What is the logic behind golden Mean – Fibonacci Series?

[Balaji]

The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

The key Fibonacci ratio of 61.8% – also referred to as “the golden ratio” or “the golden mean” – is found by dividing one number in the series by the number that follows it.

For example: 8/13 = 0.6153, 13/21 = 0.6190, 21/34 = 0.6176, 34/55 = 0.6181, 55/89 = 0.6179 and 89/144 = 0.6180

[subbu]

Golden mean is a special irrational number (0.618 or 1.618) which is obtained by dividing any two successive numbers of fibonacci series(0,1,1,2,3,5..) It occurs in all natural phenomena. Anything that is created by nature tend to follow this ratio. Financial market also follow this.

[Sakunthala]

Golden Mean:It is the sum of two previous numbers in the sequence. e.g:0,1,1,2,3,5,8,13,21,34,55,89 will get ratio by dividing the number with the previous one eg:89/55=1.618%.

[Sangeetha Subramaniam]

This ratio was found by Fibonacci which is found as follows.

 

Fibonacci Series: 0 and 1 is the original number and adding the latter with the former in the sequence will a series of numbers. 0,1,1,2,3,5,8,13 and so on.

 

It is interested to note that starting from 6th number in the series, a ration formed between higher and immediate lower number will result in 1.6xx and this value becomes constant (1.618) through out the series with higher order numbers.

 

Eg: 13/8 = 1.6xx, 89/55 = 1.618

[Padmavathi Sukumar]

Golden mean is arrived by dividing a number from the fibonacci series by the previous number from the series. The mean value is always the same.

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