122. The Golden Ratio!


Nature exhibits many regular patterns, but there is mathematics behind this magic of creation! Many patterns occur with astonishing mathematical precision.

In the beginning of the 13th century, an Italian Mathematician Leonardo Fibonacci discovered one such pattern, popularly known as The Fibonacci Series. It was discovered working on a queer, hypothetical, mathematical problem!

If a pair of rabbits is placed in an enclosed space, and if each pair begets a new pair every month, beginning from the second month, what will be the number of rabbits after one year?

One pair will be born in the second month, one pair in the third month, two pairs in the fourth month, 3 pairs in the fifth month and 5 pairs in the 6th month and so on. This series when written down is 0, 1, 1, 2, 3, 5, 8, 13, 21 etc. Each number occurring after the number 1 is the sum of the two preceding numbers.

The petal like florets in the head of a sunflower form two overlapping spirals. The clockwise spiral has 26 florets and the counterclockwise spiral has 34 florets. Both 21 and 34 occur in the Fibonacci series.

Pine cone has 8 clockwise spirals and 5 counterclockwise spirals. Both 5 and 8 occur in the Fibonacci Series. On the top of a pine apple there are normally 8 spirals in one direction and 13in the other. Both the numbers 8 and 13 are in the Fibonacci Series.

As the Fibonacci Series progresses, the ratio of any number to its predecessor becomes close to 1.62:1. Since the time of the Greeks, this has been known as “The Golden Ratio” — the most aesthetically pleasing ratio.

The Golden Ratio can be seen in the proportions of many classical buildings. Countless artists and architects have made use of this ratio–though they never knew anything about the Fibonacci rabbits or his Series!

We find the Golden Ratio in many everyday articles seen around us. Can you locate some of them?

Visalakshi Ramani

10 Responses to 122. The Golden Ratio!

  1. Arvind Narayanan says:

    Nice article maami.

    Some additional things about the Fibonacci series. Turns out an Indian mathematician called Pingala had done some work on the Fibonacci series way before Fibonacci himself. Pingala was using this, strangely enough in the context of rhyming structures of sanskrit verses. From Wikipedia – “Pingala’s work also contains the basic ideas of Fibonacci number (called mātrāmeru ).” Theres more info on the Web.

    Best wishes

    Arvind

  2. Dear Mr. Arvind,
    Thank you for the useful tip about the ancient Indian Mathematician Pingala. I have done some home work about him. I am sure you will be happy to read my article about him and his highly advance mathematical concepts in “The father of Binary Numerals?”
    with best wishes,
    Visalakshi Ramani.

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