Tower Of Hanoi Mathematical Rules

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Tower of Hanoi Mathematical Rules

Author : Jung oh Choi
Publisher : 최중오
ISBN 13 :
Total Pages : 133 pages
Book Rating : 4./5 ( download)

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Book Synopsis Tower of Hanoi Mathematical Rules by : Jung oh Choi

Download or read book Tower of Hanoi Mathematical Rules written by Jung oh Choi and published by 최중오. This book was released on 2020-07-09 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4./5 ( download)

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Book Synopsis Transformed Tower of Hanoi - Mathematical Rules by : Jung Oh Choi

Download or read book Transformed Tower of Hanoi - Mathematical Rules written by Jung Oh Choi and published by 최중오. This book was released on 2020-07-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 3034802374
Total Pages : 340 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Tower of Hanoi – Myths and Maths by : Andreas M. Hinz

Download or read book The Tower of Hanoi – Myths and Maths written by Andreas M. Hinz and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

SOFSEM 2007: Theory and Practice of Computer Science

Author : Jan van Leeuwen
Publisher : Springer
ISBN 13 : 3540695079
Total Pages : 956 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis SOFSEM 2007: Theory and Practice of Computer Science by : Jan van Leeuwen

Download or read book SOFSEM 2007: Theory and Practice of Computer Science written by Jan van Leeuwen and published by Springer. This book was released on 2007-07-13 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007, held in Harrachov, Czech Republic in January 2007. The 69 revised full papers, presented together with 11 invited contributions were carefully reviewed and selected from 283 submissions. The papers were organized in four topical tracks.

Hexaflexagons and Other Mathematical Diversions

Author : Martin Gardner
Publisher : American Mathematical Soc.
ISBN 13 : 1470463520
Total Pages : 200 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hexaflexagons and Other Mathematical Diversions by : Martin Gardner

Download or read book Hexaflexagons and Other Mathematical Diversions written by Martin Gardner and published by American Mathematical Soc.. This book was released on 2020-10-05 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.

The Canterbury Puzzles

Author : H. E. Dudeney
Publisher : Courier Corporation
ISBN 13 : 0486425584
Total Pages : 260 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Canterbury Puzzles by : H. E. Dudeney

Download or read book The Canterbury Puzzles written by H. E. Dudeney and published by Courier Corporation. This book was released on 2002-10-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes 110 puzzles, not as individual problems but as incidents in connected stories. The first 31 are amusingly posed by pilgrims in Chaucer's Canterbury Tales. Additional puzzles are presented using different characters. Many require only the ability to exercise logical or visual skills; others offer a stimulating challenge to the mathematically advanced.

S.M.A.R.T. Circle Projects

Author : Andy Liu
Publisher : Springer
ISBN 13 : 3319568116
Total Pages : 228 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis S.M.A.R.T. Circle Projects by : Andy Liu

Download or read book S.M.A.R.T. Circle Projects written by Andy Liu and published by Springer. This book was released on 2017-09-07 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes projects in a Mathematical “Circle,” i.e., an organization that discovers and nurtures young mathematical talents through meaningful extra-curricular activities. This is the second volume in a trilogy describing in particular the S.M.A.R.T. Circle project, which was founded in Edmonton, Canada in 1981. The acronym S.M.A.R.T. stands for Saturday Mathematical Activities, Recreations & Tutorials. This book, Volume II, is based on the papers published in scientific and education journals by the Circle members while they were still in junior high school (some still in elementary school). In essence, it explains the purpose of the Circle. Volume I describes how to run a Circle, and Volume III explains what actually takes place in the Circle. All three volumes provide a wealth of resources (mathematical problems, quizzes and games, together with their solutions). The books will be of interest to self-motivated students who want to conduct independent research, teachers who work with these students, and teachers who are currently running or planning to run Mathematical Circles of their own.

The Tower of Hanoi – Myths and Maths

Author : Andreas M. Hinz
Publisher : Birkhäuser
ISBN 13 : 3319737791
Total Pages : 469 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Tower of Hanoi – Myths and Maths by : Andreas M. Hinz

Download or read book The Tower of Hanoi – Myths and Maths written by Andreas M. Hinz and published by Birkhäuser. This book was released on 2018-04-17 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Games and Mathematics

Author : David G. Wells
Publisher : Cambridge University Press
ISBN 13 : 1107024609
Total Pages : 257 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Games and Mathematics by : David G. Wells

Download or read book Games and Mathematics written by David G. Wells and published by Cambridge University Press. This book was released on 2012-10-18 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique book providing a tour through the fascinating connections between mathematics and games.

Primary Mathematics

Author : Penelope Serow
Publisher : Cambridge University Press
ISBN 13 : 1107729947
Total Pages : 345 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Primary Mathematics by : Penelope Serow

Download or read book Primary Mathematics written by Penelope Serow and published by Cambridge University Press. This book was released on 2014-01-20 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Research Issues in the Learning and Teaching of Algebra

Author : Sigrid Wagner
Publisher : Routledge
ISBN 13 : 113543414X
Total Pages : 300 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Research Issues in the Learning and Teaching of Algebra by : Sigrid Wagner

Download or read book Research Issues in the Learning and Teaching of Algebra written by Sigrid Wagner and published by Routledge. This book was released on 2018-12-07 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1989. We clearly know more today about teaching and learning mathematics than we did twenty years ago, and we are beginning to see the effects of this new knowledge at the classroom level. In particular, we can point to several significant sets of studies based on emerging theoretical frameworks. To establish such a framework, researchers must be provided with the opportunity to exchange and refine their ideas and viewpoints. Conferences held in Georgia and Wisconsin during the seventies serve as examples of the role such meetings can play in providing a vehicle for increased communication, synthesis, summary, and cross-disciplinary fertilization among researchers working within a specialized area of mathematical learning. This monograph holds selected papers from four more recent conferences on Research Agenda in Mathematics Education.

Logical Methods

Author : Roger Antonsen
Publisher : Springer
ISBN 13 : 9783030637767
Total Pages : 288 pages
Book Rating : 4.6/5 (377 download)

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Book Synopsis Logical Methods by : Roger Antonsen

Download or read book Logical Methods written by Roger Antonsen and published by Springer. This book was released on 2021-02-11 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.

Rules of the Mind

Author : John R. Anderson
Publisher : Psychology Press
ISBN 13 : 131778202X
Total Pages : 334 pages
Book Rating : 4.3/5 (177 download)

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Book Synopsis Rules of the Mind by : John R. Anderson

Download or read book Rules of the Mind written by John R. Anderson and published by Psychology Press. This book was released on 2014-01-14 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Related to the earlier well-known ACT production system theory, this book's basic goal is to present evidence for the psychological reality of a production system model of mind. Distinguished from the original theory in three ways, this volume uses the rational analyses of Anderson (1990) to improve upon that theory and extend its scope. It also relates the theory to a great deal of new data on the performance and acquisition of cognitive skills. The new theory -- ACT-R -- involves a neurally plausible implementation of a production system architecture. Rational analysis is used to structure and parameterize the system to yield optimal information processing. The theory is applicable to a wide variety of research disciplines, including memory, problem solving, and skill acquisition. Using intelligent tutors, much of the data is concerned with the acquisition of cognitive skills. The book provides analyses of data sets describing the extended course of the acquisition of mathematical and computer programming skills.

A History of Modern Psychology

Author : Per Saugstad
Publisher : Cambridge University Press
ISBN 13 : 1108617808
Total Pages : 576 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis A History of Modern Psychology by : Per Saugstad

Download or read book A History of Modern Psychology written by Per Saugstad and published by Cambridge University Press. This book was released on 2018-03-31 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: A History of Modern Psychology provides students with an engaging, comprehensive, and global history of psychological science, from the birth of the field to the present. It examines the attempts to establish psychology as a science in several countries and epochs. The text expertly draws on a vast knowledge of the field in the United States, England, Germany, France, Russia, and Scandinavia, as well as on author Per Saugstad's keen study of neighboring sciences, including physiology, evolutionary biology, psychiatry, and neurology. Offering a unique global perspective on the development of psychology as an empirical science, this text is an ideal introduction to the field for students and other readers interested in the history of modern psychology.

The Math Book

Author : Clifford A. Pickover
Publisher : Union Square + ORM
ISBN 13 : 1402797494
Total Pages : 937 pages
Book Rating : 4.4/5 (27 download)

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Book Synopsis The Math Book by : Clifford A. Pickover

Download or read book The Math Book written by Clifford A. Pickover and published by Union Square + ORM. This book was released on 2011-09-27 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Neumann Prize–winning, illustrated exploration of mathematics—from its timeless mysteries to its history of mind-boggling discoveries. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, The Math Book covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic is lavishly illustrated with colorful art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

Resources for Preparing Middle School Mathematics Teachers

Author : Cheryl Beaver
Publisher : MAA
ISBN 13 : 0883851903
Total Pages : 220 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Resources for Preparing Middle School Mathematics Teachers by : Cheryl Beaver

Download or read book Resources for Preparing Middle School Mathematics Teachers written by Cheryl Beaver and published by MAA. This book was released on 2013 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Cheryl Beaver, Laurie Burton, Maria Fung, Klay Kruczek, editors"--Cover.

Relational Psychoanalysis, Volume 2

Author : Lewis Aron
Publisher : Routledge
ISBN 13 : 113589115X
Total Pages : 479 pages
Book Rating : 4.1/5 (358 download)

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Book Synopsis Relational Psychoanalysis, Volume 2 by : Lewis Aron

Download or read book Relational Psychoanalysis, Volume 2 written by Lewis Aron and published by Routledge. This book was released on 2013-04-15 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "relational turn" has transformed the field of psychoanalysis, with an impact that cuts across different schools of thought and clinical modalities. In the six years following publication of Volume 1, Relational Psychoanalysis: The Emergence of a Tradition, relational theorizing has continued to develop, expand, and challenge the parameters of clinical discourse. It has been a period of loss, with the passing of Stephen A. Mitchell and Emmanuel Ghent, but also a period of great promise, marked by the burgeoning publication of relational books and journals and the launching of relational training institutes and professional associations. Volume 2, Relational Psychoanalysis: Innovation and Expansion, brings together key papers of the recent past that exemplify the continuing growth and refinement of the relational sensibility. In selecting these papers, Editors Lewis Aron and Adrienne Harris have stressed the shared relational dimension of different psychoanalytic traditions, and they have used such commonalities to structure the best recent contributions to the literature. The topics covered in Volume 2 reflect both the evolution of psychoanalysis and the unique pathways that leading relational writers have been pursuing and in some cases establishing.