Assertion: curvature | /r/HasProperty | differentiable
Facets:
value: at p
type: TEMPORAL
value: near p
type: DEGREE
value: of the derivative of t(s
type: OTHER
value: for having a tangent
type: CAUSE
value: continuously
type: DEGREE
Source sentences:
text: For being meaningful, the definition of the curvature and its different characterizations require that the curve is continuously differentiable near P, for having a tangent that varies continuously; it requires also that the curve is twice differentiable at P, for insuring the existence of the involved limits, and of the derivative of T(s).
text: For being meaningful, the definition of the curvature and its different characterizations require that the curve is continuously differentiable near P, for having a tangent that varies continuously; it requires also that the curve is twice differentiable at P, for insuring the existence of the involved limits, and of the derivative of T(s).
text: If the curve is given in Cartesian coordinates as y(x), then the radius of curvature is (assuming the curve is differentiable up to order 2):