We know that 'phi' exist in nature as 'reality', i.e. that this ratio and proportion was existant long before anybody thought
about us human beings - who, incidentally, also to some extent are 'based' upon this ratio in our build. (Ref. Dürer,Da Vinci etc.).
We know that the ratio's 8/5 - 55/34 - 377/233 - 3571/2207 - etc.
gives phi. We know that when the fractions progressively increase in size, phi becomes more and more; 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. This simply means that the ratio 'phi' cannot possibly consist of an endless series of decimals, 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!
Hence phi is a 'live' breathing ratio and proportion, and therefore not 'irrational'??

Exactly the same scenario applies to the square roots.

47321/33461 should not be seen as mere approximation to ?2, as
in fact 47321/33461 becomes (is) ?2, in the same way that fraction e.g. 9512/6726 becomes (is) ?2 and fractions 114243/80782 - 5017856/3548160 - 17132032/12114176 and e.g.
1550614528/1096450048 becomes (is) ?2, etc. etc.

Likewise the square root of 3, as the fraction e.g. 56813/32801
becomes (is) ?3 in the same way that e.g. 367245/212029 and
3040493371/1755429667 becomes (is) ?3, etc.etc.

Thus it would be in error to assume that square roots consist of endless non-repeating decimal expansions, as this is obviously not the case!
So, it can be said again that the square roots behave in the same
manner as phi, i.e. they are 'alive' - or in other words - their
progressive fractions (or each term) is continually the sum of two preceding ones! This their property of being at the same time
additive and geometrical is a characteristic they share with phi
and its ròle ...in the growth of living organisms. Ergo, the square root of 2 therefore, is not a constant!! (Ref. phi =
1 + ?5/2)!

As I'm not a mathematician its not for me to give proper equations to the square roots and their natural progressions - or
harmoniously ordered or rhytmically repeated proportions or recurrences! This must be left to someone without my sad handicap!

The term "ratio like" I got from one of your colleagues at:
http://www.utm.edu/research/primes/glossary/rational number.html
- ...sorry!

The questions remain: Should phi be considered an irrational number, even though it is 'perfectly' rational? And why should square roots equally be considered irrationel, when they too are
'perfectly' rationel? In fact, why should any whole, natural, real number be considered irrational, when all natural numbers,
whether odds, evens or primes, consist of reciprocal fractions
which all are based upon decimal expansions with repeating equal
length blocks - or repeating root-stems - the only exemptions
being the multiples of 2 and 5?? I.e. all reciprocal numbers
(decimal expansions), mirror or reflect in various modes either 1/2, 1/3, 1/7, 1/9, 1/11 or 1/17 configuarations!

Forget about enlighten me this time, but your comments or views
to the above would nevertheless be greatly appreciated.
With kind regards
Klaus Kastberg