The Fool wrote:
>
> > 3*pi*(pi^3 - pi^2) = 2*pi*(pi^3 - pi^2) + 3(pi^3 - pi^2) + pi
> >
> > and pi is a root of a nontrivial polynomial in the rationals.
> >
> > Since pi is transcendental, this is impossible. The
> > argument generalizes...
>
> Aren't you mistaking pi for a variable here? In this case it is the base
> or just
> 3.14159265358979323846264338327950... and not what is being solved for.
This is the meaning of the word "root".
>
> Or we could move away from trancendental numbers if you prefer. How
> about the golden mean instead?
> (sqroot(1.25) + sqroot(.25)) ~=
> 1.6180339887498948482045868343656
> Coincidentally the inverse (1/x) of the golden mean (gm) is
> .6180339887498948482045868343656
No coincidence. The golden mean, phi, is a root of
x^2 - x -1 = 0, which is equivalent to x - 1 = 1/x. Other
algebraic (i.e. not transcendental) numbers will have similar
relationships...
---David
[EMAIL PROTECTED]
