convexness

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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

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