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dc.contributor.supervisor Prymak, Andriy (Mathematics) en_US
dc.contributor.author Iurchenko, Ivan
dc.date.accessioned 2012-09-26T17:06:43Z
dc.date.available 2012-09-26T17:06:43Z
dc.date.issued 2012-09-26
dc.identifier.uri http://hdl.handle.net/1993/9155
dc.description.abstract In 1948 Besicovitch proved that an affine image of a regular hexagon may be inscribed into an arbitrary planar convex body. We prove Besicovitch's result using a variational approach based on special approximation by triangles and generalize the Besicovitch theorem to a certain new class of hexagons. We survey the results on the Banach-Mazur distance between different classes of convex bodies. We hope that our generalization of the Besicovitch theorem may become useful for estimation of the Banach-Mazur distance between planar convex bodies. We examined our special approximation by triangles in some specific cases, and it showed a noticeable improvement in comparison with known general methods. We also consider the Banach-Mazur distance between a simplex and an arbitrary convex body in the three-dimensional case. Using the idea of an inscribed simplex of maximal volume, we obtain a certain related algebraic optimization problem that provides an upper estimate. en_US
dc.rights info:eu-repo/semantics/openAccess
dc.subject geometry en_US
dc.subject inscribed hexagon en_US
dc.subject convex en_US
dc.subject Banach-Mazur distance en_US
dc.subject Besicovitch en_US
dc.title Properties of extremal convex bodies en_US
dc.type info:eu-repo/semantics/masterThesis
dc.degree.discipline Mathematics en_US
dc.contributor.examiningcommittee Gunderson, David (Mathematics) Durocher, Stephane (Computer Science) en_US
dc.degree.level Master of Science (M.Sc.) en_US
dc.description.note October 2012 en_US


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