In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence: 0,1,1,2,3,5,8,13,21... By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.
The patterns in which a tree grows branches, the way water falls in spiderwebs, even the way your own capillaries are formed can all be linked to Fibonacci. Science is just beginning to understand the implications of this simple sequence and some of the most amazing discoveries may be yet to come.
If you use your fingernail length as a unit of measure, the bone in the tip of your finger should be about 2 fingernails, followed by the mid portion at 3 fingernails, followed by the base at about 5 fingernails. The final bone goes all the way to about the middle of your palm, which is a length of about 8 fingernails. Again, it's Fibonacci at work and the ratio of each bone to the next comes very close to the golden ratio.
The ratio of the lengths of the thorax and abdomen in most bees is nearly the golden ratio. Even a cross section of the most common form of human DNA fits nicely into a golden decagon. The golden ratio and its relatives also appear in many unexpected contexts in mathematics, and they continue to spark interest in the mathematical community.
Spiral galaxies show a Fibonacci pattern. Galaxy M51 has two (Fibonacci number) spirals in one direction.
It was applied, most famously, by the architects of the Parthenon, the most influential building in European history. Every classical edifice emulated it, every Renaissance building tried, in doing so, to rediscover the lost harmony of Pythagoras.
The same sequence exists on the leaves of poplar, cherry, apple, plum, oak and linden trees.
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 Fibonacci numbers are found to have many relationships to the Golden Ratio F = (1 + /5)/2, a constant of nature and a value which fascinated the ancient Greeks, appearing throughout Greek art and architecture. One can verify with a hand calculator that the ratio of Fn+1 to Fn is approximated by 1.6180339..., which is the decimal equivalent of the Golden Ratio.
This sequence is constructed by choosing the first two numbers (the "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers.
Leonardo of Pisa (1170-1250), nickname Fibonacci, was born in Pisa, Italy. He made many contributions to mathematics, but is best known by laypersons for the sequence of numbers that carries his name:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...