## Fibonacci Numbers in Nature: Study Help

written by: Suvo • edited by: Trent Lorcher • updated: 6/6/2012

This math study guide on Fibonacci numbers explains the different examples of this number presented in nature.

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Fibonacci numbers are named after Leonardo Fibonacci. In 1200, he wrote a book denoting and explaining these numbers. However, Indian mathematician Gopala and Hemachandra were the first to use them 50 years earlier.

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### Concept of the Fibonacci Numbers

The first two numbers of the Fibonacci number series are 0 and 1. Afterwards, the numbers are obtained by adding the previous two numbers like below:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34…..

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### Formula for Calculating (n+1)th Fibonacci Term Directly

We have a straight forward relation for calculating the (n+1)th term of the Fibonacci series as below:

F(n+1)= [(phi)^n – (-phi)^n] / SQRT(5)…………………..1.1

Where,

F(n+1)=(n+1)th Fibonacci series number

Phi = [1+SQRT(5)]/2

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### Golden Ratio

If for the Fibonacci number series you write the ratios of the (n+1)th term to nth term, where n starts from 2, you will get:

1/1=1

2/1=2

3/2=1.5

5/3=1.6666

8/5=1.6

13/8=1.625

21/13=1.615

So, after first few numbers of the Fibonacci number series, this ratio tends to become constant and called golden ratio or golden section or phi and its value is:

Golden ratio (phi) = [1+SQRT(5)]/2 =1.618 (approx.)

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The golden ratio (phi) can be seen in nature. If you observe the middle portion of a sunflower, the numbers of seed in one circle to the next circle follow the golden ratio. It has been said that for a perfect human body, the distance from the naval to foot and from the naval to head follow the golden ratio.