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    Random hyperplanes of a convex body, Sylvester's problem and Crofton's formula

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    Date
    2007-08
    Author
    Sharpe, Sheree Taisha
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    Abstract
    Motivated 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.
    URI
    http://purl.galileo.usg.edu/uga_etd/sharpe_sheree_t_200708_ma
    http://hdl.handle.net/10724/24279
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    • University of Georgia Theses and Dissertations

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