12. Planar sections of convex bodies

12.1 Barbier and Minkowski formulas

Theorem (formulas of Barbier, 1860 and Minkowski, 1903 for sectional areas). The average area $\bar{A_{s}}$ of an infinitesimal planar section of an isolated three-dimensional convex body in Euclidean space $ℝ^{3}$ is expressed by the following formula (p. 81 of

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Planar sections of convex bodies

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Bibliography

(1) - BAAK (J.P.A.), OORT (J.), BOUW (G.M.), STOLTE (L.A.M.) - Quantitative morphology : methods and materials I. Stereology and morphometry. - European Journal of Obstetrics & Gynecology and Reproductive Biology, Vol. 7, N° 1, pp. 43-52 (1977).
(2) - BADDELEY (A.),...

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