On the origin of the Fibonacci Sequence
نویسندگان
چکیده
Herein we investigate the historical origins of the Fibonacci numbers. After emphasising the importance of these numbers, we examine a standard conjecture concerning their origin only to demonstrate that it is not supported by historical chronology. Based on more recent findings, we propose instead an alternative conjecture through a close examination of the historical and historical/mathematical circumstances surrounding Leonardo Fibonacci and relate these circumstances to themes in medieval and ancient history. Cultural implications and historical threads of our conjecture are also examined in this light.
منابع مشابه
A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence
In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore, new sequences have been used in order to introduce a new class of series. All properties of the se...
متن کاملA Generalized Fibonacci Sequence and the Diophantine Equations $x^2pm kxy-y^2pm x=0$
In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.
متن کاملRanking of Fire Stations with Fibonacci Sequence Technique, Case Study: District Ten of Tehran Municipality
One of the effective items to reduce time for arriving fire fighters to place of event is determining the optimal location of fire stations. Ranking can define the best location of a fire station through the available options. The case of this study is the district ten of Tehran municipality. That is the smallest district of Tehran municipality in terms of size and is highest in terms of densit...
متن کاملElectronic transport through dsDNA based junction: a Fibonacci model
A numerical study is presented to investigate the electronic transport properties through a synthetic DNA molecule based on a quasiperiodic arrangement of its constituent nucleotides. Using a generalized Green's function technique, the electronic conduction through the poly(GACT)-poly(CTGA) DNA molecule in a metal/DNA/metal model structure has been studied. Making use of a renormalization schem...
متن کاملToeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
متن کاملAbsorption Spectra of a Graphene Embedded One Dimensional Fibonacci Aperiodic Structure
In this paper, we explore the linear response of one dimensionalquasiperiodic structure based on Fibonacci sequence composed of silicon dioxide,polystyrene and graphene materials. Here, a graphene monolayer is sandwichedbetween two adjacent layers. The numerical results are obtained by using the standardtransfer matrix method. Due to the presence of graphene sheet in eac...
متن کامل