View Proposal #333
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| ID | 333 |
|---|---|
| First Name | Ruth |
| Last Name | Berger |
| Institution | Luther College |
| Speaker Category | faculty |
| Title of Talk | A line need not be straight! |
| Abstract | In Geometry a line is an undefined term, governed only by whatever axioms you want to impose on it. Students have a hard time with proofs in non-Euclidean Geometries, because their Euclidean intuition about straight lines keeps interfering with their logical thinking. I try to have my students develop non-Euclidean intuition by introducing them to different worlds: The Green Jello World, inhabited by fish, consists of Jello that is less dense in one direction, but infinitely dense at the end of the world. Escher's World is as a disk populated by inhabitants in which everything shrinks towards the outside. By thinking like inhabitants of these worlds, students realize that you can get from A to B with fewer steps/flipper strokes by not necessarily following a Euclidean line. They naturally come up with the fact that lines (interpreted as shortest paths) can be curved looking paths! Having this hyperbolic intuition makes it much easier for students to write formal proofs in hyperbolic geometry. |
| Subject area(s) | Geometry |
| Suitable for undergraduates? | Yes |
| Day Preference | FridayMild |
| Computer Needed? | Y |
| Bringing a laptop? | Y |
| Overhead Needed? | |
| Software requests | powerpoint |
| Special Needs | |
| Date Submitted | 9/13/12 |
| Year | 2012 |