Fibonacci Numbers

Leonardo of Pisa also known as Leonardo Bonacci or Fibonnaci was an Italian Mathematician from Pisa who is popular for having introduced the Hindu-Arabic numeral system to Europe; he is also known to have introduced to the western world a unique set of numbers commonly known as Fibonacci numbers. Leonardo was born in 1170 to an Italian Merchant father known as Guglielmo, who was also doubled as a customs official. Because of the nature of his business, Guglielmo travelled a lot, taking the young Leonardo with him in most of his trips. It is during these trips that the young Leonardo came to learn about Hindu-Arabic numeral system and its benefits; he came to discover that unlike the Roman numerals in use at that time, the Hindu-Arabic system allowed easy calculation. He documented this finding through his book Liber Abaci (The Book of Calculation or the Book of Abacus).

Fibonacci numbers are a set of numbers that are sequenced in such a manner that each number is a sum total of the preceding two numbers. Fibonacci numbers, commonly denoted as fn, begin from 0, then, 1 and then proceed in the following manner; 0,1,1,2,3,5,8,13,21….

One interesting bit about Fibonacci numbers is how surprisingly they appear in nature and art; like for instance the numbers of petals in a flower are Fibonacci, or the numbers of spirals in a pineapple or a sunflower are Fibonacci. The occurrence of Fibonacci can also be witnessed in art and architecture.

If you take a perfect rectangle and sub-divide it into smaller squares based on Fibonacci sequence numbers, and draw an arc to cut across the subdivided rectangles, the arc would form a spiral like shape better known as a ‘Fibonacci spiral.’ This spiral like shape or a Fibonacci spiral if you like can be noticed on sand-dunes, pine-cone surfaces, the growth of an embryo, the nautilus shell, the star fish, and so on. What makes the Fibonacci numbers even more fascinating is the fact that even the spirals of the galaxies in the sky are formed with the exact design of a Fibonacci spiral.

A similar concept to the Fibonacci numbers concept is the golden mean also known as the golden ratio or divine proportion. The Golden Mean is the ratio of a line segment split into two pieces of different lengths such that the ratio of the entire segment to that of the longer segment is equivalent to the ratio of the longer segment to the shorter segment. The value of the golden ratio is approximately equal to 1.618 and is denoted by the Greek letter phi ϕ. It is believed that the Golden Ratio can be found in the dimensions of the Pyramids at Giza and a host of Renaissance buildings.

How the Fibonacci sequence seems to underlie virtually every element of nature is mystical as it is fascinating, almost like it’s trying to reveal something behind the theory of creation. This is probably the main reason why it is referred to as nature’s secret code or nature’s universal rule. There are sources which contradict the notion that the Fibonacci sequence was discovered by Leonardo of Pisa and instead attribute the discovery to ancient Sanskrit texts which first mentioned it around the 6th century.

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