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On Fibonacci Vectors

Yıl 2020, Cilt: 2 Sayı: 2, 12 - 25, 09.12.2020

Öz

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.

Kaynakça

  • [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.
Yıl 2020, Cilt: 2 Sayı: 2, 12 - 25, 09.12.2020

Öz

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Kübra Çetinberk 0000-0002-8811-9393

Salim Yüce 0000-0002-8296-6495

Yayımlanma Tarihi 9 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 2

Kaynak Göster

APA Çetinberk, K., & Yüce, S. (2020). On Fibonacci Vectors. Hagia Sophia Journal of Geometry, 2(2), 12-25.