Definition

1. Noun:
   • A shape that curves or bulges outward: "Convexity" refers to a form or outline that is curved like the exterior of a sphere or circle.
   • The property of being convex: "Convexity" is the quality or state of having a surface or line that curves outward.

Examples of Usage

• Noun:
  • The convexity of the lens helps to focus the light. (The outward curve of the lens helps to focus the light.)
  • He studied the convexity of the dome's architecture. (He studied the outward-bulging property of the dome's architecture.)

Advanced Usage

• Mathematical/Technical Context: In mathematics and optics, "convexity" precisely describes a set of points or a surface where any line segment joining two points lies entirely within the set or on the surface.
  • The convexity of the function is crucial for optimization.
• Financial Context: In finance, "convexity" is a measure of the curvature in the relationship between bond prices and bond yields.
  • Bond investors analyze duration and convexity to assess interest rate risk.

Variants and Related Words

• Convex (adj): Having an outline or surface curved like the exterior of a circle or sphere.
  • A convex mirror provides a wider field of view.
• Convexly (adv): In a convex manner; with an outward curve.
  • The surface bends convexly.

Synonyms

• Curvature: The fact of being curved or the degree to which something is curved.
• Bulge: A rounded swelling or protuberance that distorts a flat surface.
• Protuberance: A thing that protrudes from something else; a bulge.

Antonyms

• Concavity: The state or quality of being concave (curving inward).
• Hollow: A hole or depression in something.

Noun

1. a shape that curves or bulges outward
2. the property possessed by a convex shape