Faik BABADAĞ, Merve USLU

Fibonacci ve Lucas Sayı Bileşenleri ile Fibonacci Tessarinelere Yeni Bir Yaklaşım

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.

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

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.

PDF

___

[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.
[8] Knuth, D., Negafibonacci numbers and hyperbolic plane, Annual Meeting of the Mathematical Association of America, 2013.
[9] Horadam, A.F., A generalized Fibonacci sequence, American Mathematical Monthly, 68, 1961.
[10] Koshy, T., Fibonacci and Lucas numbers with applications, A Wiley-Intersience Publication, USA, 2001.
[11] Lucas, E., Theorie des Numbers, Paris, 1961.
[12] Iyer, M.R., Identities ınvolving generalized Fibonacci numbers, The Fibonacci Quarterly, 7, 66-72, 1969.
[13] David, G.G., Permanent of a square matrix, European Journal of Combinatorics, 31, 1881-1891, 2010.