Thursday, 18 May 2017

The Fibonacci Sequence

Named after Fibonacci, also known as Leonardo of Pisa or Leonardo Pisano, Fibonacci numbers were first introduced in his Liber abaci in 1202. The son of a Pisan merchant, Fibonacci travelled widely and traded extensively. Math was incredibly important to those in the trading industry, and his passion for numbers was cultivated in his youth.

Knowledge of numbers is said to have first originated in the Hindu-Arabic arithmetic system, which Fibonacci studied while growing up in North Africa. Prior to the publication of Liber abaci, the Latin-speaking world had yet to be introduced to the decimal number system. He wrote many books about geometry, commercial arithmetic and irrational numbers. He also helped develop the concept of zero.

His calculations first centred on the problem of how many rabbits would be produced by a single fertile pair in one year.  Although his method of calculation relied on a perfect case scenario - that all the rabbits lived for the full twelve months and that each became fertile - the resultant figure of a total of 233 was derived from what is now known as The Fibonacci Sequence.

The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number is found by adding up the two numbers before it.
  • The 2 is found by adding the two numbers before it (1+1)
  • The 3 is found by adding the two numbers before it (1+2),
  • And the 5 is (2+3),
  • and so on!
Example: the next number in the sequence above is 21+34 = 55
It is that simple!
Here is a longer list:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...

A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. Any two successive Fibonacci numbers have a ratio very close to the Golden Ratio, which is roughly 1.618034. The larger the pair of Fibonacci numbers, the closer the approximation. The spiral and resulting rectangle are known as the Golden Rectangle.

The amazing truth is this sequence recurs throughout nature  - in the seed heads of sunflowers, the petals of a rose, in the development of a mollusc's shell, the eye of a hurricane, the curve of a wave, even the spiral of the galaxies. When trees and plants grow, their branches and leaves appear at the exact point of the Golden Ratio, maximising their exposure to the sun. Supercharged photons from the sun's rays give them life through photosynthesis. All life on earth is attributable to the power of our sun - our earth is heliocentric. The spiral of the cochlear in our inner ear follows the Fibonacci spiral.

So were we designed or did we evolve? Fibonacci didn't have the answer to that one. Generations
since have not taught the geometry that comes out of his startling sequence.  The patterns that occur in nature are used to express the beauty of Allah in Muslim art. The Golden Rectangle is present in the Mona Lisa - to those 'in the know' it is a magical formula, aesthetically pleasing and tantalisingly mysterious. So please keep it to yourself...

from beginning
was encrypted to deceive
a written code devised by my forefathers
a means of subjugation, of suppression, devaluation of her value, denying education.
evolving simultaneously with sequential spiral structure equally consequential when the word began.
The unborn foetus spiralled in the womb of every woman, a child of human nature,
I am a wonder of the spiral universe,
the measure of a man
from beginning
I am

Thank you for reading. Adele


Anonymous said...

Very interesting.