PatronDemon, having read the Wikipedia article on the Golden Ratio, I do require now some proof of your horror. The Wikipedia article derives the Golden Ratio from the quadratic solution for x^2 - x -1 = 0 per the definition of self-similarity of line segment ratios. That is also the definition and derivation quoted by the author. The Wikipedia article also lists your continued fraction as an alternate formulation for the same number. Where's the horror?

PatronDemon, having read the Wikipedia article on the Golden Ratio, I do require now some proof of your horror. The Wikipedia article derives the Golden Ratio from the quadratic solution for x^2 - x -1 = 0 per the definition of self-similarity of line segment ratios. That is also the definition and derivation quoted by the author. The Wikipedia article also lists your continued fraction as an alternate formulation for the same number. Where's the horror?