超平面偶與凸體相交的幾何概率.pdf

1、華中科技大學(xué)碩士學(xué)位論文超平面偶與凸體相交的幾何概率姓名：趙江甫申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：謝鵬20100524AbstractInthispaperwesummarizethedevelopmentofintegralgeometrygeometricprobabilitylookfwardtothefutureofintegralgeometry.Thenweintroducetheconceptsproperties

2、ofconvexbodypairsofhyperplanesquermassintegralegeometricprobability.Wehaveknownthefactthatonthesurfacethegeometricprobabilityofwhichpairsoflinesareintersectingwithaconvexbodythepointsofintersectionareinthesameconvexbodyc

3、ouldberepresentedbytheperimeterareaoftheconvexbody.Inparticularthisprobabilityvalueisconstantwhentheconvexbodyisadisk.Thisisabeautifulresult.ThencouldweextendthisresulttondimensionalEuclideanspaceThisisthemainproblemwhat

4、wewilldiscuss.Webeginbyusingthemovingthogonalframesmethodtogetakinematicdensityfmulaflinearspaceinsolvingthisproblem.Onthebasisofthisfmulaweobtainthekinematicdensityfmulafpairsofintersectinghyperplanes.Thenwestudythesefm

5、ulasthroughtheconceptpropertyofquermassintegraleasaresultwerespectivelyfindoutthemeasureofpairsofhyperplanesintersectingwithaconvexbodythemeasureoftheirintersectionmeetingthesameconvexbody.Consequentlywecan’tonlysolvethi

6、sgeometricprobabilityproblembutalsodrawaseriesofrelevantinferences.Obviouslytheseconclusionscouldenrichtheintegralgeometrygeometricprobabilitythey.Meanwhiletheprobabilitythatpairsofintersectinglinesintersectatapointinaco

7、nvexbodyinthendimensionalEuclideanspaceisalsodiscussedinthispaper.Indiscussingthisproblemwestartwiththekinematicdensityfmulafpairsofintersectinglinesbyusingthemovingthogonalframesmethodinthesameway.thenwecalculatetherele