>Does anything exist without being observed is a philosopical
>issue...

Now you got me confused! Are you here saying that nothing existed before mankinds appearance on earth? What! - not even earth itself... just because there was nobody here to observe it!
Then reason and logic didn't exist before man either? Well what
about the perfectly reasonable and logical relationship between the sun and the moon prior to mans arrival... should that be considered non-existent also!! Oh dear - what thoughts.

>But it's not a (rational) ratio nor a (rational) proportion, its
>name notwithstanding

Who says? I mean, there exist great confusion as to what constitutes a rational number. Some say it can be written as the ratio of two integers p/q. Others say that you can only have a rational if a square root of an integer is an integer itself! Which means for example that integers from 3, 5, and 7 are irrationals, but integers from 9, 25 or 49 are rationals, doesn't
it? But then again, it also means that integer 3 is rational because it can be written 3 = 3/1? And we are told that rationals are those with terminating continued fraction expansions, and those with repeating decimal expansions. We are told that almost all real numbers are irrational, and that the decimal expansion to these numbers do not repeat in equal length blocks!
But they actually do.

If you base rationality and irrationality on how decimal expansions behave, then you will run into all kinds of trouble.
E.g., do you call Prime 499 one thing because it has one kind of decimal expansion, and do you call Primes 239 and 271 something else because their decimal expansions behave differently?
This would smell of prejudice and lack of understanding - would
it not!
All natural numbers(n) of value (i.e. born either directly or
indirectly from zero and one or unity) are interrelated such that
all integers(n) (Primes or otherwise), all roots(n) or fractions
of any kind(n), doubles in value by going through unity as shown
in the simple formula of fraction (n)/(1/n) = 2n. Because of this
common bond and interrelatedness, all natural numbers of value(n)
should hence be termed rational numbers. And all numbers which are man-made non-naturals and therefore without value, and as such are deemed meaningless, as is the case with the present pi(<pi>) and the present e (base of 'natural' logarithms), only these numbers should be called irrational, simply because they carry within them the general meaning of this word as well!

The true value of pi(<pi>) is 22/7 or 3 1/7 (=rational). Yes,
Archimedes was quite right that long ago, and this can now be proven with very little effort. But one suspect that mathematicians are not really ready for this yet perhaps!

As a curiosity only though, the reader can here be given a little
foretaste to this fact:
If we use the Fibonacci series based upon the integers 1, 3, 4, 7, 11, 18, 29,.. etc., we find that the 16th number of this series turn out to be 2207. If we use the ratio of phi (1,618034..), we find likewise that phi to the power of 16 gives us exactly the sum of 2207.
2207 is a Prime number.
Should we add together all the Fibonacci numbers above from 1 to 2207, we get the sum of 5775. 5775 multiplied by .04 gives 231,
which again equals 3 x 77. 2 x 77 equals 22 x 7. If we check the
natural Fibonacci series of 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,..
and add these 10 numbers together, also gives 231. From the same
series as 2207 we find that the 10th number gives us 123.

This of course proves nothing, but the reader must surely admit,
that this new pi of 22/7 do feel a bit nicer and a bit better to
look at, than the present one... especially when it seems, in this harmonious way, to be directly associated with the ABC of
numbers!

>Phi does not become more and more. For, it's a constant

Yes it does become more and more. It becomes endlessly more and more closer to what it in essence already is! The same happens to
square roots. And yes, it's also a constant, but that doesn't
contradict anything?

>Do please post the above to the sci.math newsgroup.
>Listen to what other people have to say

Who! And why?
I'm quite happy listening to what you have to say Mr. Bogomolny.

>Does it also breeding?

Well actually it does, but indirectly only of course, through
being present in the blueprint of living organisms such as the logarithmic spiral of Nautilus Pompilius, the Gnomonic Growth of the Triton Tritonis, marine animals, seed distribution in cactus plants, or sunflowers, or the human body etc. etc.

It is never a good idea to use mean scorn, ridicule and sarcasm,
as by established laws this will always return to the originator.
(Same as hatred and love does)!

Kind regards
Klaus Kastberg.

distribution of leaves around stems