curvature

plural curvatures

1. countableuncountableThe shape of something curved.

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

   1946 May and June, “Logging Railways”, in Railway Magazine, page 151

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   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.

   2018 October 9, A. A. Dowd, “The Star and Director of La La Land Reunite for First Man’s Spectacular Trip to the Moon”, in The A.V. Club, archived from the original on 16 Jun 2020

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

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   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.

   1980, Harold Abelson, Andrea DiSessa, Turtle Geometry : The Computer as a Medium for Exploring Mathematics, Cambridge, Massachusetts: MIT Press, archived from the original on 26 Jun 2021, pages 13–14

3. countableuncountabledifferential geometryThe extent to which a Riemannian manifold is intrinsically curved.