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Fibonacci Planes and Spaces

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Abstract

Two types of Fibonacci plane were introduced in [1], They were based on the idea of Tirman and Jablinski [4], where the infinite Fibonacci square generalizes a fourth Cartesian quadrant. The purpose of this paper is to describe a third Fibonacci plane and to outline the associated algebra.

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References

  1. Atanassov, K.T. “A remark on a Fibonacci plane.” Bulletin of Number Theory & Related Topics, Vol. 13, (1989): pp. 69–71.

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  2. Horadam, A.F. “A generalized Fibonacci sequence.” American Mathematical Monthly, Vol. 68.5 (1961): pp. 455–459.

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  3. Lee, J.Z. and Lee, J.S. “Some properties of the generalization of the Fibonacci Sequence.” The Fibonacci Quarterly, Vol. 25.2 (1987): pp. 111–117.

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  4. Tirman, A. and Jablinski, T. Jr. “Identities derived on a Fibonacci multiplication table.” The Fibonacci Quarterly, Vol. 26.4 (1988): pp. 328–331.

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  5. Turner, J.C. and Shannon, A.G. “Introduction to a Fibonacci geometry.” Applications of Fibonacci Numbers. Volume 7. Edited by G.E. Bergum, A.F. Horadam and A.N. Philippou, Kluwer Academic Publishing, Dordrecht, The Netherlands, 1998: pp. 435–448.

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© 1999 Springer Science+Business Media Dordrecht

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Atanassov, K.T., Shannon, A.G. (1999). Fibonacci Planes and Spaces. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4271-7_4

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  • DOI: https://doi.org/10.1007/978-94-011-4271-7_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5851-3

  • Online ISBN: 978-94-011-4271-7

  • eBook Packages: Springer Book Archive

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