Fibonacci numbers or Nature's numbering system:
The Fibonacci sequence is named after Leonardo of Pisa,
who was known as Fibonacci (a contraction of filius
Bonaccio, "son of Bonaccio"). Fibonacci's 1202 book
Liber Abaci introduced the sequence to Western European
mathematics, although the sequence had been previously
described in Indian mathematics.
The Fibonacci sequence was well known in ancient India,
where it was applied to the metrical sciences (prosody),
before it was known in Europe. Developments have been
attributed to Pingala (200 BC), Virahanka (6th century
AD), Gopāla (c.1135 AD), and Hemachandra (c.1150 AD).[4]
The motivation came from Sanskrit prosody, where long
syllables have duration 2 and short syllables have
duration 1. Any pattern of duration n can be formed by
adding a short syllable to a pattern of duration n − 1,
or a long syllable to a pattern of duration n − 2; thus
the prosodists showed that the number of patterns of
duration n is the sum of the two previous numbers in the
sequence. Later authors gave algorithms for ranking and
outranking these patterns (e.g. finding the kth pattern
of duration n), and discovered the higherorder
Fibonacci numbers. Donald Knuth reviews this work in The
Art of Computer Programming.[5][6]
In the West, the sequence was studied by Leonardo of
Pisa, known as Fibonacci, in his Liber Abaci (1202)[7].
He considers the growth of an idealized (biologically
unrealistic) rabbit population, assuming that: a
newlyborn pair of rabbits, one male, one female, are
put in a field; rabbits are able to mate at the age of
one month so that at the end of its second month a
female can produce another pair of rabbits; rabbits
never die and a mating pair always produces one new pair
(one male, one female) every month from the second month
on. The puzzle that Fibonacci posed was: how many pairs
will there be in one year?
A
sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181,....This system is first invented by Fibonacci. His full name is Leonardo of Pisa. He soon realized the many advantages of the "HinduArabic" system and introduced it to Europe. The ratio of successive pairs tends to the socalled golden section
(GS)  1.618033989 . . . . . whose reciprocal is 0.618033989 . . . . . so that we have 1/GS = 1 + GS. Fibonacci sequence, generated by the rule f1 = f2 = 1 , fn+1 = fn + fn1 . They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple, flowers, shells, plants, leaves etc.
