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
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