Have a personal or library account? Click to login
A Study on Dual Hyperbolic Fibonacci and Lucas Numbers Cover

References

  1. [1] O.Y. Bodnar, The golden section and non-Euclidean geometry in nature and art, Publishing House ”Svit”, Lvov, 1994(Russian).
  2. [2] W.K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc. 4 (1873), 381-395.10.1112/plms/s1-4.1.381
  3. [3] J. Cockle, On systems of algebra involving more than one imaginary, Philos. Mag. 35 (series 3) (1849), 434–436.10.1080/14786444908646384
  4. [4] H.S.M. Coxeter, S.L. Greitzer, Geometry revisited The Mathematical Association of America (nc.), International and Pan American Conventions, Washington:1967.10.5948/UPO9780883859346
  5. [5] R.A. Dunlap, The golden ratio and Fibonacci numbers, World Scientific Publishing Co. Pte. Ltd., Singapore:1997.10.1142/3595
  6. [6] C. Flaut, V. Shpakivskyi, Real matrix representations for the complex quaternions, Adv. Appl. Clifford Algebras 23 (2013), 657–671.10.1007/s00006-013-0387-3
  7. [7] M.A. Güngör, A.Z. Azak, Investigation of dual-complex Fibonacci, dual-complex Lucas numbers and their properties, Adv. Appl. Clifford Algebras 27 (2017), 3083–3096.10.1007/s00006-017-0813-z
  8. [8] S. Halıcı, On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 105–112.10.1007/s00006-012-0337-5
  9. [9] W.R. Hamilton, Lectures on quaternions: containing a systematic statement of a new mathematical method, Hodges and Smith, Dublin:1853.
  10. [10] A.F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), 289–291.10.2307/2313129
  11. [11] D.E. Knuth, Negafibonacci numbers and the hyperbolic plane, Pi Mu Epsilon J. Sutherland Frame Lecture at MathFest, The Fairmonth Hotel, San Jose, CA:2007.
  12. [12] T. Koshy, Fibonacci and Lucas numbers with applications, Wiley and Sons Publication, New York:2001.10.1002/9781118033067
  13. [13] A. Macfarlane, Hyperbolic quaternions, Proc. Roy. Soc. Edinburgh Sect. A 23 (1902), 169-180.10.1017/S0370164600010385
  14. [14] V. Majernik, Multicomponent number systems, Acta Phys. Pol. A, 90 (No. 3) (1996), 491–498.10.12693/APhysPolA.90.491
  15. [15] S.K. Nurkan, İA. Güven, A note on bicomplex Fibonacci and Lucas numbers, (2015), https://arxiv.org/abs/1508.03972v1.
  16. [16] A.P. Stakhov, I.S. Tkachenko, Hyperbolic Fibonacci trigonometry, Reports of the National Academy of Sciences of Ukraine 208 (No. 7) (1993), 9–14.
  17. [17] A.P. Stakhov, I.S. Tkachenko, The golden shofar, Chaos Soliton. Fract. 26 (Issue 3) (2005), 677-684.10.1016/j.chaos.2005.01.057
  18. [18] S. Vajda, Fibonacci and Lucas numbers and the golden section, Ellis Horwood Ltd./Halsted Press, Chichester:1989.
  19. [19] E.W. Weisstein, Fibonacci number, Mathworld(online mathematics reference work).
DOI: https://doi.org/10.2478/auom-2019-0002 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 35 - 48
Submitted on: Jan 10, 2018
|
Accepted on: Mar 30, 2018
|
Published on: Mar 2, 2019
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2019 Arzu Cihan, Ayşe Zeynep Azak, Mehmet Ali Güngör, Murat Tosun, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.