Thing is, Phi&#x27;s not really all that interesting. It&#x27;s just a simple root of a quadratic, no more &#x27;mystical&#x27; than the square root of five. It doesn&#x27;t &#x27;emerge&#x27; from arithmetic the way e or pi do. It&#x27;s a fixed point of the sequence of operations: &#x27;take a number; invert it; add one; repeat&#x27;... that&#x27;s, sort of interesting, but &#x27;add one&#x27; isn&#x27;t a very special operation - why not add 12? or add pi? or add phi?<p>Take a number, invert it, add two, repeat... eventually you get root 2 + 1. And the inverse of that is root 2 - 1! That&#x27;s pretty magical! Kind of more magical than &#x27;half plus root 5 over 2&#x27;, anyway. Maybe root 2 + 1 is the platinum ratio!