Some Properties of Fibonacci Numbers

Shriram B. Patil

doi:https://doi.org/10.14445/22315373/IJMTT-V60P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 1 | Year 2018 | Article Id. IJMTT-V60P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P506

Some Properties of Fibonacci Numbers

Shriram B. Patil

Citation :

Shriram B. Patil, "Some Properties of Fibonacci Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 1, pp. 32-39, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P506

Abstract

Fibonacci numbers are well known for some of its interesting properties [1]. Golden ratio is one of the amazing property. Fibonacci numbers and Golden ratio have applications in physics, astrophysics, biology, chemistry and technology [2]. This article proves property of determinant of Fibonacci numbers , geometric consideration for Golden ratio and construction of Fibonacci subsequence from a Fibonacci sequence. The determinant of first n2 n >= 2 of a Fibonacci numbers is zero. The golden ratio is shown to be sequence of lines converging to a line with slope as golden ratio. Method of constructing a subsequence from a Fibonacci sequence is presented. Examples presented in [2] is not exhaustive list of applications. One may find other applications in different domains of science.

Keywords

Fibonacci , Generalized Fibonacci sequence, Golden ratio, Set of lines, rational sequence, irrational number, sequence, subsequence, convergence

References

[1] Magdalena Jastrzebska , Adam Grabowski. “Some Properties of Fibonacci Numbers “ , Formalised Mathematics, Volume 12, Number 3, 2004
[2] Vladimir Pletser, Fibonacci Numbers and the Golden Ratio in Biology, Physics, Astrophysics, Chemistry and Technology: A NonExhaustive ReviewTechnology and Engineering Center for Space Utilization , Chinese Academy of Sciences, Beijing, China; Vladimir.Pletser@csu.ac.cn
[3] R.R.Goldberg, Methods of real analysis, Oxford & IBH