View Proposal #186
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| ID | 186 |
|---|---|
| First Name | David |
| Last Name | Romano |
| Institution | Grinnell College |
| Speaker Category | faculty |
| Title of Talk | Connected goalies for convex polygons |
| Abstract | Given a compact convex body K in the plane, call a connected 1-dimensional set G in the plane a goalie if it intersects all the straight lines that intersect K. This talk is concerned with the problem of finding the minimal length goalie for polygons. For any polygon P with n sides, we prove that any shortest goalie G for P has convex hull CH(G) a polygon with at most 2n sides. For triangles T, the minimal length goalie is the Steiner minimal tree for T. This is no longer true in the case of quadrilaterals, in which case a Steiner minimal tree need not be a minimal goalie. |
| Subject area(s) | Convex geometry |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | N |
| Bringing a laptop? | N |
| Overhead Needed? | N |
| Software requests | |
| Special Needs | |
| Date Submitted | 3/10/2007 |
| Year | 2007 |