The Golden Ratio and its Mysteries

Why the golden ratio? A prime-dyad model of self-similarity. The golden ratio, about one point six one eight, turns up in sunflower spirals, in quasicrystals, and in the Fibonacci numbers. This video asks a narrower and more precise question. Suppose the basic elements of a theory are irreducible, and must keep their identity under every admissible transformation. Which self-similar scaling ratio can such a system have? Under clearly stated assumptions, the answer is the golden ratio, and only the golden ratio. Along the way, we will be precise about which assumptions carry the weight.