On Sat, 25 May 2002 01:45:47 -0400, "Slime" <slm### [at] slimelandcom> wrote:

>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).

Yeah, but Benge had declared the following, and I quote:

    "#declare phi = (sqrt(5)-1)/2; // The golden ratio "

This doesn't give Phi, but it's reciprocal, just as you have said
yourself. All the definitions of Phi that I have seen, declare it to
be equal to about 1.618033989... You get that with this formula:

    (1+sqrt(5))/2

The formula (1-sqrt(5))/2 doesn't give the value of Phi. My point was
valid, in that there is a typo here. Did it really screw up his POV
scene? I don't really think so. I assume he treated his declaration of
"Phi" as the reciprocal it really is, and not as actual "Phi", which
it isn't. (I hope that made sense.)



Later,
Glen

7no### [at] ezwvcom     (Remove the numeral "7")

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