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Year 2019, , 59 - 64, 28.06.2019
https://doi.org/10.32323/ujma.473514

Abstract

References

  • [1] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly 70(1963), 289-291.
  • [2] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Proc., New York-Toronto, 2001.
  • [3] S. Vajda, Fibonacci and Lucas Numbers the Golden Section, Ellis Horrowood Limited Publ., England, 1989.
  • [4] G. Berzsenyi, Sums of Product of Generalized Fibonacci Numbers, Fibonacci Quart., 13(4), (1975), 343-344.
  • [5] A. F. Horadam, A Generalized Fibonacci sequence, American Math. Monthly, 68, (1961), 455-459.
  • [6] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3), (1965), 161-176.
  • [7] M. R. Iyer, Identities involving generalized Fibonacci numbers, Fibonacci Quart., 7(1), (1969), 66-73.
  • [8] J. E. Walton and A. F. Horadam, Some further identities for the generalized Fibonacci sequence, Fibonacci Quart., 12(3), (1974), 272-280.
  • [9] F. Catoni, R. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti and P. Zampatti, The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • [10] H. Gargoubi and S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4), (2016), 1211-1233.
  • [11] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [12] B. Jancewicz, The extended Grassmann algebra of R3, in Clifford (Geometric) Algebras with Applications and Engineering, Birkhauser, Boston, (1996), 389-421.
  • [13] D. Khadjiev and Y. Göksal, Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26, (2016), 645-668.
  • [14] A. N. Güncan and Y. Erbil, The q-Fibonacci hyperbolic functions, Appl. Math. Inf. Sci. 8 (1L), (2014), 81-88.
  • [15] L. Barreira, L. H. Popescu and C. Valls, Hyperbolic Sequences of Linear Operators and Evolution Maps, Milan J. Math., 84, (2016), 203-216.
  • [16] J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, 1994.
  • [17] K. Akutagawa and S. Nishikawa, The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Th¨oko Math., J., 42, (1990), 67-82.

Hyperbolic Fibonacci Sequence

Year 2019, , 59 - 64, 28.06.2019
https://doi.org/10.32323/ujma.473514

Abstract

In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product, cross product and mixed product for the hyperbolic Fibonacci vectors.

References

  • [1] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly 70(1963), 289-291.
  • [2] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Proc., New York-Toronto, 2001.
  • [3] S. Vajda, Fibonacci and Lucas Numbers the Golden Section, Ellis Horrowood Limited Publ., England, 1989.
  • [4] G. Berzsenyi, Sums of Product of Generalized Fibonacci Numbers, Fibonacci Quart., 13(4), (1975), 343-344.
  • [5] A. F. Horadam, A Generalized Fibonacci sequence, American Math. Monthly, 68, (1961), 455-459.
  • [6] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3), (1965), 161-176.
  • [7] M. R. Iyer, Identities involving generalized Fibonacci numbers, Fibonacci Quart., 7(1), (1969), 66-73.
  • [8] J. E. Walton and A. F. Horadam, Some further identities for the generalized Fibonacci sequence, Fibonacci Quart., 12(3), (1974), 272-280.
  • [9] F. Catoni, R. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti and P. Zampatti, The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • [10] H. Gargoubi and S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4), (2016), 1211-1233.
  • [11] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [12] B. Jancewicz, The extended Grassmann algebra of R3, in Clifford (Geometric) Algebras with Applications and Engineering, Birkhauser, Boston, (1996), 389-421.
  • [13] D. Khadjiev and Y. Göksal, Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26, (2016), 645-668.
  • [14] A. N. Güncan and Y. Erbil, The q-Fibonacci hyperbolic functions, Appl. Math. Inf. Sci. 8 (1L), (2014), 81-88.
  • [15] L. Barreira, L. H. Popescu and C. Valls, Hyperbolic Sequences of Linear Operators and Evolution Maps, Milan J. Math., 84, (2016), 203-216.
  • [16] J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, 1994.
  • [17] K. Akutagawa and S. Nishikawa, The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Th¨oko Math., J., 42, (1990), 67-82.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fügen Torunbalcı Aydın 0000-0002-4953-1078

Publication Date June 28, 2019
Submission Date October 22, 2018
Acceptance Date January 23, 2019
Published in Issue Year 2019

Cite

APA Torunbalcı Aydın, F. (2019). Hyperbolic Fibonacci Sequence. Universal Journal of Mathematics and Applications, 2(2), 59-64. https://doi.org/10.32323/ujma.473514
AMA Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. June 2019;2(2):59-64. doi:10.32323/ujma.473514
Chicago Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2, no. 2 (June 2019): 59-64. https://doi.org/10.32323/ujma.473514.
EndNote Torunbalcı Aydın F (June 1, 2019) Hyperbolic Fibonacci Sequence. Universal Journal of Mathematics and Applications 2 2 59–64.
IEEE F. Torunbalcı Aydın, “Hyperbolic Fibonacci Sequence”, Univ. J. Math. Appl., vol. 2, no. 2, pp. 59–64, 2019, doi: 10.32323/ujma.473514.
ISNAD Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2/2 (June 2019), 59-64. https://doi.org/10.32323/ujma.473514.
JAMA Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019;2:59–64.
MLA Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications, vol. 2, no. 2, 2019, pp. 59-64, doi:10.32323/ujma.473514.
Vancouver Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019;2(2):59-64.

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