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DISTRIBUTIONS OF GEOMETRICAL ELEMENTS
DISTRIBUTIONS OF POINTS IN EUCLIDEAN SPACE
The largest interval on a line
2 other sections not shown
axis centre characteristic function chord of C1 circle of radius consider convex figure convex region corresponding covered Crofton's curve defined Deltheil diameters direction cosines distance distributed at random domain equal equation Euclidean space expected number fixed number formula geometrical probability given gonal Hence infinitesimal integral invariant Jacobian joint distribution lattice points Lebesgue measure line of curvature lines intersecting M. G. KENDALL matrix mean free path mean value method needle non-overlapping number of intersections number of points obtained orthogonal orthogonal matrix particles perimeter perpendicular point inside Poisson distribution Poisson field Poisson variate polar coordinates prob probability density probability distribution probability measure problem random chord random intervals random lines random points random variable rectangle rotation ſº solid angle sphere square stars Suppose theorem theory three dimensions three-dimensional three-dimensional space tion transect transformation triangle uniformly distributed variance zero