Assertion: curvature's curvature | /r/HasProperty | the same
Facets:
value: everywhere
type: LOCATION
value: on a sphere
type: LOCATION
value: due to the symmetry of the curve
type: CAUSE
Source sentences:
text: If L 1 and L 2 are curves whose curvatures, as functions of their respective arc lengths, are the same, then L 1 and L 2 are congruent, that is, they may be superimposed by a motion.
text: Obviously, it suffices to find the curvature of the ellipse at points \(A\left( {a,0} \right)\) and \(B\left( {0,b} \right)\) (Figure \(2\)), because due to the symmetry of the curve, the curvature at the two opposite vertices of the ellipse will be the same.
text: (Note that on a sphere all the normal curvatures are the same and thus all are principal curvatures.)
text: Its intrinsic geometry has positive curvature and that curvature is the same everywhere.
text: If L 1 and L 2 are curves whose curvatures, as functions of their respective arc lengths, are the same, then L 1 and L 2 are congruent, that is, they may be superimposed by a motion.