Open AccessIs there a Similiarity between Fibonacci Sequence and Euler’s Number with Respect to Quantum Perspective Model?
Author(s) -
Tahir Ölmez
Publication year - 2021
Publication title -
global journal of science frontier research
Language(s) - English
Resource type - Journals
eISSN - 2249-4626
pISSN - 0975-5896
DOI - 10.34257/gjsfrfvol20is9pg35
Subject(s) - fibonacci number , lucas number , fibonacci polynomials , mathematics , pisano period , euler's formula , series (stratigraphy) , lucas sequence , decimal , combinatorics , golden ratio , base (topology) , arithmetic , mathematical analysis , geometry , paleontology , orthogonal polynomials , biology , difference polynomials
According to Quantum Perspective Model, this article studies whether there is a link between the Euler’s numbers and the Fibonacci series. When the digits of the Euler’s number after the comma are converted from decimal(10) number base system to binary(2) number base system, it corresponds to the number in the Fibonacci series.(0,1,1,2,3,5,8,13,21,34,55...)[7].From this point of view, when the first hundred digits of the Euler’s numbers after the comma were calculated, the number "55" (ten times) in the Fibonacci series was found, in particular. Besides, the eleventh number in the Fibonacci series is also "55".In other words, the approximate unchanged numbers of the golden ratio numbers after the comma can be reached for the first time after dividing them from “55” to “34” (1,618). In sum, Euler’s numbers are not only attributed to the Fibonacci series in mathematics, but also attributed to the golden ratio in nature.