We solve the Buffon-Laplace problem of calculating the probability that a "small" convex body T (regular hexagon of constant side) in the Euclidean plane intercepts a line-segment of lenght at least s on a line of the lattice R_a (strips of constant width) and the probability that T intercepts on R_{a,\alpha} (rectangles with constant sides) a line segment of lenght at least equal s on a line of the lattice R_a and (respectively, or) a line-segment of lenght at least equal to $\sigma$ on a line of the lattice R_\alpha.
Intersection of a "small" convex body in a plane lattice
CONSERVA, Vincenzo;
2008-01-01
Abstract
We solve the Buffon-Laplace problem of calculating the probability that a "small" convex body T (regular hexagon of constant side) in the Euclidean plane intercepts a line-segment of lenght at least s on a line of the lattice R_a (strips of constant width) and the probability that T intercepts on R_{a,\alpha} (rectangles with constant sides) a line segment of lenght at least equal s on a line of the lattice R_a and (respectively, or) a line-segment of lenght at least equal to $\sigma$ on a line of the lattice R_\alpha.File in questo prodotto:
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