A concave surface curves inward. The word is easy to remember because a concave indentation in a wall makes a cave. A convex surface curves outward. Like many pairs of antonyms that are relatively rare and similar in sound, these two adjectives are easy to confuse.
Concave and convex are also geometrical terms; a concave polygon has at least one angle greater than 180 degrees, and a convex polygon is made of angles each less than or equal to 180 degrees.
[O]ur resourceful Neanderthal cousins made sinks—or, rather, water basins—out of big rocks that eroded into a concave shape by centuries of rain. [Ottawa Citizen]
Long-sightedness can usually be corrected using convex (thinner at the edge than at the centre) lenses, which make objects appear larger. [Daily Mail]
What about those concave cheeks – are they natural or drug-induced? [Guardian]
Once trigger hairs are tripped by the prey, the plant bends its rubbery leaves into a convex shape, like a tennis ball. [CBC]
Some guys will chase anything that’s concave rather than convex in the appropriate location. [comment on Sydney Morning Herald]
Her contouring had the unfortunate effect of making her forehead look wildly convex, as if a toboggan were trying to emerge from it, fully formed. [Salon]