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Re: Golden ratio [Was: the real question and answer is]



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Fibs are good, how about binary; or 6 as a base # such as hrs., mins. secs____
another good one to try is base 3( the trinity) GOOD LUCK

UG wrote:

> 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.  =)
>
> --
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