Measure of segments which intersect a convex body from rotational formulae |
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Authors: | Ximo Gual-Arnau Silena Herold-García |
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Institution: | 1. Departament de Matemàtiques-INIT, Universitat Jaume I. 12071-Castelló, Spain;
2. Departamento de Computación, Universidad de Oriente. 90900-Santiago de Cuba, Cuba |
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Abstract: | 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. |
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Keywords: | Convex body flower integral geometry stereology rotational formulae segment support set |
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