Indication of Greek Omega
In words derived from Ancient Greek, the circumflex over o often indicates the presence of the Greek letter omega (ω) when the word is pronounced with the sound /o/: diplôme (δίπλωμα), cône (κῶνος). Where Greek omega does not correspond to /o/ in French, the circumflex is not used: comédie /kɔmedi/ (κωμῳδία).
This rule is sporadic, because many such words are written without the circumflex; for instance, axiome and zone have unaccented vowels despite their etymology (Greek ἀξίωμα and ζώνη) and pronunciation (/aksjom/, /zon/). On the other hand, many learned words ending in -ole, -ome, and -one (but not tracing back to a Greek omega) acquired a circumflex accent and the closed /o/ pronunciation by analogy with words like cône and diplôme: trône (θρόνος), pôle (πόλος), binôme (from Latin binomium).
The circumflex accent was also used to indicate French vowels deriving from Greek eta (η), but this practice has not survived in modern orthography. For example, the spelling théorême (θεώρημα) was later replaced by théorème.
Read more about this topic: Use Of The Circumflex In French
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