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A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components

Year 2021, Volume: 11 Issue: 2, 263 - 275, 31.12.2021

Faik Babadağ Merve Uslu

https://doi.org/10.37094/adyujsci.852037

Abstract

In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas numbers we define Fibonacci tessarines and Lucas tessarines. We obtain Binet formulae, D’ocagnes identity and Cassini identity for these tessarines. We also give the identities of Fibonacci negatessarines and Lucas negatessarines and define new vector which are called Fibonacci tessarine vector. 

Keywords

Tessarines Fibonacci Numbers Fibonacci Tessarine Vector

References

  • [1] Cockle, J., On certain functions resembling quaternions and on a new imaginary in algebra, Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh, 3(33), 435-439, 1848.
  • [2] Cockle, J., On a new imaginary in algebra, Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh, 3(34), 37-47, 1849.
  • [3] Cockle, J., On the symbols of algebra and on the theory of tessarines, Philosophical magazine and Journal of Science, London-Dublin-Edinburgh, 3(34), 406-410, 1849.
  • [4] Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific, 35-50, 1997.
  • [5] Vajda, S., Fibonacci and Lucas numbers and the golden section, Theory and Application (Mathematics & Its Applications), Dover Publications, Inc, Mineola, New York, 1989.
  • [6] Verner, E., Hoggatt, Jr., Fibonacci and Lucas Numbers, Canadian Mathematical Bulletin, 3(12), 367, 1969.
  • [7] Iyer, M.R., Some results on Fibonacci quaternions, The Fibonacci Quarterly, 7(2), 201-210, 1969.

Fibonacci ve Lucas Sayı Bileşenleri ile Fibonacci Tessarinelere Yeni Bir Yaklaşım

Year 2021, Volume: 11 Issue: 2, 263 - 275, 31.12.2021

Faik Babadağ Merve Uslu

https://doi.org/10.37094/adyujsci.852037

Abstract

Bu makalede, tessarineler, Fibonacci ve Lucas sayılarıyla ilgili özdeşlikleri kullanarak Fibonacci tessarineler ve Lucas tessarineleri tanımladık. Bu tessarineler için Binet formüllerini, D’ocagnes özdeşliğini ve Cassini özdeşliğini elde ettik. Ayrıca, negatif Fibonacci tessarineler ve negatif Lucas tessarinelerin özdeşliklerini verdik ve Fibonacci tessarine vektörü olarak yeni bir vektör tanımladık.

Keywords

Tessarineler; Fibonacci sayıları; Fibonacci tessarine vektör.

References

  • [1] Cockle, J., On certain functions resembling quaternions and on a new imaginary in algebra, Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh, 3(33), 435-439, 1848.
  • [2] Cockle, J., On a new imaginary in algebra, Philosophical Magazine and Journal of Science, London-Dublin-Edinburgh, 3(34), 37-47, 1849.
  • [3] Cockle, J., On the symbols of algebra and on the theory of tessarines, Philosophical magazine and Journal of Science, London-Dublin-Edinburgh, 3(34), 406-410, 1849.
  • [4] Dunlap, R.A., The golden ratio and Fibonacci numbers, World Scientific, 35-50, 1997.
  • [5] Vajda, S., Fibonacci and Lucas numbers and the golden section, Theory and Application (Mathematics & Its Applications), Dover Publications, Inc, Mineola, New York, 1989.
  • [6] Verner, E., Hoggatt, Jr., Fibonacci and Lucas Numbers, Canadian Mathematical Bulletin, 3(12), 367, 1969.
  • [7] Iyer, M.R., Some results on Fibonacci quaternions, The Fibonacci Quarterly, 7(2), 201-210, 1969.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Faik Babadağ 0000-0001-9098-838X

Merve Uslu 0000-0003-2464-8736

Publication Date December 31, 2021
Submission Date January 11, 2021
Acceptance Date September 10, 2021
Published in Issue Year 2021 Volume: 11 Issue: 2

Cite

APA Babadağ, F., & Uslu, M. (2021). A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. Adıyaman University Journal of Science, 11(2), 263-275. https://doi.org/10.37094/adyujsci.852037
AMA Babadağ F, Uslu M. A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. ADYU J SCI. December 2021;11(2):263-275. doi:10.37094/adyujsci.852037
Chicago Babadağ, Faik, and Merve Uslu. “A New Approach to Fibonacci Tessarines With Fibonacci and Lucas Number Components”. Adıyaman University Journal of Science 11, no. 2 (December 2021): 263-75. https://doi.org/10.37094/adyujsci.852037.
EndNote Babadağ F, Uslu M (December 1, 2021) A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. Adıyaman University Journal of Science 11 2 263–275.
IEEE F. Babadağ and M. Uslu, “A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components”, ADYU J SCI, vol. 11, no. 2, pp. 263–275, 2021, doi: 10.37094/adyujsci.852037.
ISNAD Babadağ, Faik - Uslu, Merve. “A New Approach to Fibonacci Tessarines With Fibonacci and Lucas Number Components”. Adıyaman University Journal of Science 11/2 (December 2021), 263-275. https://doi.org/10.37094/adyujsci.852037.
JAMA Babadağ F, Uslu M. A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. ADYU J SCI. 2021;11:263–275.
MLA Babadağ, Faik and Merve Uslu. “A New Approach to Fibonacci Tessarines With Fibonacci and Lucas Number Components”. Adıyaman University Journal of Science, vol. 11, no. 2, 2021, pp. 263-75, doi:10.37094/adyujsci.852037.
Vancouver Babadağ F, Uslu M. A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components. ADYU J SCI. 2021;11(2):263-75.
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