__About Fibonacci__
The
Fibonacci numbers first appeared in a work written
in ancient India sometime between 450 and 200 BC.
The 13th century Italian mathematician Leonardo
Pisano Bigollo described one origin of the series in his work *
Liber Abbaci*.
Leonardo's father's name was Guglielmo Bonaccio. Leonardo was given the
invented name
Fibonacci in the nineteenth century. Fibonacci is
short for "filius Bonacci" latin for
"son of Bonacci".
In
Leonardo's mathematical treatise *Liber Abbaci *
he described a hypothetical problem and its solution as follows. A
pair of rabbits produce another pair in a single
month and at the end of the second month the new
pair also produce a pair of rabbits. This
continues each month for each pair of rabbits. At
the end of the first month there are two pairs of
rabbits, the second month three pair, the third
month five pair, the fourth month 8 pair, the fifth
month 13 pair and so on to create the Fibonacci
series 1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, etc..
In the Fibonacci series each number is equal to the sum of
the previous two numbers. In the Fibonacci game the two rabbits
on a base card illustrate the possibility of the
start of a set.
The
ratio of one number to the prior number as the
series becomes longer approaches an irrational
number known as Phi, which is close to
1.618. For example 13/8 = 1.625 and 144/89 = 1.618.
Phi is
also known as the Golden Ratio or the Divine
Proportion.
The Golden Ratio occurs in nature and across the universe and is
believed to create order in the relationship of one thing to
another. It has been used by architects, sculptors, painters and
designers to create pleasing proportions in their work for many
centuries.
The Fibonacci
numbers appear in nature to an extent not likely due to chance.
For example, the number of petals on different flowers is often
a Fibonacci number.
The Golden Ratio
first appeared in Euclid's *Elements* written around 350
BC. The connection between the Golden Ratio and the Fibonacci
series was first verified in the nineteenth century.
The mathematical
relationship defined by the Golden Ratio is shown in the
diagram.
A great
deal of information is available on the internet about the
Fibonacci series, the Golden Ratio and related matters.
Search with the word
Fibonacci.
The *Fibonacci
Association*, incorporated in 1963, focuses on Fibonacci
numbers and related mathematics, emphasizing new results,
research proposals, challenging problems, and new proofs of old
ideas. Their web site is
www.mscs.dal.ca/Fibonacci/. |