DMcG, thanks for putting the "golden ratio" through that preliminary "dissection" for me.

The precise value is found quite easily by solving the simple bit of algebra you quoted, but it involves the square root of five, so it is irrational (mathematically speaking!)

Well! There's that mysterious and irrational "power" of 5 again! ;-)

But before anyone waxes lyrical about the the fact you can add one to one side of the ratio and get the same ratio: of course you can.

Now, that's exactly what I found confusing. I'll just take your word about those "whirling squares" though. My brain cells are whirling at the very idea ...

Amos, thanks for your comments - makes a lot of sense. I'm wondering about this though...

There is nothing scientific about anything to do with symbols. Symbols are elective, non-objective, and have no basis other than human convenience. There is no "external" symbolism in the universe. We invented them (we meaning humans).

This may be splitting hairs a bit, but how can there be nothing scientific about anything to do with symbols, when without those same symbols (numbers, letters, formulae etc) there could be no "science" in the first place? Seems to me that Science itself is totally dependent on symbols.

daylia