|
PureBytes Links
Trading Reference Links
|
Lionel Issen writes:
> Stephen:
>
> Fibonacci is usually translated as discussing the rate of increase in rabbit
> population, starting with 2 rabbits (male and female) and the rabbits have
> to be one month old to breed. the ratio of population increase rapidly
> approaches the Fibonacci ratio.
Just to add a little to this...
Phi, the golden ratio, is defined as the ratio of 2 numbers (x and y), such
that the ratio of y to x is the same as (x+y) to y; i.e., the larger to the
smaller is the same as the sum to the larger. Its mathematical value is
(sqrt(5) + 1) / 2
There's a close relationship of phi to the fib numbers. The ratio of fib(x)
to fib(x-1) (that is, a fibonacci number to the fibonacci number preceding it)
approaches phi as x approaches infinity. In fact, take *ANY* 2 integers, and
start a fibonacci sequence with them, and you get the same result.
For example, start with 100 and 3.
100 3 103 106 209 315 524 839 ... take any of those, divide by the one to
its left and you get a better and better approximation of phi.
Also, fib(x) = phi^x / sqrt(5) <-- closed form fibonacci formula.
It has all sorts of wacky properties; phi^2 = phi + 1; 1/phi = phi - 1
The Greeks knew that this ratio was sacred, or at least very special; the
ratio of width to height on many of their buildings is this ratio.
Statistically large samples of people, when asked to choose a rectangle that
was most pleasing to them from a sample of rectangles of all w/h ratios and
sizes, choose the golden ratio rectangles by a very large margin. (I think
the exact curve is damn near a perfect bell curve.)
The golden ratio appears in a pentagram in dozens of places.
Anyway, I know a lot of people are trying to find all sorts of magic formulas
with fibonacci numbers for the market, and while I don't PERSONALLY believe
they have much merit, if I did, I'd look more at how it relates to Phi.
But as Dennis Miller would say, that's just my opinion; I could be wrong. =)
--
========================================================================
My name is not Dr. Death. -- Bart Simpson
http://www.unixgeek.com/cgi-bin/motd.pl - PGP email preferred
|