convexity

Meanings

1. 1noununcountabletechnical

   The shape of a surface or line that curves outward, like the outside of a ball.

   Grammar: Usually uncountable: the convexity of the lens.

   Patterns

   • the convexity of something

   The convexity of the mirror makes distant objects look smaller.

   Opticians measure the convexity of each lens before grinding it.

   You can see the slight convexity of the hill from the road.

2. 2noununcountablefinancetechnical

   In finance, a measure of how much the relationship between a bond's price and interest rates curves, used to refine risk estimates.

   Grammar: Uncountable in finance: bond convexity rises with longer maturity.

   Patterns

   • the convexity of something

   Analysts adjusted their forecast to account for the bond's convexity.

   Higher convexity means a bond's price falls less when rates rise than duration alone predicts.

   The fund manager bought long bonds because of their strong convexity.

3. 3noununcountablemathematics

   In mathematics, the property of a shape or function in which any line joining two of its points stays inside or above it.

   Grammar: Uncountable: the convexity of the function is proved in the first lemma.

   Patterns

   • the convexity of something

   The proof depends on the convexity of the function.

   A set's convexity guarantees that its midpoints lie inside it.

   Students test convexity by drawing lines between two points on the curve.

Word forms

Common combinations

bond convexity

Bond convexity helps investors judge risk when rates move sharply.

degree of convexity

The degree of convexity differs between the two lenses.

slight convexity

The table has a slight convexity in its center.

convexity of a function

The convexity of a function guarantees one minimum.

negative convexity

Mortgage securities often show negative convexity.

Synonyms and how they differ

curvature

Curvature is the general amount of bending, in any direction, while convexity specifically means bulging outward.

bulge

Bulge is an informal word for an outward swelling, whereas convexity is the precise, technical term.

roundness

Roundness is an everyday word for being round, while convexity describes the outward curve of a surface.

Opposites

Word family

convex adjective

curving outward, as the outside of a ball

convexly adverb

in a convex or outward-curving way

biconvex adjective

curved outward on both sides, like a magnifying lens

convexness noun

a rarer synonym for convexity

Commonly confused: convexity or concavity?

Practice

Make it your own

Write a sentence using “convexity”, then check it and compare it with the examples above.

Explore more words