Tower Of Hanoi Mathematical Rules

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Tower of Hanoi Mathematical Rules

Author : Jung oh Choi
Publisher : 최중오
Page : 133 pages
File Size : 43,9 Mb
Release : 2020-07-09
Category : Juvenile Fiction
ISBN : 8210379456XXX

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Tower of Hanoi Mathematical Rules by Jung oh Choi Pdf

Tower of Hanoi is a simple mathematical puzzle that finds the minimum number of moves to move all discs to another peg(column) under two conditions. But in Tower of Hanoi, which looks simple, you can find various mathematical rules. Also you can create some Transformed Tower of Hanoi by adding moving conditions of the disc or by increasing the number of pegs. I want to stress that finding rules and expressing them logically are different. Of course, you can only express the rules if you can find the rules of movement of the disc. Therefore, you should not stop by discovering the rules of the disc, but consider how to express the rules you have found. There are many other rules to be found in Tower of Hanoi besides the minimum number of movements. You can also know the minimum number of movements in which each disc has moved or you can explore the rules using binary. To do this, you must be able to understand and express ‘the rules of sequence’. If you can explore the rules of Tower of Hanoi, then you can also explore Transformed Tower of Hanoi. But you don’t have to rush. This is because you need to know the difficult sequence of rules, including recurrence formula, to explore Transformed Tower of Hanoi.

Transformed Tower of Hanoi - Mathematical Rules

Author : Jung Oh Choi
Publisher : 최중오
Page : 192 pages
File Size : 40,6 Mb
Release : 2020-07-09
Category : Juvenile Nonfiction
ISBN : 8210379456XXX

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Transformed Tower of Hanoi - Mathematical Rules by Jung Oh Choi Pdf

The transformed Tower of Hanoi is made by adding a condition to move a disc or by increasing the number of pegs. There are three ways to make Transformed Tower of Hanoi . ◇ Three ways ‣ Adding discs of the same size - In case that the number of discs with same size is all the same - In case that the number of discs with same size is different ‣ Adding moves condition of discs - Tower of Hanoi with Adjacency Requirement - Cyclic Tower of Hanoi ‣ Increase the number of pegs - Tower of Hanoi with 4 pegs or more - p-peg Tower of Hanoi

The Tower of Hanoi – Myths and Maths

Author : Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 45,8 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9783034802376

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The Tower of Hanoi – Myths and Maths by Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr Pdf

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.

The Tower of Hanoi – Myths and Maths

Author : Andreas M. Hinz,Sandi Klavžar,Ciril Petr
Publisher : Birkhäuser
Page : 452 pages
File Size : 41,7 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319737799

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The Tower of Hanoi – Myths and Maths by Andreas M. Hinz,Sandi Klavžar,Ciril Petr Pdf

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.

Math Geek

Author : Raphael Rosen
Publisher : Simon and Schuster
Page : 256 pages
File Size : 47,8 Mb
Release : 2015-06-18
Category : Mathematics
ISBN : 9781440583810

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Math Geek by Raphael Rosen Pdf

The new "sine" of mathematical geekdom! Do you dream about long division in your sleep? Does the thought of solving abstruse equations bring a smile to your face? Do you love celebrating pi every March? Then, Math Geek was made for you! With this guide, you'll learn even more about the power of numbers as you explore their brilliant nature in ways you've never imagined. From manhole covers to bubbles to subway maps, each page gives you a glimpse of the world through renowned mathematicians' eyes and reveals how their theorems and equations can be applied to nearly everything you encounter. Covering dozens of your favorite math topics, you'll find fascinating answers to questions like: How are the waiting times for buses determined? Why is Romanesco Broccoli so mesmerizing? How do you divide a cake evenly? Should you run or walk to avoid rain showers? Filled with compelling mathematical explanations, Math Geek sheds light on the incredible world of numbers hidden deep within your day-to-day life.

About Mathematics

Author : Gerald R. Rising,James R. Matthews,Eileen Schoaff,Judith Matthew
Publisher : Linus Learning
Page : 314 pages
File Size : 45,6 Mb
Release : 2021
Category : Mathematics
ISBN : 9781607978923

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About Mathematics by Gerald R. Rising,James R. Matthews,Eileen Schoaff,Judith Matthew Pdf

Mathematics is an essential component of the educated mind. It has two important roles to play: as queen of the sciences (providing the logical structure that holds science together) and as a handmaiden to those sciences (carrying out the computations that apply scientific concepts.) Unfortunately, a gulf exists between science and the humanities, and our text, About Mathematics, seeks to bridge that gap, to serve humanities students just as humanities texts are offered to inform science students. In doing so, unlike most math texts, we avoid the usual focus on detailed techniques to expose instead some of the important concepts and values of mathematics.

Handbook of Discrete and Combinatorial Mathematics

Author : Kenneth H. Rosen
Publisher : CRC Press
Page : 1612 pages
File Size : 44,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781584887812

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Handbook of Discrete and Combinatorial Mathematics by Kenneth H. Rosen Pdf

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Math from Three to Seven

Author : Aleksandr K. Zvonkin
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 55,6 Mb
Release : 2011
Category : Education
ISBN : 9780821868737

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Math from Three to Seven by Aleksandr K. Zvonkin Pdf

This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Another Fine Math You've Got Me Into. . .

Author : Ian Stewart
Publisher : Courier Corporation
Page : 288 pages
File Size : 49,9 Mb
Release : 2013-02-20
Category : Science
ISBN : 9780486150789

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Another Fine Math You've Got Me Into. . . by Ian Stewart Pdf

Sixteen columns from the French edition of Scientific American feature oddball characters and wacky wordplay in a mathematical wonderland of puzzles and games that also imparts significant mathematical ideas. 1992 edition.

Teaching and Learning Patterns in School Mathematics

Author : Ferdinand Rivera
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 45,5 Mb
Release : 2014-07-08
Category : Education
ISBN : 9789400727120

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Teaching and Learning Patterns in School Mathematics by Ferdinand Rivera Pdf

This book synthesizes research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. While research results drawn from investigations conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent due to other pertinent factors such as the complexity of patterning tasks. The book proposes an alternative view of pattern generalization, that is, one that is not about shifts or transition phases but graded depending on individual experiences with target patterns. The theory of graded representations involving pattern generalization offers a much more robust understanding of differences in patterning competence since it is sensitive to varying levels of entry into generalization. Empirical evidence will be provided to demonstrate this alternative view, which is drawn from the author’s longitudinal work with elementary and middle school children, including several investigations conducted with preservice elementary majors. Two chapters of the book will be devoted to extending pattern generalization activity to arithmetic and algebraic learning of concepts and processes. The concluding chapter addresses the pedagogical significance of pattern learning in the school mathematics curriculum. ​

50 Visions of Mathematics

Author : Sam Parc
Publisher : Oxford University Press
Page : 225 pages
File Size : 43,7 Mb
Release : 2014-05
Category : Mathematics
ISBN : 9780198701811

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50 Visions of Mathematics by Sam Parc Pdf

"To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain"--Provided by publisher.

Games and Mathematics

Author : David G. Wells
Publisher : Cambridge University Press
Page : 257 pages
File Size : 42,7 Mb
Release : 2012-10-18
Category : Games & Activities
ISBN : 9781107024601

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Games and Mathematics by David G. Wells Pdf

A unique book providing a tour through the fascinating connections between mathematics and games.

A History of Modern Psychology

Author : Per Saugstad
Publisher : Cambridge University Press
Page : 575 pages
File Size : 44,9 Mb
Release : 2018-11-08
Category : Psychology
ISBN : 9781107109896

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A History of Modern Psychology by Per Saugstad Pdf

This textbook presents an engaging and global history of psychological science, from the birth of the field to the present.

Primary Mathematics

Author : Penelope Serow,Rosemary Callingham,Tracey Muir
Publisher : Cambridge University Press
Page : 345 pages
File Size : 50,5 Mb
Release : 2014-01-20
Category : Education
ISBN : 9781107729940

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Primary Mathematics by Penelope Serow,Rosemary Callingham,Tracey Muir Pdf

Primary Mathematics provides a comprehensive introduction to teaching and learning mathematics in today's classrooms. Drawing links to the Australian Curriculum, this book covers the core learning areas of measurement, space and geometry, early number concepts, data and statistics, chance and probability, and patterns and algebra. At the centre of this book is the belief that ICT can be a powerful tool for enhancing student learning. Although many classrooms have been resourced with computers, interactive whiteboards and mobile technology, teachers need to be able to transform these technological tools into meaningful teaching and learning experiences. This book explores the ways in which technology can be integrated into the mathematics classroom. The book also explores issues around student diversity, assessment 'for', 'of' and 'as' learning, and teaching in rural and remote areas. Primary Mathematics is an indispensable resource for pre- and in-service teachers alike.

Handbook of Psychology, Experimental Psychology

Author : Irving B. Weiner,Donald K. Freedheim
Publisher : John Wiley & Sons
Page : 746 pages
File Size : 48,5 Mb
Release : 2003
Category : Medical
ISBN : 0471392626

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Handbook of Psychology, Experimental Psychology by Irving B. Weiner,Donald K. Freedheim Pdf

Healy provides an overview of basic areas of perception, learning, memory, motivation and emotion. Chapters cover other cognitive processes and special topics such as attention, decision-making, information processing, problem solving and psycholinguistics.