New Visual Perspectives on Fibonacci NumbersWorld Scientific, 2002 - 313 páginas 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. |
Contenido
PART A NUMBER THEORETIC PERSPECTIVES | 1 |
The 2Fibonacci sequences | 27 |
Extensions of the concepts of 2Fibonacci sequences | 35 |
Other ideas for modification of the Fibonacci sequence | 41 |
vii | 51 |
Generalizations using tableaux | 61 |
Fibonacci Vector Geometry | 83 |
Vector sequences from linear recurrences | 95 |
Fibonacci tracks groups and plusminus sequences | 153 |
Goldpoint Geometry | 181 |
The goldpoint rings of a linesegment | 205 |
Some fractals in goldpoint geometry | 215 |
Triangles and squares marked with goldpoints | 229 |
Plane tessellations with goldpoint triangles | 245 |
Tessellations with goldpoint squares | 269 |
Games with goldpoint tiles | 293 |
The Fibonacci honeycomb plane | 107 |
Fibonacci and Lucas vector polygons | 119 |
Vector sequences generated in planes | 137 |
Otras ediciones - Ver todas
New Visual Perspectives on Fibonacci Numbers K T Atanassov,V Atanassova,A G Shannon,J C Turner Vista previa limitada - 2002 |
New Visual Perspectives on Fibonacci Numbers Krassimir T. Atanassov Sin vista previa disponible - 2002 |
Términos y frases comunes
4-tiles a₁ algebras an+2 ATANASSOV B-point B-ring b₁ b₂ basic Fibonacci Bn+2 Burnside's theorem Chapter chimney colour construction coordinates count cross-ratio cube cyclic groups defined diagram elements equilateral triangles equivalent ET-transform example Fibonacci numbers Fibonacci Quarterly Fibonacci sequence Fibonacci vector sequence fixed points Fn+1 formulae four fractal G₁ geometric given golden ratio golden tiles goldpoint Goldpoint Geometry Hence honeycomb plane horizontal side identity initial vectors inner hexagons integer point integer triangle Is-string jigging jigging matrix jigsaw jigsaw rules labelled limit ray line-segment linear form ls-string Lucas vector mathematical node Number Theory number trees obtain pairs pentagon permutation pieces player plus-minus Proof properties recurrence equation recurrence relation respectively rhombus rhombuses rotational symmetry S₁ schemes segment SGPs shown solution square T₁ T₂ TGPs tile figures track tracksets Turner vector recurrence Xn+1