What does convexness mean?
Convexness is a noun denoting the quality or state of being convex — that is, curving or bulging outward, like the exterior of a sphere or the outside of an arch. It names the property itself rather than any particular object, so one might speak of the convexness of a lens, a mirror, or a gently swelling wall. The word is formed straightforwardly from the adjective "convex" by adding the suffix "-ness," the same pattern that produces "awareness" or "darkness." Despite this regular formation, it is genuinely uncommon: in mathematics, physics, and economics, where outward curvature matters most, writers almost invariably use the alternative term "convexity." Convexness therefore survives mainly in general descriptive prose, where it conveys the same idea in plain language. Its antonym is concavity, the quality of curving inward. For readers encountering it, the meaning is easy to grasp, but knowing that "convexity" is the standard term helps place this word as a legitimate yet peripheral member of the vocabulary of curvature.
nounThe quality or state of being convex; the degree to which a surface curves outward.
- The quality or condition of being convex; outward curvature of a surface or figure.
"The lensmaker adjusted the convexness of each surface until the image fell precisely into focus."
"The architect praised the subtle convexness of the façade, which caught the afternoon light along its entire curve."
"In optics, even a small change in the convexness of a lens can shift the focal point noticeably."
Mathematicians overwhelmingly say "convexity" — "convexness" is its little-used sibling, built the same way as "awareness" but rarely invited to the party.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of convexness
Convexness derives from the Latin adjective convexus, meaning "arched" or "vaulted," which itself comes from the verb convolvere, "to roll together." The English adjective "convex" was borrowed directly from Latin in the early 17th century, and nouns such as "convexness" were then formed from it using the native Germanic suffix "-ness." Its close relative "convexity" follows the same Latin root via the Latinate suffix "-ity." Other words sharing the Latin origin include "convolve" and "convolution," both reflecting the sense of rolling or winding together.
Related word forms
How convexness is actually used
"Convexness" is a rare word in modern English; writers and scientists almost always prefer "convexity," especially in mathematics and economics. It is formed regularly from the adjective "convex" plus the suffix "-ness," so its meaning is transparent, but it appears chiefly in older or non-specialist prose.
Easily confused with convexness
"Convexity" is the established mathematical and scientific term for the state of being convex, while "convexness" is a rarer variant carrying the same meaning.
"Convex" is an adjective describing an outward-curving shape, whereas "convexness" is the noun naming that property.