Properties of extremal convex bodies
| dc.contributor.author | Iurchenko, Ivan | |
| dc.contributor.examiningcommittee | Gunderson, David (Mathematics) Durocher, Stephane (Computer Science) | en_US |
| dc.contributor.supervisor | Prymak, Andriy (Mathematics) | en_US |
| dc.date.accessioned | 2012-09-26T17:06:43Z | |
| dc.date.available | 2012-09-26T17:06:43Z | |
| dc.date.issued | 2012-09-26 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| 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.description.note | October 2012 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/9155 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| 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 | master thesis | en_US |