How far into the past was significance ascribed to the Golden Ratio?

Question

I think everyone knows about the golden ratio or the divine proportion (I got to know more about it after reading the wikipedia article on it). It's present everywhere in nature and also in the human body.

When I googled for golden ratio, I found links to a lot of myths behind it. I would like to know how important it was historically. Also are there any religious references?

How did people know about the golden ratio in ancient times? Some of the articles I read were about how important it was to ancient Greeks and other civilizations but none of them talked about how they found it and why they thought its important to use it in everyday life.

Answer 1

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.