> I'm certainly not a math expert, but the formula you give above
> disagrees with the "Golden Ratio" web pages I've visited. The formula
> I see on the web is:   Golden Ratio = ( 1 + sqr(5) ) / 2

Sigh.

The idea of the golden ratio is that it's the number that satisfies the
equation

1/x = x - 1

This is, of course, a quadratic equation, meaning that it has two solutions:
(1+sqrt(5))/2 and (1-sqrt(5))/2. Plug either of these into the above
equation and it is satisfied.

Notice, however, that one of these is the negative reciprocal of the other
one. The useful one is the one that's positive ( (1+sqrt(5)/2 ).

Now, if you have a ratio, taking the reciprocal of that ratio is still
useful; you just have to use it slightly differently in whatever
calculations you do (meaning, divide by it where you would have multiplied
by it and vice versa).

Borge merely took the reciprocal of (1+sqrt(5))/2, which is (sqrt(5)-1)/2
(do the math).

 - Slime
[ http://www.slimeland.com/ ]

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