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Sunday, May 18, 2008

Examples of Fibonacci Numbers in Nature

In mathematics, the limit of Fibonacci series is called as Golden Ratio. This ratio is approximately equal to 1,618. In nature, one can come across this ratio in many areas of art and science.


I kept on researching over it on the net and wanted to see them by naked eyes. Everything I read was completely true and the realm was really amazing. This is a list of Fibonacci numbers in nature. I believe that some of the facts will astonish you.

The distribution of seeds in sunflower is spiral. The seeds of the sunflower spiral outwards in both clockwise and counterclockwise directions from the center of the flower. The number of clockwise and counterclockwise spirals are two consecutive numbers in the Fibonacci sequence.

The shells of the snails follow the Fibonacci sequence. In the same way, the shells of the nautilus follow the same rule. The only difference between these two is that nautilus' shells grow in a three-dimensional spiral, whereas snails' shells grow in a two-dimensional spiral.

Pine cones are one of the well-known examples of Fibonacci sequence. All cones grow in spirals, starting from the base where the stalk was, and going round and round the sides until they reach the top.

Another notable example is human body.In human body, the ratio of the length of forearm to the length of the hand is equal to 1.618, that is, Golden Ratio. Another well-known examples on human body are:

  1. The ratio between the length and width of face
  2. Ratio of the distance between the lips and where the eyebrows meet to the length of nose
  3. Ratio of the length of mouth to the width of nose
  4. Ratio of the distance between the shoulder line and the top of the head to the head length
  5. Ratio of the distance between the navel and knee to the distance between the knee and the end of the foot
  6. Ratio of the distance between the finger tip and the elbow to the distance between the wrist and the elbow

The same sequence exists on the leaves of poplar, cherry, apple, plum, oak and linden trees.

Original here

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