Applications of Fibonacci Numbers: Volume 3 Proceedings of by A. G. Akritas, P. G. Bradford (auth.), G. E. Bergum,

By A. G. Akritas, P. G. Bradford (auth.), G. E. Bergum, Professor A. N. Philippou, Professor A. F. Horadam (eds.)

This e-book comprises thirty-six papers from one of the forty-five papers offered on the 3rd overseas convention on Fibonacci Numbers and Their functions which was once held in Pisa, Italy from July 25 to July 29, 1988 in honor of Leonardo de Pisa. those papers were chosen after a cautious overview by way of popular referees within the box, and so they diversity from hassle-free quantity conception to chance and information. The Fibonacci numbers are their unifying bond. it truly is expected that this ebook, like its predecessors, could be valuable to analyze staff and graduate scholars drawn to the Fibonacci numbers and their functions. August 1989 The Editors Gerald E. Bergum South Dakota nation collage Brookings, South Dakota, U. S. A. Andreas N. Philippou Ministry of schooling Nicosia, Cyprus Alwyn F. Horadam collage of recent England Armidale N. S. W. , Australia xv THE ORGANIZING COMMITTEES neighborhood COMMITTEE foreign COMMITTEE Dvornicich, Roberto, Chairman Horadam, A. F. (Australia), Co-chairman Filipponi, Piero Philippou, A. N. (Cyprus), Co-chairman Perelli, Alberto Ando, S. (Japan) Viola, Carlo Bergum, G. E. (U. S. A. ) Zannier, Umberto Johnson, M. B. (U. S. A. ) Kiss, P. (Hungary) Tijdeman, Robert (The Netherlands) Tognetti, okay. (Australia) XVII checklist OF individuals TO THE convention' ADLER, I. , RR 1, field 532, North Bennington, VT 05257-9748. "Separating the organic from the Mathematical facets of Phyllotaxis. " *AKRITAS, A. G. , (coauthor P. G. Bradford). "The position of the Fibonacci series within the Isolation of the genuine Roots of Polynomial Equations.

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Extra resources for Applications of Fibonacci Numbers: Volume 3 Proceedings of ‘The Third International Conference on Fibonacci Numbers and Their Applications’, Pisa, Italy, July 25–29, 1988

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0· . 0 . · . }) Figure 3. Tokyo Bow 23 S. AN DO AND D. } = (GCD, LCM) {o} [ Figure 4. 0. } = (GCD, Figure 5. Fujiyama LCM) {o} [ TRANSLATABLE AND ROTATABLE CONFIGURATIONS ... 25 m, GCD){A,C,E,H,J,R}=m, GCD){B,D,F,I,L,T} =m, GCD){A,C,E,I,L,T}=m, GCD){B,D,F,H,J,R} Figure 6A. North Star Figure 6B. North Star REFERENCES [1] Hoggatt, V. E. , and Hansell, Walter. 120-133. [2] Gould, H. W. " The Fibonacci Quarterly, 10 (1972): pp. 579-584, 628. [3] Hillman, A. P. and Hoggatt, V. E. Jr. " The Fibonacci Quarterly, 10 (1972): pp.

111 It is to be noted that in constructing "Julia's snowflake", and "Saskatchewan hexagon", more points have been used than mathematically required, in order to achieve a high degree of symmetry and a better artistic impression. For example, in the case of "Julia's snowflake", the central hexagon which itself has the equal product and GCD properties, may be removed without violating Theorem 3. In constructing "Tokyo bow" and "Fujiyama", on the other hand, effort was made to minimize the number of points.

F(r) j+r' (r ) (r) + F j+4 + F j+5 + ... k-r-I L Fk-(r+j) (r-l) F j + where for convenience we set F~r) 2 + (r-l) ( r) F j +3 = 0 when k + (r-2) (r) Fj+4 (r) (r») + ... + 2Fj+r + Fj+r+1 , :S 0 . L k~1 (r) ( . J Fk-(r+j) l--r+l )=-r+l (r) (r-l) F j +2 (r) ( (r) F k-(r+j) (r-l) F j+3 + (r- 'l_) + (r-2) ,(rl F j+4 (r) F j +3 + (r-3) (rl (r) Fj+4 (r l (r) + ... + 'l_Fj+r-I + ) k r I +- .. + 2F j+r + F j+r+1 + (r-l) . L J=-r+l (r) ( Fk-(r+j) (rl (r-l) F j +2 + (r-2) (rl Fj+3 + (r-3) (r) F j +5 ( r) (r) ) + ...

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