Assertion: curvature | /r/HasProperty | circle
Facets:
value: for the metric
type: CAUSE
Source sentences:
text: In 1939 Schmidt proved that the classical isoperimetric inequality for curves in the Euclidean plane is also valid on the sphere or in the hyperbolic plane: namely he showed that among all closed curves bounding a domain of fixed area, the perimeter is minimized by when the curve is a circle for the metric.
text: the curvature is that of a circle with radius \(\approx
text: In 1939 Schmidt proved that the classical isoperimetric inequality for curves in the Euclidean plane is also valid on the sphere or in the hyperbolic plane: namely he showed that among all closed curves bounding a domain of fixed area, the perimeter is minimized by when the curve is a circle for the metric.