Fibonacci And Lucas Numbers With Applications Volume 2

Author : Thomas Koshy
Publisher : John Wiley & Sons
Page : 752 pages
File Size : 47,8 Mb
Release : 2019-01-07
Category : Mathematics
ISBN : 9781118742082

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Fibonacci and Lucas Numbers with Applications, Volume 2 by Thomas Koshy Pdf

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them. Examples of the beauty, power, and ubiquity of the extended gibonacci family. An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models. Abbreviated solutions provided for all odd-numbered exercises. Extensive references for further study. This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.

Author : Thomas Koshy
Publisher : John Wiley & Sons
Page : 676 pages
File Size : 44,9 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118031315

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Fibonacci and Lucas Numbers with Applications by Thomas Koshy Pdf

The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.

Author : Thomas Koshy
Publisher : John Wiley & Sons
Page : 755 pages
File Size : 49,5 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781118742143

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Fibonacci and Lucas Numbers with Applications, Volume 2 by Thomas Koshy Pdf

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them. Examples of the beauty, power, and ubiquity of the extended gibonacci family. An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models. Abbreviated solutions provided for all odd-numbered exercises. Extensive references for further study. This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.

Author : Andreas N. Philippou,Alwyn F. Horadam,G.E. Bergum
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401578011

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Applications of Fibonacci Numbers by Andreas N. Philippou,Alwyn F. Horadam,G.E. Bergum Pdf

This book contains nineteen papers from among the twenty-five papers presented at the Second International Conference on Fibonacci Numbers and Their Applications. These papers have been selected after a careful review by well known referee's in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers are their unifying bond. It is anticipated that this book will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 1987 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Andreas N. Philippou University of Patras Patras, Greece Alwyn F. Horadam University of New England Armidale, N.S.W., Australia xiii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERN A TIONAL COMMITTEE Bergum, G., Chairman Philippou, A. (Greece), Chairman Edgar, H., Co-chalrman Horadam, A. (Australia), Co-chalrman Bergum, G. (U.s.A.) Thoro, D. Kiss, P. (Hungary) Johnson, M. Long, C. (U.S.A.) Lange, L.

Author : G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120586

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Applications of Fibonacci Numbers by G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam Pdf

This book contains 58 papers from among the 68 papers presented at the Fifth International Conference on Fibonacci Numbers and Their Applications which was held at the University of St. Andrews, St. Andrews, Fife, Scotland from July 20 to July 24, 1992. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its four predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 5, 1993 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou Government House Z50 Nicosia, Cyprus xxv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Campbell, Colin M., Co-Chair Horadam, A.F. (Australia), Co-Chair Phillips, George M., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Foster, Dorothy M.E. Ando, S. (Japan) McCabe, John H. Bergum, G.E. (U.S.A.) Filipponi, P. (Italy) O'Connor, John J.

Author : Thomas Koshy
Publisher : OUP USA
Page : 439 pages
File Size : 50,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780195334548

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Catalan Numbers with Applications by Thomas Koshy Pdf

This book presents a clear and comprehensive introduction to one of the truly fascinating topics in mathematics: Catalan numbers. They crop up in chess, computer programming and even train tracks. In addition to lucid descriptions of the mathematics and history behind Catalan numbers, Koshy includes short biographies of the prominent mathematicians who have worked with the numbers.

Author : Thomas Koshy
Publisher : John Wiley & Sons
Page : 1090 pages
File Size : 54,9 Mb
Release : 2017-12-06
Category : Mathematics
ISBN : 9781118742174

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Fibonacci and Lucas Numbers with Applications, Volume 1 by Thomas Koshy Pdf

Praise for the First Edition “ ...beautiful and well worth the reading ... with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson

Author : Steven Vajda
Publisher : Courier Corporation
Page : 194 pages
File Size : 44,9 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486462769

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Fibonacci and Lucas Numbers, and the Golden Section by Steven Vajda Pdf

This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.

Author : Thomas Koshy
Publisher : John Wiley & Sons
Page : 704 pages
File Size : 54,5 Mb
Release : 2017-12-04
Category : Mathematics
ISBN : 9781118742129

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Fibonacci and Lucas Numbers with Applications, Volume 1 by Thomas Koshy Pdf

Praise for the First Edition “ …beautiful and well worth the reading … with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson

Author : S. Vajda
Publisher : Unknown
Page : 202 pages
File Size : 54,7 Mb
Release : 1989
Category : Fibonacci numbers
ISBN : CORNELL:31924051551723

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Fibonacci & Lucas Numbers, and the Golden Section by S. Vajda Pdf

Author : G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401150200

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Applications of Fibonacci Numbers by G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam Pdf

Proceedings of `The Seventh International Research Conference on Fibonacci Numbers and Their Applications', Technische Universität, Graz, Austria, July 15-19, 1996

Author : Fredric T. Howard
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401142717

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Applications of Fibonacci Numbers by Fredric T. Howard Pdf

This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its seven predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 1, 1999 The Editor F. T. Howard Mathematics and Computer Science Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC USA xvii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Anderson, Peter G. , Chairman Horadam, A. F. (Australia), Co-Chair Arpaya, Pasqual Philippou, A. N. (Cyprus), Co-Chair Biles, John Bergum, G. E. (U. S. A. ) Orr, Richard Filipponi, P. (Italy) Radziszowski, Stanislaw Harborth, H. (Germany) Rich, Nelson Horibe, Y. (Japan) Howard, F. (U. S. A. ) Johnson, M. (U. S. A. ) Kiss, P. (Hungary) Phillips, G. M. (Scotland) Turner, J. (New Zealand) Waddill, M. E. (U. S. A. ) xix LIST OF CONTRIBUTORS TO THE CONFERENCE AGRATINI, OCTAVIAN, "Unusual Equations in Study. " *ANDO, SHIRO, (coauthor Daihachiro Sato), "On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences. " *ANATASSOVA, VASSIA K. , (coauthor J. C.

Author : G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401135863

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Applications of Fibonacci Numbers by G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam Pdf

This book contains thirty-three papers from among the thirty-eight papers presented at the Fourth International Conference on Fibonacci Numbers and Their Applications which was held at Wake Forest University, Winston-Salem, North Carolina from July 30 to August 3, 1990. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its three predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. March 1, 1991 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Alwyn F. Horadam University of New England Armidale, N. S. W. , Australia Andreas N. Philippou Minister of Education Ministry of Education Nicosia, Cyprus xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Howard, Fred T. , Co-Chair Horadam, A. F. (Australia), Co-Chair Waddill, Marcellus E. , Co-Chair Philippou, A. N. (Cyprus), Co-Chair Hayashi, Elmer K. Ando, S. (Japan) Bergum, G. E. (U. S. A. ) Vaughan, Theresa Harrell, Deborah Bicknell-Johnson, M. B. (U. S. A. ) Campbell, Colin (Scotland) Filipponi, Piero (Italy) Kiss, P. (Hungary) Turner, J. C. (New Zealand) xvii LIST OF CONTRIBUTORS TO THE CONFERENCE *ALFORD, CECIL 0. , (coauthor Daniel C. Fielder) "Pascal's Triangle: Top Gun or Just One of the Gang?" *ANDERSON, PETER G. , "A Fibonacci-Based Pseudo-Random Number Generator.

Author : Prof. Dr. Erol Asiltürk
Publisher : EĞİTİM YAYINEVİ
Page : 76 pages
File Size : 53,6 Mb
Release : 2023-01-28
Category : Education
ISBN : 9786256382237

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İnternational Research in Math Sciences III by Prof. Dr. Erol Asiltürk Pdf

İnternational Research in Math Sciences III

Author : R. A. Dunlap
Publisher : World Scientific
Page : 174 pages
File Size : 52,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9812386300

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The Golden Ratio and Fibonacci Numbers by R. A. Dunlap Pdf

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences. Contents: Basic Properties of the Golden Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.