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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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    Cited by:

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    2. 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.
    3. Şenol, Ali & Yayli, Yusuf, 2009. "LC helices in space forms," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2115-2119.
    4. Camcı, Çetin & İlarslan, Kazım & Kula, Levent & Hacısalihoğlu, H. Hilmi, 2009. "Harmonic curvatures and generalized helices in En," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2590-2596.
    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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