New Visual Perspectives On Fibonacci Numbers

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.

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. Contents:Number Theoretic Perspectives — Coupled Recurrence Relations:Introductory Remarks by the First AuthorThe 2–Fibonacci SequencesExtensions of the Concepts of 2–Fibonacci SequencesOther Ideas for Modification of the Fibonacci SequencesNumber Theoretic Perspectives—Number Trees:Introduction — Turner's Number TreesGeneralizations Using TableauxOn Gray Codes and Coupled Recurrence TreesStudies of Node Sums on Number TreesConnections with Pascal–T TrianglesGeometric Perspectives — Finonacci Vector Geometry:Introduction and Elementary ResultsVector Sequences from Linear RecurrencesThe Fibonacci Honeycomb PlaneFibonacci and Lucas Vector PolygonsTrigonometry in the Honeycomb PlaneVector Sequences Generated in PlanesFibonacci Tracks, Groups, and Plus–Minus SequencesGeometric Perspectives — Goldpoint Geometry:On Goldpoints and Golden-Mean ConstructionsThe Goldpoint Rings of a Line-SegmentSome Fractals in Goldpoint GeometryTriangles and Squares Marked with GoldpointsPlane Tessellations with Goldpoint TrianglesTessellations with Goldpoint SquaresGames with Goldpoint Tiles Readership: Researchers, academics, college teachers and general readers interested in Fibonacci mathematics. Keywords:Reviews:“… the authors explored many applications of the Fibonacci-type sequences that are new and point the way to many additional lines of study. Their ideas were original and well-described and I recommend this book to anyone interested in iterative processes on integers.”MAA Online Book Review “Altogether this is a very stimulating book.”Mathematics Abstracts “… much of the number-theoretical work gains a good deal of interest if the reader has some knowledge of these traditional results and techniques.”New Zealand Mathematical Society Newsletter “Vorobiev's book presents a solid overview, perfectly pitched to undergraduates … it speaks to a more sophisticated audience and reflects the new developments of the intervening years, especially the beautiful role of Fibonacci numbers in Matiyasevich's groundbreaking negative solution of Hilbert's tenth problem.”Choice

In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents.

This book concisely presents a broad range of models and theories on social systems. Because of the huge spectrum of topics involving social systems, various issues related to Mathematics, Statistics, Teaching, Social Science, and Economics are discussed. In an effort to introduce the subject to a wider audience, this volume, part of the series “Studies in Systems, Decision and Control”, equally addresses the needs of mathematicians, statisticians, sociologists and philosophers. The studies examined here are divided into four parts. The first part, “Perusing the Minds Behind Scientific Discoveries”, traces the winding path of Syamal K. Sen and Ravi P. Agarwal’s scholarship throughout history, and most importantly, the thought processes that allowed each of them to master their subject. The second part covers “Theories in Social Systems” and the third discusses “Models in Social Systems”, while the fourth and final part is dedicated to “Mathematical Methods in the Social Sciences”. Given its breadth of coverage, the book will offer inquisitive readers a valuable point of departure for exploring these rich, vast, and ever-expanding fields of knowledge.

This book contains best selected research papers presented at ICTCS 2022: Seventh International Conference on Information and Communication Technology for Competitive Strategies. The conference will be held in Chandigarh, India during 9 – 10 December 2022. The book covers state-of-the-art as well as emerging topics pertaining to ICT and effective strategies for its implementation for engineering and managerial applications. This book contains papers mainly focused on ICT for computation, algorithms and data analytics and IT security. The work is presented in two volumes.

The book offers a comprehensive and timely overview of advanced mathematical tools for both uncertainty analysis and modeling of parallel processes, with a special emphasis on intuitionistic fuzzy sets and generalized nets. The different chapters, written by active researchers in their respective areas, are structured to provide a coherent picture of this interdisciplinary yet still evolving field of science. They describe key tools and give practical insights into and research perspectives on the use of Atanassov's intuitionistic fuzzy sets and logic, and generalized nets for describing and dealing with uncertainty in different areas of science, technology and business, in a single, to date unique book. Here, readers find theoretical chapters, dealing with intuitionistic fuzzy operators, membership functions and algorithms, among other topics, as well as application-oriented chapters, reporting on the implementation of methods and relevant case studies in management science, the IT industry, medicine and/or education. With this book, the editors wish to pay homage to Professor Krassimir Todorov Atanassov for his pioneering work on both generalized nets and intuitionistic fuzzy set.

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.