  A Bonnesen-type inequality is a sharp isoperimetric inequality that includes
an error estimate in terms of inscribed and circumscribed regions. A kinematic
technique is used to prove a Bonnesen-type inequality for the Euclidean sphere
(having constant positive Gauss curvature) and the hyperbolic plane (having
constant negative Gauss curvature). These generalized inequalities each
converge to the classical Bonnesen-type inequality for the Euclidean plane as
the curvature approaches zero.
