curvature love

# curvature

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. The act of curving or the state of being curved.
• n. Mathematics The ratio of the change in the angle of a tangent that moves over a given arc to the length of the arc.
• n. Mathematics The limit of this ratio as the length of the arc approaches zero.
• n. Mathematics The reciprocal of the radius of a circle.
• n. Medicine A curving or bending, especially an abnormal one: curvature of the spine.

• n. The shape of something curved.
• n. The extent to which a subspace is curved within a metric space.
• n. The extent to which a Riemannian manifold is intrinsically curved.

### from the GNU version of the Collaborative International Dictionary of English

• n. The act of curving, or the state of being bent or curved; a curving or bending, normal or abnormal, as of a line or surface from a rectilinear direction; a bend; a curve.
• n. The amount of degree of bending of a mathematical curve, or the tendency at any point to depart from a tangent drawn to the curve at that point.

### from The Century Dictionary and Cyclopedia

• n. Continuous bending; the essential character of a curve: applied primarily to lines, but also to surfaces. See phrases below.
• n. Any curving or bending; a flexure.
• n. Something which is curved or bent.
• n. In projective geometry, susceptibility of being cut in two different points by a straight, independently of whether the construct possessing this property has any point at which two straights inclined to one another and lying in this construct might meet. In metric geometry curvature is often used for the measure of curvature or the reciprocal of the radius of curvature.