Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 702-708.

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Some New Kinematic Formulae and Their Applications

 ZU Du1,2, LI De-Yi2, XIE Feng-Fan2   

  1. 1.School of Mathematics and Information, Pingdingshan University, Henan Pingdingshan 467000|2.School of Science, Wuhan University of Science and Technology, Wuhan 430081
  • Received:2008-04-03 Revised:2009-10-18 Online:2011-06-25 Published:2011-06-25

Abstract:

By Minkowski differences of sets, the containment measures of line segments inside bounded Lebesgue measurable sets are studied and some new integral formulae are obtained. An application to the Buffon's needle problem leads to a new conclusion.

Key words: Integral geometry, Kinematic formula, Containment measure

CLC Number: 

  • 53C65
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