curvature

noun

Etymology: From Latin curvare, from Latin curvatura. See also curve. Displaced native Old English ġebīeġednes.

1. The shape of something curved.

   “Constructional costs are kept to a minimum by the admissibility of heavy grades and sharp curvature.”

   “In the first of the movie's many striking images, we share his majestic view from the top, the curvature of the planet and the glow of the horizon brilliantly reflected in his helmet.”

2. The extent to which a subspace is curved within a metric space.

   “A turtle drawing an ellipse would have to turn more per distance traveled to get around its “pointy” sides than to get around its flatter top and bottom. This notion of how “pointy something is,” expressed as the ratio of angle turned to distance traveled, is the intrinsic quantity that mathematicians call curvature.”

3. The extent to which a Riemannian manifold is intrinsically curved.