Fibonacci Sequence

Everyone knows that math is basically a language. But, what many people don’t realize is that math occurs in nature more frequently than just the number of leaves on a given plant or flower. There is an equation to it, it is not random! Early Indian and Greek scientists, artists, architects and mathematicians recognized and utilized this basic formula in their designs and work. It’s called, The Golden Ratio, and is often represented by the Greek letter Φ (Phi). The equation is: a + b/a = a/b = Φ ≈ 1.625. The Fibonacci sequence is as simple as 1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5, 5 + 3 = 8, and so on. The resulting sequence of prime numbers is this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…. Because it starts small and “grows” outwardly proportionately, it was given a visual representation of a spiral, in particular the Nautilus shell spiral, which is also another name the Fibonacci numbers go by, The Golden Spiral.

The Golden Spiral

The Nautilus shell is an example of the Fibonacci sequence at work in nature, so it’s no coincidence for the representation. Plants, leaves, seed growth, petal arrangement, pine cones (grows in a double spiral), fruit, vegetables, insect and animal reproduction.

The Golden Spiral as found in Nature

The Golden Ratio has been used by architects and artists of the past, (there is a debate that Da Vinci may have used it), as it was used by architects of Greek and Roman structures, and by Renaissance builders seeking “perfection” in their designs. The thought being, if it is found in nature, is beautiful in nature, then the formula may also work to

The Great Mosque at Uqba, also known as the Kairouan Mosque.

make buildings functional and beautiful, and it was a fad. (sorry a joke) The Parthenon is an example of The Golden Ratio in use, the Great Mosque at Uqba also utilizes the ratio, and an even earlier example is The Great Pyramid (also known as the Pyramid of Khufu or Cheops).

The Great Pyramid of Khufu or Cheops

A side note on the person named Fibonacci (though oddly, he went by many names). He was an Italian mathematician born in the 12th century, and most noted for publishing a book, “Liber Abaci”, in which he promoted the use of Arabic numerals (0-9 and the decimal placement). He stated the practical advantage of this math system in all aspects of business. Not surprisingly, it was a big influence in Europe. In this same book, he introduced the (Fibonacci) number sequence to the West, as it was already in use by mathematicians in the East as early as the 6th century.

There’s been resurgence in interest of The Golden Ratio or the Fibonacci number, (nothing new under the sun). The modern artist, Mondrian, utilized the Golden Rectangle,  (scientists aren’t always that creative in naming things). As well as, the modern architect and designer, Le Corbusier, utilized the Golden Ratio in his creations.

Golden Rectangle by Mondrian

Home designed by Le Corbusier

Just like their Renaissance predecessors, artists, photographers and poets are trying their hand at utilizing the ratio in their works. Some is experimental at best, though some works are quite thoughtful. Fibonacci Poems are quite similar to Haiku.  Instead of Haiku’s 5, 7, 5 syllable sequence, one uses 1, 1, 2, 3, 5, 8, 13, etc. I’ve only seen them go to about 34, but one could go on in the sequence, as long as the reader isn’t too bored. Here is an example of a poem using the Fibonacci number sequence that I wrote (experimental):

Two sides,
Love and Happiness,
Or Hell on Earth for all others.

In the near future, I plan to experiment with the Golden spiral in my art and photography. I hope you learned something, were inspired to research and learn more, and that you will try to see the Golden Ratio around you in nature, and maybe even try to create something utilizing it.

Crop circles in England

Here’s a math site meant to be used by parents to help teach their children about Fibonacci numbers found in nature. It’s very simple, easy to understand and has short lesson activities to assist in understanding.   *(sorry, you’ll have to cut and paste, as it’s not accepting my tags!)

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1 Response to Fibonacci Sequence

  1. Pingback: Fibonacci numbers: Mathematical proportions found in nature. | James Minshall

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