Poincare And Blaschke Translative Kinematic Formulae In The Plane

In this paper, we follow Zhou’s method of containment measure and obtain the Poincare kinematic formula and the Blaschke fundamental kinematical formulae for the planar transla-tive group in integral geometry. Then drive a sufficient condition for a planer convex body to contain or to be contained in another convex body by a translation. As an application of this sufficient condition, we give a simplified proof of the classical isoperimetric inequal-ity, Bonnesen’s isoperimetric inequality and Minkowski’s inequality by following the idea of containment measure of Zhou Jiazu.