Buffon Problem On Lattice With Asymmetric Fundamental Cell

Buffon throws the needle problem is a earliest geometry probability problem, says it is also that one has the typical maximal effect geometry probability problem in a certain senseBuffon problem comes out already having various extension is:The small needle is thrownrandomly the probability asking the small needle to meet with grid on the flat surface havingthe lattice taking some convex domains as basic area in cloth.Kinematic formulas in integral geometry are integral formulas that represent integrals of geometric functions on the intersection of fixed and moving domains. These formulas can be viewed as integral formulas for various intersection measures. They are useful for solving problems in geometric probabilities.Complex lattice which has the fundamental cell composed by the union of triangle with the angles 30 ,60 and 90 are the research objects in the paper. The paper includes more research in the basis of the promotion of the above. Geometry probability problem becomes more complex because of triangle's asymmetry. In this paper, by using the methods of kinematic measure with generalized support function and restricted chordfunction, we obtain the geometry probability formula of the complex lattice.