Revision #763 → #1140 · back to history
addedCurvature (intuitive)7f2bc1292cf8
addedCurvature of a curve as rate of change of tangent directione2c56bf3d56c
addedCurvature at a point via osculating circle40f8bfbfcaef
addedMaximal, minimal, and mean curvature for surfaces71219c19ff1c
addedCauchy: center of curvature as intersection of normals751fa9c5f79f
addedCurvature as limit of arc-tangent angle ratiod2f7119016d9
addedCurvature is parametrization-independent86653016aca2
addedArc-length parametrization6855bb84a50d
addedFirst derivative of arc-length parametrization is unit tangent59506280e2c1
addedSecond derivative is the curvature vectorc7ae92f20aaa
addedCurvature as magnitude of second derivative13e99b184262
addedRe-parametrization by arc length5af98daa41c5
addedArc-length parameter455e7e51b62c
addedSame curvature under reparametrization6d1ef13163b8
addedCurvature vector as perpendicular component89a4924fa0af
addedContinuity of curvature under differentiabilityaeb5236f30cc
addedCurvature vector3c124e82bf70
addedProperties of the curvature vectorb910433762e1
addedCurvature vector points toward center of osculating circlea0c1983db4f8
addedTangent and curvature vectors span osculating plane94d54087d81f
addedUnit normal vectorea3b7addc062
addedCurvature vector is parametrization-independent820e08786e5d
addedOsculating circle1d2c600f050c
addedRadius of curvaturebf2517fa81c9
addedCenter of curvaturef010c9f7f4b3
addedCurvature from arc and chord lengthc3930e75aaf9
addedPiecewise curve with differing one-sided derivativesfb1c3d64efe8
addedIndeterminate curvature evaluated via l'Hôpital's rule87a555b80717
addedCurvature of a circle is 1/Rfc6c9eecfa01
addedCircle via standard parametrizationf2ab937d8a5b
addedArc-length parametrization of the circle0a404da4b2f4
addedCircle defined implicitly55e9ad0c8544
addedSigned curvature of a parabola4f2357035514
addedMaximum curvature at parabola's vertex174ceaf73fa6
addedParabola via general parametrizatione33646f68d74
addedParabola defined implicitly18d35b5f6f0d
addedProper parametric representation of a plane curvea79b476942a3
addedCurvature formula for plane curves278e76b3c313
addedCoordinate-free expression of plane curve curvature511aef4480e0
addedSigned curvatureb9469f43dbc7
addedSign of k via orientationd64b1a60bb15
addedCurvature vector as product of signed curvature and unit normalef553b94e8b3
addedCenter of curvature via signed curvature44f1419691a2
addedCurvature of a graph y = f(x)93a7781f8f8a
addedSign of signed curvature equals sign of f''b760ac050a3b
addedSmall-slope approximation by the second derivative6e71108d1b65
addedCurvature of an implicit curve4e1ef7ae38ff
addedSigned curvature undefined for implicit curvesad2aec8f2cda
addedSingular point of an implicit curve813b9e020d7f
addedCurvature in polar coordinates345c12577425
addedCurvature combfd62c65c57be
addedContinuity levels G0–G3d63e7a921c37
addedFirst Frenet–Serret formula83b6333ac456
addedSecond Frenet–Serret formula for planar curves63d163f1a90e
addedFrenet–Serret in general parametrization50ee52380196
addedCurvature of a space curved0180bad4228
addedCross product formula for space curvesa8be4f1888e9
addedNormal curvature, geodesic curvature, geodesic torsion01b47e0728ef
addedDarboux frame315e5fb2ce96
addedPrincipal curvatures and directions72fff72a8598
addedDevelopable surfaceeb3a1d9c9712
addedGaussian curvatureacdd93e8cedc
addedGaussian curvature is intrinsicdba3eb8e4b5c
addedTheorema Egregiumc124e19ac6cd
addedBertrand–Diguet–Puiseux theorem4af2bf3b7ffb
addedGauss–Bonnet theorem6b6c2ac12c93
addedDescartes' theorem on total angular defect90ef5c1fe7bc
addedMean curvaturecea2c1fdf1ad
addedSecond fundamental form1d6af0c28af8
addedPrincipal axis form of the second fundamental form766f7f98329a
addedShape operator6f5c4cfed67f
addedWeingarten equations07617920cf3e
addedPrincipal curvatures as eigenvalues of shape operator4596cc8cda10
addedIntrinsic curvature of higher-dimensional spaceb7e87271cb76
addedFlat space6b57eeb979ed
addedSectional curvature as tidal force4bd09893cddf
addedHolonomyea8ec0882d6a
addedScalar curvature and Ricci curvature369b87f5fac7
addedCAT(k) spaces300d5bd317f1