Is the golden ratio really used in art and architecture?

Sometimes, but far less than popular accounts suggest. The best-known claims, that the Parthenon, the Great Pyramid and Leonardo da Vinci's drawings were built on the golden ratio, are not supported by measurement or by historical records. Some artists and architects have used the ratio on purpose, and a few ancient Greek structures appear to have used it, but these are exceptions. [1] [2]

Patrice Foutakis examined measurements of 15 temples, 18 monumental tombs, 8 sarcophagi and 58 grave stelae from the fifth century BC to the second century AD. He found the golden ratio totally absent from Greek architecture of the fifth century BC and only very rarely used in the third and second centuries BC. He identified four rare examples: a tower, an altar, a tomb and a grave stele. According to [cambridge.org](https://www.cambridge.org/core/journals/cambridge-archaeological-journal/article/abs/did-the-greeks-build-according-to-the-golden-ratio/CB9C3B841188FF449BD7DCC1E0C566B1), this was the first clear evidence of the ratio in ancient Greek construction. [3]

For the Parthenon, a review in the Notices of the AMS gives its length, width and height as about 228 feet, 101 feet and 45 feet. The obvious ratios come to roughly 2.25, far from 1.618. Mathematician George Markowsky argues that the Parthenon is not a clean rectangle, so a measurer can choose dimensions to fit. A paper in PubMed Central adds that the idea that the Parthenon and the pyramids used the ratio dates to the mid-nineteenth century, with no mention in classical manuscripts. Many diagrams of a golden rectangle on the Parthenon include empty air above the building or omit steps below it. Markowsky also notes that the Great Pyramid is only approximately a golden pyramid, and that the only record suggesting intent is by Herodotus, written about 2000 years later and inaccurate in several details. [4] [1] [2]

Luca Pacioli completed De Divina Proportione in 1498 (it was printed in 1509), with illustrations of polyhedra by Leonardo. Despite the popular story, Pacioli did not argue that the ratio was the secret of beauty, and Leonardo was an illustrator rather than a co-author. Leonardo knew of the concept but does not mention it in his notebooks or proportional drawings, and the PubMed Central paper concludes he is unlikely to have tied it to beauty. [2]

Mathematician Keith Devlin's column takes a more cautious line on the Vitruvian Man, The Birth of Venus and Seurat's Parade de cirque: there is no concrete evidence against the claims, but none for them either. Markowsky says overlays on paintings often use thick lines and arbitrary placement, and that rectangles on Leonardo's old-man drawing are too roughly drawn to be called golden. [5] [1]

Devlin lists Paul Serusier, Juan Gris, Gino Severini and Salvador Dali as painters who did use the ratio, apparently experimenting with it for its own sake. Dali's The Sacrament of the Last Supper is on a golden-rectangle canvas and features a dodecahedron. The 1912 Cubist exhibition called Section d'Or showed no art involving the ratio. Le Corbusier advocated and used it, but Devlin finds no foundation for claims that the United Nations Secretariat building is based on golden rectangles. Markowsky also notes that the ratio's mystical reputation has led to its intentional inclusion in later works. [5] [1]

The claim that the golden rectangle is the most beautiful is also weak. In Fechner's 1860s experiment, 76% of participants chose one of three medium-proportioned rectangles, and later studies have shown little preference for the golden ratio. [1]