View Proposal #117
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| ID | 117 |
|---|---|
| First Name | Eugene |
| Last Name | Herman |
| Institution | Grinnell College |
| Speaker Category | faculty |
| Title of Talk | Equidistant Sets and Similarity Transformations |
| Abstract | The main result to be presented is the following: If f is a nonconstant function from R^n to R^n that preserves equality of distances, then f is a similarity transformation. A key concept in the proof is a special type of affinely independent set of points -- a set of points that are equidistant from one another. The proof uses elementary linear algebra and geometric reasoning and little else. Much of the emphasis in the presentation will be on the interplay of algebra and geometry. Also, there will be some remarks on the connections with classical geometry, including the Fundamental Theorem of Affine Geometry. |
| Subject area(s) | Linear geometry |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | N |
| Bringing a laptop? | N |
| Overhead Needed? | Y |
| Software requests | |
| Special Needs | |
| Date Submitted | 3/1/2005 |
| Year | 2005 |