Comment by jerf

The golden ratio is very mathematically interesting and shows up in many places. Not as prolific as pi or e, but it gets around.

I find the aesthetic arguments for it very overrated, though. A clear case of a guy says a thing, and some other people say it too, and before you know it it's "received wisdom" even though it really isn't particularly true. Many examples of how important the "golden ratio" are are often simply wrong; it's not actually a golden ratio when actually measured, or it's nowhere near as important as presented. You can also squeeze more things into being a "golden ratio" if you are willing to let it be off by, say, 15%. That creates an awfully wide band.

Personally I think it's more a matter of, there is a range of useful and aesthetic ratios, and the "golden ratio" happens to fall in that range, but whether it's the "optimum" just because it's the golden ratio is often more an imposition on the data than something that comes from it.

It definitely does show up in nature, though. There are solid mathematical and engineering reasons why it is the optimal angle for growing leafs and other patterns, for instance. But there are other cases where people "find" it in nature where it clearly isn't there... one of my favorites is the sheer number of diagrams of the Nautilus shell, which allegedly is following the "golden ratio", where the diagram itself disproves the claim by clearly being nowhere near an optimal fit to the shell.