Editing Golden ratio (section)

===The Parthenon===
[[File:The_Parthenon_in_Athens.jpg|thumb|280px|Many of the proportions of the [[Parthenon]] are alleged to exhibit the golden ratio, but this has largely been discredited.{{sfn|Livio|2002|pp=[https://archive.org/details/goldenratiostory00livi/page/74 74–75]}}]]

The [[Parthenon]]'s façade (c. 432 BC) as well as elements of its façade and elsewhere are said by some to be circumscribed by golden rectangles.<ref name=Polemic /> Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, [[Keith Devlin]] says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation."<ref name=mathinstinct /> [[Midhat J. Gazalé]] affirms that "It was not until Euclid ... that the golden ratio's mathematical properties were studied."<ref name=gazalé />

From measurements of 15 temples, 18 monumental tombs, 8 sarcophagi, and 58 grave stelae from the fifth century BC to the second century AD, one researcher concluded that the golden ratio was totally absent from Greek architecture of the classical fifth century BC, and almost absent during the following six centuries.<ref name=foutakis />
Later sources like Vitruvius (first century&nbsp;BC) exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.