Fibonacci Elliptic Biquaternions
Fibonacci Elliptic Biquaternions
A. F. Horadam defined the complex Fibonacci numbers and Fibonacci quaternions in the middle of the 20th century. Half a century later, S. Hal{\i}c{\i} introduced the complex Fibonacci quaternions by inspiring from these definitions and discussed some properties of them. Recently, the elliptic biquaternions, which are generalized form of the complex and real quaternions, have been presented. In this study, we introduce the set of Fibonacci elliptic biquaternions that includes the set of complex Fibonacci quaternions as a special case and investigate some properties of Fibonacci elliptic biquaternions. Furthermore, we give the Binet formula and Cassini's identity in terms of Fibonacci elliptic biquaternions. Finally, we give elliptic and real matrix representations of Fibonacci elliptic biquaternions.
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- [1] B. L. van der Waerden, Hamilton’s discovery of quaternions, Math. Mag., 49 (1976), 227-234.
- [2] W. R. Hamilton, Lectures on quaternions, Hodges and Smith, Dublin, 1853.
- [3] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Mon., 70 (1963), 289-291.
- [4] S. Halıcı, On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 105-112.
- [5] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Q., 7 (1969), 201-210.
- [6] T. Erişir, M. A. Güngör, On Fibonacci spinors, Int. J. Geom. Methods Mod. (2020), DOI: 10.1142/S0219887820500656.
- [7] M. Akyiğit, H. H. Kösal, M. Tosun, Fibonacci generalized quaternions, Adv. Appl. Clifford Algebras, 24 (2014), 631-641.
- [8] C. Flaut, V. Shpakivskyi, Real matrix representations for the complex quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 657-671.
- [9] K. E. Özen, M. Tosun, Elliptic biquaternion algebra, AIP Conf. Proc., 1926 (2018), 020032.
- [10] I. M. Yaglom, Complex Numbers in Geometry, Academic Press, Newyork, 1968.
- [11] A. A. Harkin, J. B. Harkin, Geometry of generalized complex numbers, Math. Mag., 77(2) (2004), 118-129.
- [12] K. Eren, S. Ersoy, Burmester theory in Cayley-Klein planes with affine base, J. Geom., 109(3) (2018), 45.
- [13] K. Eren, S. Ersoy, Revisiting Burmester theory with complex forms of Bottema’s instantaneous invariants, Complex Var. Elliptic Equ., 62(4) (2017), 431-437.
- [14] Z. Derin, M. A. Güngör, On Lorentz transformations with elliptic biquaternions. In: Hvedri, I. (ed.) Tblisi-Mathematics, pp 121-140. Sciendo, Berlin (2020).
- [15] Y. Kulaç, M. Tosun, Some equations on p-complex Fibonacci numbers, AIP Conf. Proc., 1926 (2018), 020024.
- [16] R. A. Dunlap, The golden ratio and Fibonacci numbers, World Scientific, 1997.
- [17] T. Koshy, Fibonacci and Lucas numbers with applications, A Wiley-Interscience publication, U.S.A, 2001.
- [18] K. E. Özen, M. Tosun, Further results for elliptic biquaternions, Conf. Proc. Sci. Technol., 1 (2018), 20-27.
- [19] K. E. Özen, M. Tosun, Elliptic matrix representations of elliptic biquaternions and their applications, Int. Electron. J. Geom., 11 (2018), 96-103.
- [20] K. E. Özen, M. Tosun, A general method for solving linear elliptic biquaternion equations, Complex Var. Elliptic Equ., (2020), 1-12, DOI: 10.1080/17476933.2020.1738409.
- [21] K. E. Özen, A general method for solving linear matrix equations of elliptic biquaternions with applications, AIMS Math., 5 (2020), 2211–2225.
- ISSN: 2645-8845
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Fuat USTA
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