'Curve' shares its PIE root with 'crown,' 'corona,' and 'crescent' — all things that bend.
A line or outline that gradually departs from being straight for some or all of its length; a smooth, continuous bending; a line on a graph showing how one quantity varies with respect to another.
English 'curve' comes from Latin 'curvus' (bent, crooked, curved), which descends from Proto-Indo-European *ker- (to turn, to bend). This root is one of the most productive in the Indo-European family, also producing Latin 'circus' (ring), Greek 'koronḗ' (anything curved, a crown), and English 'crown,' 'ring,' and 'crisp.' The word entered English first as an adjective in the 15th century; the noun