The Tower of Hanoi – Myths and Maths PDF Download
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Author: Andreas M. Hinz
Publisher: Springer Science & Business Media
ISBN: 3034802374
Category : Mathematics
Languages : en
Pages : 340
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Book Description
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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.
Author: Andreas M. Hinz
Publisher: Springer Science & Business Media
ISBN: 3034802374
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
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.
Author:
Publisher: Odile Jacob
ISBN: 2738174914
Category :
Languages : en
Pages : 169
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Book Description
Author: Mark Kac
Publisher: Courier Corporation
ISBN: 0486670856
Category : Philosophy
Languages : en
Pages : 189
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Book Description
Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
Author: James M. Van Verth
Publisher: CRC Press
ISBN: 0123742978
Category : Art
Languages : en
Pages : 706
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Book Description
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.
Author: Urban Larsson
Publisher: Cambridge University Press
ISBN: 1108485804
Category : Computers
Languages : en
Pages : 499
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Book Description
Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.
Author: Kids Chill Editions
Publisher:
ISBN:
Category :
Languages : fr
Pages : 78
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Book Description
CHILDREN'S BOOKS - LEARNING - CRAFTS & GAMES - GIFT IDEAS This 4-in-1 bilingual workbook is packed with kid friendly learning activities and games for kids aged from 5 years old onwards. This workbook includes: A colouring workbook (animals, house equipments, food...), French-English Vocabulary Flashcards, Writing workbook, Maths workbook and miscellaneous games. Smart workbook for Smart kids. Help your child develop the required skills while having fun !LIVRES POUR ENFANTS - ÉDUCATION - JEUX - IDÉES CADEAUX Ce cahier d'activités bilingue 4-en-1 est destiné aux enfants à partir de 5 ans, qui veulent allier jeux et apprentissage. Ce cahier contient: une section coloriage (animaux, équipements maison, nourriture...) une section vocabulaire français-anglais, une section écriture, une section maths et jeux divers. Offrez à votre enfant un moment simultané de plaisirs et d'apprentissage pour une meilleure stimulation intellectuelle et une satisfaction personnelle.
Author: Matt Parker
Publisher: Farrar, Straus and Giroux
ISBN: 0374710376
Category : Games & Activities
Languages : en
Pages : 465
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Book Description
A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1686
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Book Description
Author: Alexander Bogomolny
Publisher: Wolfram Media
ISBN: 9781579550417
Category :
Languages : en
Pages : 310
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Book Description
He who untied the Gordian knot would rule all of Asia So goes the legend of the tricky knot of Gordius, king of Phrygia.Many had tried; many had failed, but Alexander the Great simplycut the knot with his sword. He went on to conquer most of Asia, eventually reaching as far east as Northern India. Cut the Knot is a book of probability riddles curated to challenge the mind andexpand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around theworld. Follow along as Alexander Bogomolny presents these selected riddles bytopical progression. Try them for yourself before reading their solutions. Just like itwas for Alexander the Great, the non-trivial, unexpected solution might be exactlythe one you need.
Author: Zbigniew Romanowicz
Publisher: Tom eMusic
ISBN: 1623210283
Category : Games & Activities
Languages : en
Pages : 92
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Book Description
100 Math Brainteasers (Grade 7-10) is a subtle selection of one hundred arithmetic, algebra, and geometry assignments, which efficiently train the mind in math skills. It will be helpful for students attending High School and also in preparation for Mathematical competitions or Olympiads at a younger age. The assignments can equally be used in the classroom or in extracurricular activities. The fun and games are delightful, original, and solving them is even more enjoyable thanks to the funny illustrations. Most of the math problems do not require any exceptional mathematical proficiency, but above all, they challenge one’s creativity and ability to think logically. Only a few solicit the knowledge of algebraic expressions and rules of geometry.
