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dc.contributor.authorSharpe, Sheree Taisha
dc.date.accessioned2014-03-04T02:47:52Z
dc.date.available2014-03-04T02:47:52Z
dc.date.issued2007-08
dc.identifier.othersharpe_sheree_t_200708_ma
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/sharpe_sheree_t_200708_ma
dc.identifier.urihttp://hdl.handle.net/10724/24279
dc.description.abstractMotivated by a problem on the 67th William Lowell Putnam Mathematical Competition, we will summarize three different solutions found on a website. This Putman problem is a special case of Sylvester’s four point problem! Suppose four points are taken at random in a convex body; what is the probability that they form a convex quadrilateral? We will see that there exists a relationship among Crofton’s formula, random secants in two dimensions and the solution to this question. We will then present the solution following Kingman [3] to the Sylvester’s four point problem in two and three dimensions for a unit ball by looking at convex bodies in three and four dimensions, respectively.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectCrofton\'s Formula
dc.subjectConvex Body
dc.titleRandom hyperplanes of a convex body, Sylvester's problem and Crofton's formula
dc.typeThesis
dc.description.degreeMA
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorMalcolm R. Adams
dc.description.committeeMalcolm R. Adams
dc.description.committeeTheodore Shifrin
dc.description.committeeEdward A. Azoff


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