Definition

1. Noun:
   • The property of being convex: "Convexness" refers specifically to the geometric characteristic of a shape or surface that curves outward or bulges outward, like the exterior of a sphere or a dome. It is the state or quality of having a surface or outline that is curved like the exterior of a circle or sphere.

Examples of Usage

• Noun:
  • The convexness of the lens helps to focus light.
  • Mathematicians study the convexness of polygons and other shapes.
  • The gentle convexness of the hill made it easy to climb.

Advanced Usage

• In mathematics and geometry: "Convexness" is a formal property used to describe sets, functions, and shapes. A set is convex if the line segment between any two points in the set lies entirely within the set.
  • The proof relies on the convexness of the feasible region.

Variants and Related Words

• Convex (adj): Having a surface or shape that curves outward.
  • A convex mirror provides a wider field of view.
• Convexity (n): A more common synonym for "convexness," often used in technical contexts like mathematics, finance, and optics.
  • The bond's price is affected by its convexity.
• Concaveness (n): The opposite property; the quality of being concave, or curving inward.

Synonyms

• Convexity: The state of being convex (the most direct synonym).
• Bulge: A rounded swelling or protuberance (describes the effect, not the abstract property).
• Curvature: The degree to which a surface is curved (a related, more general term).

Antonyms

• Concaveness: The property of being concave.
• Concavity: The state of being concave.

Noun

1. the property possessed by a convex shape