04608nam 2200529 a 450 991081486600332120240404154059.0981-277-683-4(CKB)1000000000404617(EBL)1681653(OCoLC)879025553(MiAaPQ)EBC1681653(WSP)00005061(Au-PeEL)EBL1681653(CaPaEBR)ebr10201311(CaONFJC)MIL505392(EXLCZ)99100000000040461720030328d2002 uy 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierNew visual perspectives on Fibonacci numbers /K.T. Atanassov ... [et al.]1st ed.River Edge, NJ World Scientificc20021 online resource (331 p.)Description based upon print version of record.981-238-114-7 Includes bibliographical references and index.Contents ; Introduction ; Foreword ; Preface ; PART A. NUMBER THEORETIC PERSPECTIVES ; Section 1. Coupled Recurrence Relations ; 1. Introductory remarks by the first author ; 2. The 2-Fibonacci sequences ; 3. Extensions of the concepts of 2-Fibonacci sequences4. Other ideas for modification of the Fibonacci sequence Bibliography ; Section 2. Number Trees ; 1. Introduction - Turner's Number Trees ; 2. Generalizations using tableaux ; 3. On Gray codes and coupled recurrence trees ; 4. Studies of node sums on number trees5. Connections with Pascal-T triangles Bibliography ; PART B. GEOMETRIC PERSPECTIVES ; Section 1. Fibonacci Vector Geometry ; 1. Introduction and elementary results ; 2. Vector sequences from linear recurrences ; 3. The Fibonacci honeycomb plane4. Fibonacci and Lucas vector polygons 5. Trigonometry in the honeycomb plane ; 6. Vector sequences generated in planes ; 7. Fibonacci tracks groups and plus-minus sequences ; Bibliography ; Section 2. Goldpoint Geometry ; 1. On goldpoints and golden-mean constructions2. The goldpoint rings of a line-segment 3. Some fractals in goldpoint geometry ; 4. Triangles and squares marked with goldpoints ; 5. Plane tessellations with goldpoint triangles ; 6. Tessellations with goldpoint squares ; 7. Games with goldpoint tiles ; Bibliography ; IndexThis 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 thFibonacci numbersFibonacci numbers.512.7/2Atanassov Krassimir T911826MiAaPQMiAaPQMiAaPQBOOK9910814866003321New visual perspectives on Fibonacci numbers4109806UNINA