Nature does, it seem, favor the golden ratio. But not exclusively so. In my 2004 debunking article in "Devlin's Angle" I inadvertently let yet another falsehood slip in. I claimed there that you can find the golden ratio in the growth of the Nautilus shell. Not so. The Nautilus does grow its shell in a fashion that follows a logarithmic spiral, i.e., spiral that turns by a constant angle along its entire length, making it everywhere self-similar. But that constant angle is not the golden ratio. Pity, I know, but there it is.
It's when you leave the mathematical world and the natural world, however, that the falsehoods start to come thick and fast.
Numerous tests have failed to show up any one rectangle that most observers prefer, and preferences are easily influenced by other factors. As to the Parthenon, all it takes is more than a cursory glance at all the photos on the Web that purport to show the golden ratio in the structure, to see that they do nothing of the kind. (Look carefully at where and how the superimposed rectangle - usually red or yellow - is drawn and ask yourself: why put it exactly there and why make the lines so thick?)
Another spurious claim is that if you measure the distance from the tip of your head to the floor and divide that by the distance from your belly button to the floor, you get GR. But this nonsense. When you measure the human body, there is a lot of variation. True, the answers are always fairly close to 1.6. But there's nothing special about 1.6. Why not say the answer is 1.603? Besides, there's no reason to divide the human body by the navel. If you spend a half an hour or so taking measurements of various parts of the body and tabulating the results, you will find any number of pairs of figures whose ratio is close to 1.6, or 1.5, or whatever you want.
Then there is the claim that Leonardo Da Vinci believed the golden ratio is the ratio of the height to the width of a "perfect" human face and that he used GR in his Vitruvian Man painting. While there is no concrete evidence against this belief, there is no evidence for it either, so once again the only reason to believe it is that you want to. The same is also true for the common claims that Boticelli used GR to proportion Venus in his famous painting The Birth of Venus and that Georges Seurat based his painting The Parade of a Circus on GR.