How far into the past was significance ascribed to the Golden Ratio?
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The ancient Greeks discovered great swaths of mathematics by a process I would describe as "playing with shapes and numbers". I think that the golden ratio was discovered in just this fashion—more though playful experimentation than any particular need to be solved.
Παρ' Εὐκλείδη τις ὰρξάμενος γεωμετρεῖν ὡς τὸ πρῶτον θεώρημα ἔμαθεν, ἤρετο τὸν Εὐκλείδην, "τί δέ μοι πλέον ἔσται ταῦτα μανθάνοντι;" καὶ ὁ Εὐκλείδης τὸν παῖδα καλέσας, "δός," ἔφη, "αὐτῷ τριώβολον, ἐπειδὴ δεῖ αὐτῷ ἐξ ὧν μανθάνει κερδαίνειν."
Some one who had begun to read geometry with Euclid, when he had learnt the first theorem, asked Euclid, "What shall I get by learning these things?" Euclid called his slave and said, "Give him threepence, since he must make gain out of what he learns."
So I wouldn't say that it was important, in a historical sense, to the Greeks.
Now in art and architecture I think it took on a life of its own for a time, probably in the late Middle Ages or early Renaissance. But its classical importance has been much overstated in modern times.
I'm not aware of any special religious significance of the golden ratio.
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