Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (2): 410-414.

• Articles • Previous Articles     Next Articles

On Buffon Problem for Bounded Lattices in E3

 XIE Feng-Fan, HU Shi-Geng   

  1. School of Mathematics and Statistics, Huazhong University |of Science and Technology, Wuhan 430074
  • Received:2008-11-15 Revised:2009-10-09 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    华中科技大学博士后专项基金(0128011005)资助

Abstract:

Two new concepts, the restricted chord function and the restricted chord projection function, both referring to the convex body in En, were  introduced in Reference[1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex body in En,  were established based on these concents and a discussion was given with respect to right parallelepiped domain in E3. In this paper, by using restricted chord projection method, the authors could solve Buffon needle problem for three kinds of bounded lattices in E3

Key words: Random segment, Kinematic density, Kinematic measure, Integral geometry

CLC Number: 

  • 53C65
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