>We know that 'phi' exist in
>nature as 'reality',

Does anything exist without being observed is a philosophical issue which I am sure has been and is being debated till this very day.

>i.e. that
>this ratio and proportion was
>existant long before anybody thought

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

>about us human beings - who,
>incidentally, also to some extent
>are 'based' upon this ratio
>in our build. (Ref. Dürer,Da
>Vinci etc.).

Let them be based on that ratio, which is OK with me. Are they equal to it?

>We know that the ratio's 8/5
>- 55/34 - 377/233 -
>3571/2207 - etc.
>gives phi.

I do not undertsand this. 8/5 is a ratio. 55/34 is a ratio, and so are 377/233 and 3571/2207. And the sequence thus constructed converges to phi. That's OK. But this does not make phi a ratio.

>We know that when
>the fractions progressively increase in
>size, phi becomes more and
>more;

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

>because when a graph
>is drawn and the sums
>of the various fractions are
>plotted along a x-axis, a
>'wavelength' or 'oscillation' is formed
>which more and more
>approaches the x-axis (although never meets
>it) as the size of
>the fractions progressively approaches infinity.

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

>This simply means that the
>ratio 'phi' cannot possibly consist
>of an endless series of
>decimals,

Nonetheless, as any irrational number phi has a decimal represenation which is neither finite nor periodic.

>but must forever alternate
>near its 'shortest' point of
>ratio, which in this case
>would be near
>1.618034..., and alternating on both sides
>of ..034.. e.g.
>..039999...n, and ..0340000...1n. Therefore one can
>confidently say that phi is
>still phi regardless whether it
>manifest itself through the smallest
>or 'largest' fraction, i.e. its
>lowest or highest oscillation as
>plotted!

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

>Hence phi is a 'live' breathing
>ratio and proportion, and therefore
>not 'irrational'??

Does it also breeding?

>Exactly the same scenario applies to
>the square roots.

I understand what you mean, but

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

>47321/33461 should not be seen as
>mere approximation to ?2, as

I wish you all the best.

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

>As I'm not a mathematician

You do not have to state the obvious.

>its
>not for me to give
>proper equations to the square
>roots and their natural progressions

You seem however quite determined about
your viewpoints.

Etc.