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.
Alberto Monteiro
