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Fibonacci Numbers and The Golden Number

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Masuma Parvin:
If we take the ratio of two successive numbers in Fibonacci's series, (1, 1, 2, 3, 5, 8, 13...) and we divide each by the number before it, we will find the following series of numbers:
1/1 = 1,   2/1 = 2,   3/2 = 1•5,   5/3 = 1•666...,   8/5 = 1•6,   13/8 = 1•625,   21/13 = 1•61538...

  The ratio seems to be settling down to a particular value, which we call the golden ratio or the golden number. It has a value of approximately 1•618034
The golden ratio 1•618034 is also called the golden section or the golden mean or just the golden number. It is often represented by a Greek letter Phi . The closely related value which we write as phi with a small "p" is just the decimal part of Phi, namely 0•618034.

sonia_tex:
Nice post.. :)

tasnuva:
Wow it's great..Thanks for the post :)

Masuma Parvin:
The most common example of the golden ratio is the nautilus shell (see image). As it spirals in on itself, the spirals get smaller and smaller in the same proportion to each other as they do to the whole. You can also see the ratio in things like sunflower petals, and the curvature of fern fronds (see image).

nashid:
Interesting topic.....Thank you for such a nice post.

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