> From: Alberto Monteiro <[EMAIL PROTECTED]> > > David Hobby wrote: > > > > 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... > > > Ok, but in order to prove the reverse of this trivial statement > [namely: if an integer number N can be represented as > a period power series of base x using integer numbers > that are lesser than x for the coefficients ** then ** > x is algebraic] you have a little more work to do. And I don't > know if it's possible; it would require that for each N, > for each algebraic number x, there is a special polynomial > whose root is x.
To much work. But there is a series, that would probably conform to such a set of equations. It is trivial figuring out the entire series.
