Was the golden ratio deliberately used for aesthetics in ancient or Renaissance times?

Question

Everyone has heard of the golden ratio, and that the golden rectangle made in this ratio is somehow the most aesthetically pleasing.

We know that knowledge of the ratio dates back to at least Euclid (300 BC), but he just noted it as interesting in mathematics, not aesthetics. Then, it doesn't seem to really turn up in writing until about 1500, when Italian mathematician Luca Pacioli wrote about it as "the divine proportion."

The story goes that the ancient Greeks used the ratio in art and architecture, and that the Renaissance masters did likewise.

But, on examination, all of the claimed uses only happen if you line things up just so, ignoring whatever inconvenient parts of the painting, building, or sculpture don't line up. And, no one from the time seems to write about it. All of the references that I can find to the golden ratio being used in such and such older work turn out to be modern in origin: someone (sometimes "expert", sometimes not) took measurements and declared them to match the golden ratio to some degree of precision. This appears to never be supported by direct evidence (construction lines, sketches, notes) from the time itself.

Now, one could perhaps buy the idea that, to the ancient Greeks, it was all about secret mysticism, and any texts have been lost. We certainly have lost more from that time than has carried over. But there's plenty of writing on art from the Renaissance — does any of it mention the golden ratio, by Pacioli's name "divine proportion", or by Euclid's term "extreme and mean ratio"?

From what I can tell, the idea that the number was important outside of being interesting in math comes from a guy named Adolph Zeising in 19th century Germany. There's pretty credible evidence that this is pretty much the start of the modern idea.

(More on Zeising: here, here, here, and here.)

But, just because Zeising popularized the idea doesn't mean he's wrong. I'm just coming up empty coming up with anything credible before the 19th century.

Can you?

Answer 1

I think that a lot of the claims are quite believable.

The measurements of the Parthenon are quite objectively due to phi. As you can notice in the image below, all major measurements are strictly related to the golden ratio.

I find way more believable that the Greek would have used some symmetrically pleasing geometric construction, such as phi, to design the Parthenon, than assuming it's a mere coincidence. The figures match to within 5%.

Regarding the Renaissance, the artists that extensively used the golden section during the Reinassance are:

• Leon Battista Alberti (1404-1472)

  

  See this design and the following quote:

  Di questi numeri si servono gli architetti non confusamente e alla mescolata, ma in modo che corrispondano e consentano da ogni banda all’armonia

  What he means is that architects should use integers to scale the various parts. To be honest he never explained how he chose the small integers used in his designs so that the composition was harmonious, but subsequent studies have shown he must have used the golden ration extensively.

• Piero della Francesca (1416-1492)

  A very notable painter, he was also a famous geometer at the time and wrote a book on perspective and proportions which was heavily referenced by Pacioli in his magnum opus. I cannot find an online version but it's cited on Wikipedia (FWIW).

• Luca Pacioli (1445-1517) He literally wrote the book on the golden ratio.