Acta Mathematica Sinica, English Series

, Volume 31, Issue 2, pp 345–352 | Cite as

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.


Convex body flower integral geometry stereology rotational formulae segment support set 

MR(2010) Subject Classification

53C65 52A38 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Departament de Matemàtiques-INITUniversitat Jaume I.CastellóSpain
  2. 2.Departamento de ComputaciónUniversidad de OrienteSantiago de CubaCuba

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