What is the golden ratio?
It is the proportion you get when you cut a line so that the whole line is to the longer part as the longer part is to the shorter. The number that comes out is about 1.618, often written with the Greek letter φ (phi). The Greeks knew it: the earliest surviving definition is in Euclid’s Elements, which calls it cutting a line “in extreme and mean ratio” and uses it to construct regular pentagons. Nothing in Euclid, though, connects it with temples.
Why the claim keeps coming back
The Parthenon looks calm and measured, and a golden rectangle drawn over a photograph of its front seems to fit. The trouble is the choice of rectangle. Should the width run between the outer edges of the corner columns or between their centres? Should the height stop at the top of the columns, at the top of the entablature, or at the peak of the pediment? Each choice gives a different ratio, and a photograph taken from below distorts all of them. With enough freedom, a golden rectangle can be found on almost any building.
What do the real numbers say?
Start from its real measurements. On the stylobate, the top step, the Parthenon is 30.88 metres wide and 69.50 metres long. Divide one by the other and you get 2.25: the length is nine-fourths of the width. That is a ratio of two small whole numbers, nowhere near 1.618, and not close to the square of φ (2.618) either.
What did a survey of Greek buildings find?
The researcher Patrice Foutakis tested the question on the measurements of 15 temples, 18 monumental tombs, 8 sarcophagi and 58 grave stelae, from the fifth century BCE to the second century CE, and published the results in the Cambridge Archaeological Journal in 2014. His conclusion was clear: the golden ratio was absent from Greek architecture of the Classical fifth century BCE and only very rarely used in the third and second centuries BCE. He identified four examples in all, in a tower, an altar, a tomb and a grave stele. None of them is the Parthenon.
What did the Greeks themselves write about proportion?
A great deal, but in other terms. The one ancient treatise on architecture that survives, by the Roman architect Vitruvius, says that a temple must be designed with symmetry and proportion like a well-shaped human body, and gives the body’s proportions as simple fractions: the face a tenth of a man’s height, the foot a sixth. Sculptors thought the same way: the canon of Polykleitos related every part of the body to every other part. Vitruvius never mentions the golden ratio.
A building with no perfect rectangle
There is a further problem for any single “golden” outline: the Parthenon’s main lines are not straight. Its stylobate rises towards the middle, by about 10 centimetres on the north side, its columns swell slightly, and the spacing at the corners is narrower than elsewhere. These optical refinements were built in on purpose, so every rectangle drawn on the building is an approximation to begin with.
The fair verdict is that the Parthenon was designed with care for proportion, in whole-number ratios that its builders could measure and repeat, and then adjusted for the eye. The golden ratio belongs to later readings of the building, and the evidence for it on the Acropolis is missing.
Where to see it
The Parthenon stands on the Acropolis of Athens. To judge its proportions for yourself, look at the east front from a distance and then walk the length of the north side. Opening hours change with the season, so check the official sites before you go.
Sources
- P. Foutakis, “Did the Greeks Build According to the Golden Ratio?”, Cambridge Archaeological Journal 24.1 (2014), 71-86.
- Euclid, Elements VI, definition 3, ed. D. E. Joyce (Clark University).
- Vitruvius, On Architecture 3.1 (LacusCurtius).
- M. Voutyras and A. Goulaki-Voutyra, Ancient Greek Art and Its Legacy, Centre for the Greek Language (2012); J. R. Senseney, The Art of Building in the Classical World (Cambridge University Press), on Stevens’ survey of the stylobate.
- Acropolis Restoration Service (YSMA), “Parthenon”.
