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On the 3-dimensional k-Fibonacci spirals

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  • Falcón, Sergio
  • Plaza, Ángel

Abstract

The 3-dimensional k-Fibonacci spirals are studied from a geometric point of view. These curves appear naturally from studying the k-Fibonacci numbers {Fk,n}n=0∞ and the related hyperbolic k-Fibonacci functions. In this paper, after a summary of the main properties for the k-Fibonacci numbers, we focus on the geometry features (curvature and torsion) of the 3-dimensional k-Fibonacci spirals. Finally, the Metallic Shofars and their projections on the coordinate planes are also given.

Suggested Citation

  • Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:993-1003
    DOI: 10.1016/j.chaos.2007.02.009
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    References listed on IDEAS

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    1. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    2. Stakhov, Alexey & Rozin, Boris, 2006. "The continuous functions for the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1014-1025.
    3. Stakhov, Alexey & Rozin, Boris, 2005. "The Golden Shofar," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 677-684.
    4. Falcón, Sergio & Plaza, Ángel, 2008. "The k-Fibonacci hyperbolic functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 409-420.
    5. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    6. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    7. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    8. Marek-Crnjac, L., 2006. "Different Higgs models and the number of Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 575-579.
    9. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    10. El Naschie, M.S., 2007. "Hilbert space, Poincaré dodecahedron and golden mean transfiniteness," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 787-793.
    11. El Naschie, M.S., 2005. "Experimental and theoretical arguments for the number and the mass of the Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1091-1098.
    12. Naschie, M.S.El, 2005. "Deriving the essential features of the standard model from the general theory of relativity," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 941-946.
    13. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
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    3. Cristina E. Hretcanu & Adara M. Blaga, 2021. "Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey," Mathematics, MDPI, vol. 9(19), pages 1-22, October.
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    5. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.

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