it's the root of a simple equation, x^2 - x - 1 = 0. that is, x^2 - x = 1. this can be solved using the quadratic equation. it can also be expressed as a limit. sure, it's sort of neat that the pattern is easily and intuitively grasped, but there's an underlying theory that makes this connection rather unremarkable.

there's nothing mysterious or divine about this. it's just the root of an equation.