wrote in message
ups.com...
K wrote:
So what exactly is the link to Fibonacci - is it that the ratio of
successive terms tends to .618?

Nothing so simple. There is a formula by Jacques Binet which lets you
calculate the n-th Fibonacci number directly rather than by itteration,
based on raising the golden ratio to the power of n. In its own way it
is nearly as remarkable as the Euler identity we started with, as there
is no obvious reason why the two are related. They appear to share
some hidden scaffolding round the back of the universe, one of the best
reasons for stydying maths.


Binet is another of those imortals produced by the Ecole Polytechnique
in Paris. The whole history of 20th century technology appears to
depend on that group of mathematicians (Fourier, Dirac, etc) from the
E-P, of whome Binet is just another.

A friend of mine describes theoretical mathematicians as "mad
toolmakers". They produce shelf after shelf of bizzare contraptions,
with jaws and teeth and ratchets and clamps and wheels in seemingly
pointles juxtaposition. Then, usually a couple of hundred years later,
someone comes into the the shop looking for something to "hold this
just here and twist it like that", and on the shelf somewhere is a
dusty old thing that will do it perfectly.


I know some of them "mad toolmakers" they are called theoretical chemists.
When you track down their background you find they were mathematicians or
physicists who suddenly saw the light and decided Chemistry is fun.