What does convex mean?
Convex describes something that curves or bulges outward, like the exterior of a ball, a dome, or the back of a spoon. It stands in direct opposition to concave, which describes surfaces that curve inward. Though familiar from everyday objects — convex mirrors on cars widen the driver's field of view, and convex lenses focus light — the word carries particular weight in mathematics, where a convex set is one that contains every straight line drawn between two of its points, and where convex functions have the useful property of a single global minimum. Derived from the Latin verb convolvere, 'to roll together,' it entered English in the early seventeenth century alongside its counterpart concave. Precise and technical in register, convex is essential vocabulary for anyone studying geometry, physics, economics, or optimization.
adjectiveCurving or bulging outward, like the exterior of a circle or sphere; having a surface or boundary that curves away from the interior. In mathematics, describes a set or shape in which any line segment joining two points lies entirely within it.
- (Of a surface or shape) curving or bulging outward.
- (Mathematics) Of a set or function: containing all line segments between any two of its points, or curving consistently upward (a convex function).
- (Of a mirror or lens) Having an outwardly curved reflecting or refracting surface.
"The convex surface of the lens bent the light inward toward a single focal point."
"A convex mirror on the side of the car gave her a wide view of the traffic behind."
"In optimization, minimizing a convex function guarantees a single global minimum."
The word 'convex' and 'concave' come from the same Latin root meaning 'to roll' — one rolled up into a mound, the other hollowed out like an arch.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of convex
The word convex derives from the Latin convexus, past participle of convolvere, meaning 'to roll together or round.' It entered English in the early seventeenth century, largely through scientific writing, paired with its natural opposite concave (from cavus, 'hollow'). It shares its root with other verbs built on the Latin volvere, 'to roll,' including evolve, involve, revolve, and convolve.
How convex is actually used
Primarily a technical and formal term, common in geometry, optics, economics, and mathematics; rarely used casually outside those fields. The stress falls on the second syllable.
Easily confused with convex
Concave means curving inward like the inside of a bowl, whereas convex means curving outward like the outside of a dome.