LEADER 04520nam 2200481 a 450 001 9910814866003321 005 20230607221457.0 010 $a981-277-683-4 035 $a(CKB)1000000000404617 035 $a(EBL)1681653 035 $a(OCoLC)879025553 035 $a(MiAaPQ)EBC1681653 035 $a(WSP)00005061 035 $a(Au-PeEL)EBL1681653 035 $a(CaPaEBR)ebr10201311 035 $a(CaONFJC)MIL505392 035 $a(EXLCZ)991000000000404617 100 $a20030328d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 200 00$aNew visual perspectives on Fibonacci numbers$b[electronic resource] /$fK.T. Atanassov ... [et al.] 210 $aRiver Edge, NJ $cWorld Scientific$dc2002 215 $a1 online resource (331 p.) 300 $aDescription based upon print version of record. 311 $a981-238-114-7 320 $aIncludes bibliographical references and index. 327 $aContents ; 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 sequences 327 $a4. 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 trees 327 $a5. 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 plane 327 $a4. 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 constructions 327 $a2. 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 ; Index 330 $aThis 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 th 606 $aFibonacci numbers 615 0$aFibonacci numbers. 676 $a512.7/2 701 $aAtanassov$b Krassimir T$0911826 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814866003321 996 $aNew visual perspectives on Fibonacci numbers$94109806 997 $aUNINA