Skip to main content

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.

Labels:

Comments

Post a Comment

Popular posts from this blog

Universe Secret Code 369 Theory

When it comes to the origin of the universe secret code 369 theory, one name associated with this amazing concept is ‘Nikola Tesla’. Nikola Tesla [10 July 1856 – 07 January 1943] was not only a great inventor / scientist, but also the greatest mind of all the time. He has done a plenty of research throughout his life, and highly recognized for his contributions towards the following : High Voltage, High Frequency Power Experiments Alternating Current (AC) Electricity Supply System Apart from the above-mentioned contributions, he has given ‘Universe Secret Code 369 Theory’ and has called the number 369 – the key to the universe. Now the question that will come to the curious minds is that why Nikola Tesla has called this number the key to the universe. The answer to this question is described in this post. Let start with a specific pattern as shown below: 1 1 + 1 => 2 2 + 2 => 4 4 + 4 => 8 8 + 8 => 16; 1 + 6 => 7 16 + 16 => 32; 3 + 2 => 5 >>>>>>...
Post a Comment
Read more

Kaprekar Constant 495 for Three-digit Number

Dattatreya Ramchandra Kaprekar (D. R. Kaprekar; 1905 – 1986) was an Indian mathematician who discovered several classes of natural numbers including Kaprekar Constant. The number  495  is called Kaprekar Constant for three-digit number. Why is the number 495 called Kaprekar Constant? In 1949, D. R. Kaprekar discovered an interesting property of the number 495 through the mathematical calculations. D. R. Kaprekar observed that when any three-digit number of non-identical digits (not all digits are same) is arranged in two parts – highest number and lowest number, and difference is calculated using subtraction method, then the end-result will be always 495. If the process is continued even after getting the end-result 495, then the end-result will be always 495 at each Iteration, therefore the number 495 is known as Kaprekar Constant. Steps to Follow Take any three-digit number with different digits. Form the highest number and lowest number from this three-digit number. Fi...
Post a Comment
Read more