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Curvature

In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space. Curvature…

History & Measurement

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Overview

History

Curves

Surfaces

Curvature of space

Generalizations

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Map overview Semantic statistics

Curvature

Nodes154
Edges153
Triples129
Avg. degree1.99
Density0.012987
Components1

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Curvature

Top relations

related to References · 29
Curvature → Albert, American Mathematical Monthly, An Intuitive, Braunschweig, Calculus, Calculus Refresher, Casey, Coolidge, Date, Dmitriĭ Dmitrievich, Dover, EMS PressKline, Encyclopedia, Exploring Curvature, Google Books, ISBN, James, JSTOR, Julian, Jun
related to history · 11
Curvature → Apollonius, Aristotle, Euler, Gauss's, Greeks, In Tractatus, Leibniz, Newton, Nicole Oresme, Riemann's, The
related to External links · 8
Curvature → CurvatureCurvature, Curved SpaceThe History, Extrinsic, II Ch, Intrinsic, MathPages, Physics Vol, The Feynman Lectures
related to Gaussian curvature · 8
Curvature → Carl Friedrich Gauss, Euclidean, For, Gaussian, In, It, On, The Gaussian
is a · 7
Curvature → differential-geometric property of the curve, extrinsic measure of curvature equal to half the sum of the principal curvatures, intersection point of two infinitely close normal lines to the curve, intrinsic property of the surface, magnitude of the second derivative of . κ, radius of the circle, same as the sign of the second derivative of f
related to Curvature of space · 7
Curvature → After, By, Euclidean, In, Once, Riemannian, The
related to Curves · 6
Curvature → For, Greek, Intuitively, So, The, Using
related to Mean curvature · 6
Curvature → In, It, Mean, Sophie Germain, The, Unlike Gauss
see also · 6
Curvature → Bonnet, Euclidean, Gauss, Least ActionMean, Principle, Riemannian
related to Generalizations · 5
Curvature → Jacobi, Many, One, The, This

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Important terminology

curve displaystyle vector surface tangent point boldsymbol gamma kappa frac space defined circle left right unit length direction zero plane

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Curvatureis aintersection point of two infinitely close normal lines to the curve0.90text
Curvatureis adifferential-geometric property of the curve0.90text
Curvatureis amagnitude of the second derivative of . κ0.90text
Curvatureis aradius of the circle0.90text
Curvatureis asame as the sign of the second derivative of f0.90text
Curvatureis aintrinsic property of the surface0.90text
Curvatureis aextrinsic measure of curvature equal to half the sum of the principal curvatures0.90text
a soap film has mean curvature zeroinstance ofa minimal surface0.80text
a soap bubble has constant mean curvatureinstance ofa minimal surface0.80text
the sphereinstance ofIn a curved surface0.80text
the area of a disc on the surface differs from the area of a disc of the same radius in flat spaceinstance ofIn a curved surface0.80text
Curvaturerelated to Curvature from arc and chord lengthGiven0.60section

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    Min side: 3
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