Definition

1. Noun:
   • The property of being curved: The state or quality of having a shape that deviates from being straight or flat.
   • The degree to which something is curved: A measure of the amount of bending in a line or surface.
   • (Mathematics) A precise measure of the rate of change of direction of a curve: The rate at which a curve deviates from being a straight line at a given point.
   • (Medicine) An abnormal bending or curving of a body part: Often referring to the spine.

Usage and Examples

• General Property:
  • The graceful curvature of the bridge is admired by architects.
  • He studied the curvature of the ancient vase.
• Mathematical Context:
  • The formula calculates the curvature of the parabola at its vertex.
  • In differential geometry, curvature is a fundamental concept.
• Medical Context:
  • The X-ray revealed a slight curvature in the patient's spine.
  • Scoliosis is a condition involving lateral curvature of the spine.

Advanced Usage

• "Radius of curvature": (Mathematics) The radius of the circle that most closely approximates the curve at a given point.
  • A smaller radius of curvature indicates a sharper bend.
• "Gaussian curvature": (Mathematics) An intrinsic measure of curvature for surfaces.
  • A sphere has constant positive Gaussian curvature.

Variants and Related Words

• Curve (n/v): A line or outline that gradually deviates from being straight; to bend.
  • The road makes a sharp curve ahead.
• Curved (adj): Having the shape of a curve; bent.
  • The shelf has a curved front.
• Curvilinear (adj): Consisting of or bounded by curved lines.
  • The design featured curvilinear patterns.

Synonyms

• Bend: A curved or angled part of something.
• Arc: A part of the circumference of a circle or other curve.
• Camber: A slightly convex or arched shape of a surface.

Antonyms

• Straightness: The quality or condition of being straight.
• Flatness: The quality of having a level, even surface without curves.

Noun

1. the property possessed by the curving of a line or surface
2. the rate of change (at a point) of the angle between a curve and a tangent to the curve
3. (medicine) a curving or bending; often abnormal
   • curvature of the spine