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FIBONACCI CALCULATOR
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The Fibonacci numbers are 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377, 610, 987,… The golden
section numbers are ±0·61803 39887... and ±1·61803
39887... The golden
string is 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ... |
Fibonacci was the “greatest European mathematician of the
middle ages”, his full name was Leonardo of Pisa, or Leonardo Pisano in Italian
since he was born in
Probably Fibonacci is a shortening of the Latin
“filius Bonacci”, used in the title of his book Libar Abaci, which means the son of Bonaccio.
In fact, his father’s name was Guglielmo Bonaccio.
Fi-Bonacci is like the English names of Robin-son and John-son.
But (in Italian) Bonacci is also the plural of
Bonaccio; therefore, two early writers on Fibonacci (Boncompagni and Milanesi)
regard Bonacci as his family name (as in “the Smiths” for the family of John
Smith). Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee]
short for filius Bonacci.
Fibonacci travelled widely in Barbary (
Fibonacci sequence
Fibonacci is perhaps best known for a simple series of
numbers, introduced in Liber Abaci
and later named the Fibonacci numbers
in his honour.
The series begins with 0 and 1. After that, use the
simple rule: add the last two numbers to get the next.
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,
987,... Mathematical competitions and challenges were common.
For example, in 1225 Fibonacci took part in a
tournament at
It was in just this type of competition that the
following problem arose:
Beginning with a
single pair of rabbits, if every month each productive
pair bears a new pair, which becomes productive when they are 1 month old, how
many rabbits will there be after n months?
The Golden Section
A special value,
closely related to the Fibonacci series, is called the golden section.
This value is
obtained by taking the ratio of successive terms in the Fibonacci series:
Ratio of successive Fibonacci
terms
If you plot a graph of these values you will
see that they seem to be tending to a limit.
This limit is
actually the positive root of a quadratic equation (see box)
and is called the golden section, golden ratio or sometimes the golden mean.
Leonardo da
Vinci's drawings of the human body emphasised its proportion.
The ratio of the
distances (foot to navel) : (navel to head) is the Golden Ratio.
Phi and geometry
Phi also
occurs surprisingly often in geometry. For example, it is the ratio of the side
of a regular pentagon to its diagonal.
If we draw in all the diagonals then they each
cut each other with the golden ratio too (see picture).
The resulting
pentagram describes a star which forms part of many of the flags of the world.
The pentagram star
features in many of the world's flags,
including the
There are
also many other Fibonacci’s mathematical studies,
but
this is not the appropriate place to talk too much about that .
Fibonacci in Nature
The rabbit breeding problem that caused Fibonacci to
write about the sequence in Liber Abaci
may be unrealistic, but the Fibonacci numbers really do appear in Nature.
Some plants
develop in such a way that they always have a Fibonacci number of growing
points.
Flowers often have a Fibonacci number of petals,
daisies can have 34, 55 or even as many as 89 petals.
Finally, the sunflower shows the arrangement of the
seeds. They appear to be spiralling outwards both to the left and the right.
There are a Fibonacci number of spirals. It seems that this arrangement keeps
the seeds uniformly packed no matter how large the seed head.
Fibonacci
in Finance (Fibonacci Retracements)
For the precious discoveries of the Pisan mathematician Leonardo Fibonacci, the scholars of the
following centuries, applying the same rules in the financial field , arrived
at conclusions of extremy interest.
As we already saw
above, the sequence of numbers
(1,2,3,5,8,13,21,34,5,89,144 and so on) are obtained adding the last two
to get the next. In finance is used the ratio between any number and the successive,
that is 61.8%. Also the opposite of 61.8% is used , that is 100%-61.8% = 38.2%,
and so on.
Consequently they
obtained the following percentages:
23.6%, 38.2%, 50%,
61.8% , 78.6%
They are used as retracements of a certain change
of trend and in cycles .
Anyway the most used are 38.2% (38%) , 50% and 61.8% (62%).
In fact, when the market changes the trend after a top or a bottom in a
long term cycle or in a short term cycle, usually there are some levels where
the prices stop : these levels are
called retracements . They often
correspond to the above indicated Fibonacci percentages.
Furthermore the
ratio between any number and the previous one is about 1.62 that is used to obtain a target
price value.
An example from
the chart : 121-105=16 ; 16 x 1.62=25.9 ;
105+25.9 = 130.9
Another approach is to add a second copy of the
original Fibonacci grid above or below the first (depending on which way the
market is trending).
This will give you potential price
targets based on adding a new set of 38%, 50% and 62% lines.
That means 138%, 150% and 162%
121-105=16 ;
16x138%=22 ;
105+22=127
121-105=16 ;
16x150%=24 ;
105+24=129
121-105=16 ;
16x162%=25.9 ;
105+25.9=130.9
Best
viewed at a screen resolution of 1024 x 768 pixels
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