View Proposal #467
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| ID | 467 |
|---|---|
| First Name | Christopher |
| Last Name | Frayer |
| Institution | University of Wisconsin - Platteville |
| Speaker Category | faculty |
| Title of Talk | Geometry of Polynomials with Three Roots |
| Abstract | Given a complex-valued polynomials of the form p(z)=(z-1)^k (z-r_1 )^m (z-r_2 )^n with k,m,n in the natural numbers and r_1 and r_2 on the unit circle, where are the critical points located? The Gauss-Lucas Theorem guarantees that the critical points of such a polynomial will lie within the unit disk. We will further explores the location and structure of these critical points. Surprisingly, when m≠n, the unit disk contains two `desert' regions in which critical points cannot occur, and each c inside the unit disk and outside of the desert regions is the critical point of exactly two such polynomials. Special attention will be given to the development of geometric intuition and using GeoGebra to provide graphical illustrations. |
| Subject area(s) | |
| Suitable for undergraduates? | Y |
| Day Preference | SaturdayStrong |
| Computer Needed? | Y |
| Bringing a laptop? | Y |
| Overhead Needed? | |
| Software requests | |
| Special Needs | I will need a VGA hookup for the laptop. The laptop does not have a HDMI port. I am only able to present on Saturday. I will not be able to make the conference on Friday. |
| Date Submitted | 09/22/2017 |
| Year | 2017 |