Measure of segments which intersect a convex body from rotational formulae
Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in ℝ3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.
KeywordsConvex body flower integral geometry stereology rotational formulae segment support set
MR(2010) Subject Classification53C65 52A38
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