Chord Length Distribution Of Parallelograms

The convex body has a lot of good nature, and the object possess the convex struction can beseen everywhere in our life, So researchers paid close attention to the convex. Qualitative surveyand analysis of these properties through its unique convex body, such as through a convexbodychord length distribution to examine the reconstruction of the original convex body. Integralgeometry is one method can get good effect in the research.Integral geometry and geometric probability have very deep origin, so probability and analysisare two important tool used in the integral geometry. In the last century German mathemationW.Blaschke formulated the problem of investigation of bounded convex domains in the planeusing probabilistic methods. In particular, the problem of recognition bounded convex domainsD by chord length distribution function. Till recently explicit expressions for the chord lengthdistribution function in the case when D is a dise, a regular triangle（see R.Sulanke,1961）and arectangle(see W.Gille,1988). Following that, Gill,s students have obtained explicit expression ofthe chord length distribution function for any regular polygon. These questions are connectedwith Covariogram Problem.G.Matherom in1986conjectured a positive answer for this problem.In fact, the problem is equivalent to the problem of determining a covex domain from all itsorientation-dependent chord length distributions. So the chord length distribution function is ofuse in proving Matheron guess.Chord length distribution function has spread use in many research area, such as in thechemistry field, building field, reactor physics field, where the function join in an important role.But existing references only got the function about relative regular convex domains, therehaven’t good method for the irregular convex domains. This article analysis the convex at thepoint view of integral geometry, after introducing the two important tools of the generalizedsupport function and chord length distribution function, we get the chord length distributionfunction of the parallelogram by the theory of the integral geometry.