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The Number 1.6: Base of Fibonacci Sequence and the Golden Ratio

This post is about the number 1.6 that forms the base of the mathematical concepts Fibonacci sequence and the Golden ratio. For better understanding of this amazing number 1.6, it is important to know about Fibonacci sequence and the Golden ratio.

Golden Ratio

The Golden ratio is the ratio of a line segment cut into two pieces of distinct lengths such that the ratio of the longer segment to the shorter segment is equal to the whole segment to that of the longer segment. It is denoted by the symbol Phi [ΓΈ].

Suppose there is a line segment AB, and C is any point that divides the line segment AB into two pieces of distinct lengths such that AC is greater than CB.

Then, as per the definition, [ΓΈ] = AC/CB = AB/AC.

The value of the Golden ratio [ΓΈ] is 1.61803398875.

As you can see, the value of the Golden ratio starts with the number 1.6.

For more information on the Golden ratio, see https://theamazingconcepts.blogspot.com/2021/07/the-golden-ratio-key-to-amazing-design.html.

Fibonacci Sequence

Fibonacci sequence is an infinite sequence of the numbers where the next number is the sum of the last two numbers.

Fibonacci sequence starts with 0, 1, then as per the definition, the next number is 1 [0 + 1], 2 [1 + 1], and so on.

The sequence is as shown below:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, .....

Two important points that come after analyzing the above Fibonacci sequence are:

Point 1: The first number of the Fibonacci sequence is 0 which is an even number, the next two numbers in the sequence are odd followed by an even number. This sequence continues in the same way as you can see above. The numbers in red indicate the even numbers.

Point 2: The first and the second smallest numbers that are greater than 2 in the Fibonacci sequence are 3 and 5, respectively.

Now, start dividing the next number (starting from 5) with its preceding number as shown below:

5/3 => 1.66666666667.

8/5 => 1.6.

13/8 => 1.625.

21/13 => 1.61538461538.

34/21 => 1.61904761905.

55/34 => 1.61764705882.

89/55 => 1.61818181818.

….., and so on.

As you can see, the resultant after dividing the numbers of the Fibonacci sequence starts with the number 1.6.

Hence, it can be concluded that the number 1.6 forms the base of the mathematical concepts Fibonacci sequence and the Golden ratio.

Hope you have understood this amazing concept of the number 1.6. In case of any issue, kindly provide your valuable comments.

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