'fan-shaped' originates from Modern English as a compound of the noun 'fan' and the past-participle adjective 'shaped'.

'fan' (the noun) ultimately traces back to Latin 'vannus' (a winnowing fan) via Old/Middle English borrowings, while 'shape' comes from Old English roots meaning 'form' and developed into the Modern English verb and noun 'shape'; these two elements were combined in Modern English to form the compound adjective 'fan-shaped'.

Initially it simply described something 'having the shape of a fan'; over time the phrase has retained that core meaning and is still used to describe objects, patterns, or formations that spread outward like a fan.