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, Fibonacci number is simply numbers that are consisted in the Fibonacci sequence and are obtained by sum up the two previous numbers of the terms. Thus, 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 its nature’s numbering system can provide 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 number by its previous number in the Fibonacci 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