Research Article
BibTex RIS Cite

Year 2019, Volume: 2 Issue: 2, 59 - 64, 28.06.2019

Fügen Torunbalcı Aydın

https://doi.org/10.32323/ujma.473514
Cited By: 7

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, Volume: 2 Issue: 2, 59 - 64, 28.06.2019

Fügen Torunbalcı Aydın

https://doi.org/10.32323/ujma.473514
Cited By: 7

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.

Keywords

Hyperbolic number Fibonacci number Hyperbolic Fibonacci number Hyperbolic vector Hyperbolic Fibonacci vector

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 Volume: 2 Issue: 2

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.

Cited By

Hyperbolic functions obtained from $${\varvec{k}}$$-Pell sequences
Afrika Matematika
https://doi.org/10.1007/s13370-023-01160-7
Unrestricted Fibonacci and Lucas quaternions
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.752758
On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.617415
Gaussian-hyperbolic Numbers Containing Pell and Pell-Lucas Numbers
Journal of Advanced Research in Natural and Applied Sciences
https://doi.org/10.28979/jarnas.1110421
Hyperbolic functions obtained from k-Jacobsthal sequences
Asian-European Journal of Mathematics
https://doi.org/10.1142/S1793557122501789
Split complex bi-periodic Fibonacci and Lucas numbers
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.704435
Hyperbolic Jacobsthal-Lucas Sequence
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.958524
 Download Cover Image

 23181

Universal Journal of Mathematics and Applications 

29207              

Creative Commons License  The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.