Research Article
Year 2020,
Volume: 2 Issue: 2, 12 - 25, 09.12.2020
Abstract
The purpose of this article is to study vector products of Fibonacci 3-vectors, Fibonacci 4-vectors and Fibonacci 7-vectors. To achieve this, we first describe the corresponding anti-symmetric matrix for the Fibonacci 3-vector and reconsider the vector product with the aid of this matrix. We examine certain properties of this vector product. Furthermore, we define vector products for Fibonacci 4-vectors and Fibonacci 7-vectors. We also give in the same vein the corresponding anti-symmetric matrix for Fibonacci 7-vector and redefine the vector product by using this matrix. In the final instance we investigate the Lorentzian inner products, Lorentzian vector products and Lorentzian triple scalar products for Fibonacci 3-vectors, Fibonacci 4-vectors and Fibonacci 7-vectors.
References
- [1] Atanassov, K. T. (2002). New visual perspectives on Fibonacci numbers. World Scientific.
- [2] Salter, E. (2005). Fibonacci Vectors. Graduate Theses and Dissertations, University of South Florida, USA.
- [3] Güven, İ. A., & Nurkan, S. K. (2015). A new approach to Fibonacci, Lucas numbers and dual vectors. Advances in Applied Clifford Algebras, 25(3), 577-590, https://doi.org/10.1007/s00006-014-0516-7.
- [4] Yüce, S., & Torunbalcı Aydın, F. (2016). Generalized dual Fibonacci sequence. The International Journal of Science & Technoledge, 4(9), 193-200.
- [5] Kaya, O., & Önder, M. (2018). On Fibonacci and Lucas Vectors and Quaternions. Universal Journal of Applied Mathematics, 6(5), 156-163.
- [6] Knuth, D. (2008). NegaFibonacci numbers and the hyperbolic plane. In San Jose-Meeting of the Mathematical Association of America, (Vol. 5).
- [7] Struyk, A. (1970). One Curiosum Leads to Another. Scripta Mathematica. 17, 230.
- [8] Vajda, S. (1989). Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Ellis Horwood Series. Mathematics and Applications.
- [9] Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. John Wiley and Sons, Proc., Toronto, New York.
- [10] Weisstein, E.W., Fibonacci Number. MathWorld, (online mathematics reference work).
- [11] Ratcliffe, J. G., Axler, S., & Ribet, K. A. (2006). Foundations of hyperbolic manifolds. (Vol. 149), New York: Springer.
Year 2020,
Volume: 2 Issue: 2, 12 - 25, 09.12.2020
Abstract
References
- [1] Atanassov, K. T. (2002). New visual perspectives on Fibonacci numbers. World Scientific.
- [2] Salter, E. (2005). Fibonacci Vectors. Graduate Theses and Dissertations, University of South Florida, USA.
- [3] Güven, İ. A., & Nurkan, S. K. (2015). A new approach to Fibonacci, Lucas numbers and dual vectors. Advances in Applied Clifford Algebras, 25(3), 577-590, https://doi.org/10.1007/s00006-014-0516-7.
- [4] Yüce, S., & Torunbalcı Aydın, F. (2016). Generalized dual Fibonacci sequence. The International Journal of Science & Technoledge, 4(9), 193-200.
- [5] Kaya, O., & Önder, M. (2018). On Fibonacci and Lucas Vectors and Quaternions. Universal Journal of Applied Mathematics, 6(5), 156-163.
- [6] Knuth, D. (2008). NegaFibonacci numbers and the hyperbolic plane. In San Jose-Meeting of the Mathematical Association of America, (Vol. 5).
- [7] Struyk, A. (1970). One Curiosum Leads to Another. Scripta Mathematica. 17, 230.
- [8] Vajda, S. (1989). Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Ellis Horwood Series. Mathematics and Applications.
- [9] Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. John Wiley and Sons, Proc., Toronto, New York.
- [10] Weisstein, E.W., Fibonacci Number. MathWorld, (online mathematics reference work).
- [11] Ratcliffe, J. G., Axler, S., & Ribet, K. A. (2006). Foundations of hyperbolic manifolds. (Vol. 149), New York: Springer.
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 9, 2020 |
| Published in Issue | Year 2020 Volume: 2 Issue: 2 |
