Hyperbolic Fibonacci Sequence

Fügen Torunbalcı Aydın

doi:10.32323/ujma.473514

EN

Hyperbolic Fibonacci Sequence

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Fügen Torunbalcı Aydın ^*
0000-0002-4953-1078
Türkiye

Publication Date

June 28, 2019

Submission Date

October 22, 2018

Acceptance Date

January 23, 2019

Published in Issue

Year 2019 Volume: 2 Number: 2

DOI

https://doi.org/10.32323/ujma.473514

IZ

https://izlik.org/JA69MW96MZ

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

1.Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019;2(2):59-64. doi:10.32323/ujma.473514

Chicago

Torunbalcı Aydın, Fügen. 2019. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2 (2): 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

[1]F. Torunbalcı Aydın, “Hyperbolic Fibonacci Sequence”, Univ. J. Math. Appl., vol. 2, no. 2, pp. 59–64, June 2019, doi: 10.32323/ujma.473514.

ISNAD

Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2/2 (June 1, 2019): 59-64. https://doi.org/10.32323/ujma.473514.

JAMA

1.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, June 2019, pp. 59-64, doi:10.32323/ujma.473514.

Vancouver

1.Fügen Torunbalcı Aydın. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019 Jun. 1;2(2):59-64. doi:10.32323/ujma.473514