Fibonacci Numbers
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The Golden Ratio And Fibonacci Numbers
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Author : R. A. Dunlap
language : en
Publisher: World Scientific
Release Date : 1997
The Golden Ratio And Fibonacci Numbers written by R. A. Dunlap and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
New Visual Perspectives On Fibonacci Numbers
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Author : Krassimir T. Atanassov
language : en
Publisher: World Scientific
Release Date : 2002
New Visual Perspectives On Fibonacci Numbers written by Krassimir T. Atanassov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Discusses new ground on Fibonacci sequences and the well-known Fibonacci numbers. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.
The Fabulous Fibonacci Numbers
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Author : Alfred S. Posamentier
language : en
Publisher:
Release Date : 2007
The Fabulous Fibonacci Numbers written by Alfred S. Posamentier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Explores the complexity and wide-ranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers.
Applications Of Fibonacci Numbers
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Author : Fredric T. Howard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Fibonacci Numbers written by Fredric T. Howard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
New Visual Perspectives On Fibonacci Numbers
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Author : Krassimir T Atanassov
language : en
Publisher: World Scientific
Release Date : 2002-10-01
New Visual Perspectives On Fibonacci Numbers written by Krassimir T Atanassov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-01 with Mathematics categories.
This book covers new ground on Fibonacci sequences and the well-known Fibonacci numbers. It will appeal to research mathematicians wishing to advance the new ideas themselves, and to recreational mathematicians, who will enjoy the various visual approaches and the problems inherent in them.There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.
Perfect Numbers And Fibonacci Sequences
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Author : Tianxin Cai
language : en
Publisher: World Scientific
Release Date : 2022-07-07
Perfect Numbers And Fibonacci Sequences written by Tianxin Cai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.
In this book, we first review the history and current situation of the perfect number problem, including the origin story of the Mersenne primes, and then consider the history and current situation of the Fibonacci sequence. Both topics include results from our own research. In the later sections, we define the square sum perfect numbers, and describe for the first time the secret relationships connecting the square sum perfect numbers, the Fibonacci sequence, the Lucas sequence, the twin prime conjecture, and the Fermat primes. Throughout, we raise various interesting questions and conjectures.
Fibonacci Numbers
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Author : Nikolai Nikolaevich Vorob'ev
language : en
Publisher: Courier Corporation
Release Date : 2011-01-01
Fibonacci Numbers written by Nikolai Nikolaevich Vorob'ev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its light and entertaining style will engage recreational readers as well as students and teachers.
Applications Of Fibonacci Numbers
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Author : Fredric T. Howard
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29
Applications Of Fibonacci Numbers written by Fredric T. Howard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-29 with Mathematics categories.
This book contains 28 research articles from among the 49 papers and abstracts presented at the Tenth International Conference on Fibonacci Numbers and Their Applications. These articles have been selected after a careful review by expert referees, and they range over many areas of mathematics. The Fibonacci numbers and recurrence relations are their unifying bond. We note that the article "Fibonacci, Vern and Dan" , which follows the Introduction to this volume, is not a research paper. It is a personal reminiscence by Marjorie Bicknell-Johnson, a longtime member of the Fibonacci Association. The editor believes it will be of interest to all readers. It is anticipated that this book, like the eight predecessors, will be useful to research workers and students at all levels who are interested in the Fibonacci numbers and their applications. March 16, 2003 The Editor Fredric T. Howard Mathematics Department Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Calvin Long, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv LIST OF CONTRlBUTORS TO THE CONFERENCE * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, ART, "Mathemagics.
Applications Of Fibonacci Numbers
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Author : G.E. Bergum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Fibonacci Numbers written by G.E. Bergum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of `The Seventh International Research Conference on Fibonacci Numbers and Their Applications', Technische Universität, Graz, Austria, July 15-19, 1996
Applications Of Fibonacci Numbers
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Author : Andreas N. Philippou
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Applications Of Fibonacci Numbers written by Andreas N. Philippou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.