Before starting my investigation

Before starting my investigation, I need to know the basic knowledge of the Fibonacci number and the golden ratio first. So, the Fibonacci number is simply numbers that are consisted in the Fibonacci sequence and can be obtained by adding up the two previous numbers. Also, this can be represented by the general formula shown below:
U_n= U_(n-1 )+ U_(n-2)
Here are the examples of the first few terms of the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. These numbers were considered to be important in nature because this nature’s numbering system provides efficiency for plants growth as well as driving the arrangement of seeds, leaves, spirals, and etc.
When discussing about Fibonacci sequence, golden ratio cannot be separated because both of them are related. Golden ration can be obtained by dividing each Fibonacci number by its previous number in the sequence and was known to give the constant values of 1.618 as the number gets greater.
5/ 3 = 1.667, 13/ 8 = 1.625, 34/ 21 = 1.619