In order to analyze the convariograms of axisymmetric convex domains, taking the regular pentagon as an example, the explicit expression of the covariogram for a regular pentagon is obtained by using the generalized support function. The orientation-dependent chord length distribution function of the regular pentagon is given by using the covariogram. Further, through establishment of a relationship between the covariogram and the kinematic measure, a needle within a regular pentagon is given, when the length of needle does not exceed the side length of the regular pentagon. On this basis, the...
