integer sequences. 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, together with their correctness proofs, form an essential part of the book. In view of the most important practical applications, namely in physics, network theory and cognitive (neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and its variants. The updated second edition includes, for the first time in English, the breakthrough reached with the solution of the “The Reve's Puzzle" in 2014. This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years. 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. Excerpts from reviews of the first edition: “The book is an unusual, but very welcome, form of mathematical writing: recreational mathematics taken seriously and serious mathematics treated historically. I don’t hesitate to recommend this book to students, professional research mathematicians, teachers, and to readers of popular mathematics who enjoy more technical expository detail.” Chris Sangwin, The Mathematical Intelligencer 37(4) (2015) 87f. “The book demonstrates that the Tower of Hanoi has a very rich mathematical structure, and as soon as we tweak the parameters we surprisingly quickly find ourselves in the realm of open problems.” László Kozma, ACM SIGACT News 45(3) (2014) 34ff. “Each time I open the book I discover a renewed interest in the Tower of Hanoi. I am sure that this will be the case for all readers.” Jean-Paul Allouche, Newsletter of the European Mathematical Society 93 (2014) 56.
Categories: Mathematics

The Tower of Hanoi Myths and Maths

The Tower of Hanoi     Myths and Maths

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.

Author: Andreas M. Hinz

Publisher: Birkhäuser

ISBN: 3034807694

Category: Mathematics

Page: 335

View: 883

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.
Categories: Mathematics

The Tower of Hanoi Myths and Maths

The Tower of Hanoi     Myths and Maths

Stockmeyer, P. K., Bateman, C. D., Clark, J. W., Eyster, C. R., Harrison, M. T.,
Loehr, N. A., Rodriguez, P. J., Simmons, J. R. III, Exchanging disks in the Tower of
Hanoi, International Journal of Computer Mathematics 59 (1995) 37–47.

Author: Andreas M. Hinz

Publisher: Springer Science & Business Media

ISBN: 9783034802376

Category: Mathematics

Page: 335

View: 545

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.
Categories: Mathematics

Alvaro Siza

Alvaro Siza

Studio Paperback monographs on the outstanding architects of the 20th century-concise and informative overviews of their complete works written and edited by noted authors. Each volume contains biographical details and a work chronology.

Author: Peter Testa

Publisher: Birkhauser

ISBN: 3764355980

Category: Technology & Engineering

Page: 192

View: 492

Studio Paperback monographs on the outstanding architects of the 20th century-concise and informative overviews of their complete works written and edited by noted authors. Each volume contains biographical details and a work chronology.
Categories: Technology & Engineering

Math Around the World

Math Around the World

MATHS Around the World THE TOWER OF HANOI • Region Of Origin : France
Where Tower of Hanoi Is Played Today ... When the priests finished their work ,
the myth said , the temple would crumble into dust and the world would vanish .

Author: Beverly Braxton

Publisher: Gems

ISBN: PSU:000058012079

Category: Education

Page: 190

View: 528

A collection of eight games from four continents that use mathematics as students participate. The activities also provide opportunities for students to explore the geography and history connected to the games and broaden their awareness of other cultures.
Categories: Education

Discrete Mathematics

Discrete Mathematics

(7.1.9) Example 7.1.9 The Tower of Hanoi puzzle was invented by the French
mathematician ́Edouard Lucas in the late nineteenth ... The following myth was
also created to ac- company the puzzle (and, one assumes, to help market it).

Author: Richard Johnsonbaugh

Publisher: Prentice Hall

ISBN: 9780131593183

Category: Mathematics

Page: 766

View: 689

Focused on helping readers understand and construct proofs – and, generally, expanding their mathematical maturity – this best-seller is an accessible introduction to discrete mathematics. Takes an algorithmic approach that emphasizes problem-solving techniques. Expands discussion on how to construct proofs and treatment of problem solving. Increases number of examples and exercises throughout.
Categories: Mathematics

The Rainbow of Mathematics

The Rainbow of Mathematics

Math Around the World is filled with games and other compelling challenges that
bring the international , multicultural ... might gain an intuitive understanding of
exponential growth from The Tower of Hanoi , while older students might extend
this ... When students make myths about scientific phenomena , they look for
patterns to explain such events as the phases of the moon or the life cycle of a
butterfly .

Author: Jaine Kopp

Publisher: Gems

ISBN: PSU:000058011461

Category: Education

Page: 56

View: 540

Presents the main ideas and current approaches in inquiry-based, content-rich mathematics education.
Categories: Education

Resources in Education RIE 1985

Resources in Education  RIE   1985

7.1-7.14 Trade Math . ED 254 701 Stationary Engineers ... ED 251 388 Tower of
Hanoi ( Puzzle ) Problem Solving and Beginning Programming . ED 259 032 Toy
Lending ... ED 258 267 The Great Grammar Myth . Occasional Paper No. 5 .

Author:

Publisher: Greenwood

ISBN: 089774215X

Category:

Page:

View: 299

Categories:

Understanding Programming and Problem Solving with C

Understanding Programming and Problem Solving with C

However , as Guy Steele has shown ( in " Debunking the ' expensive procedure
call myth , " Proceedings of the ... Unfortunately , some functions , like the one
used to solve the Towers of Hanoi problem , are difficult or impossible to convert
to tail - recursive versions , and ... else return fact_iter ( n - 1 , n * result ) ; ܝܟ
EXERCISES 12.1 { } 1 ) ; math Function Declaration Purpose double acos (
double x ).

Author: Kenneth A. Lambert

Publisher: West Group

ISBN: PSU:000026235707

Category: C++ (Computer program language)

Page: 538

View: 805

This text features a gradual approach to object-oriented programming that covers problem solving and algorithm development but also offers solid grounding in objects and classes. Problem solving is emphasized throughout the text through numerous exercises, programming problems, and projects.
Categories: C++ (Computer program language)

Psychology 89 90

Psychology 89 90

... 181-185 Tower of Hanoi puzzle , 99 trance , hypnotic , 57 , 59 triarchic theory of
intelligence , Sternberg's , 87 trust vs. mistrust , Erikson's theory of , 164 , 165 two
- brain myth , 20-24 Type - A behavior , 119 rivalry of affections , Freud's theory of
, 217 Rogers , Carl , 108 , 177 ... and criminal behavior , 172-176 ; in math ability ,
89-90 ; and sense of smell , 45-46 ; and touching , 182 , 183 sexual abuse , of ...

Author:

Publisher:

ISBN: 0879677740

Category: Psychology

Page: 244

View: 242

Categories: Psychology

Books in Print

Books in Print

Author:

Publisher:

ISBN: STANFORD:36105210120304

Category: American literature

Page:

View: 904

Categories: American literature

Book Review Index

Book Review Index

Author:

Publisher:

ISBN: UOM:39015066121404

Category: Books

Page:

View: 720

Every 3rd issue is a quarterly cumulation.
Categories: Books

Encyclopedia Americana

Encyclopedia Americana

15 : 258 Victoria Tower ( London , Eng . ) 17 : 713 Victoria University College (
Wellington , N.Z. ) 28 : 614 Victoria University of Manchester ( Manchester , Eng .
) 18 ... 24 : 723 VICTORY ( novel , Conrad ) 28:95 Victory , Goddess of ( myth . ) ...

Author:

Publisher:

ISBN: PSU:000059160809

Category: Encyclopedias and dictionaries

Page:

View: 250

Categories: Encyclopedias and dictionaries