For more information about this meeting, contact Mary Anne Raymond.
| Title: | Tire tracks geometry, hatchet planimeter and Menzin's conjecture |
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| Seminar: | Slow Pitch Seminar |
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| Speaker: | Sergei Tabachnikov, Penn State |
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| Abstract: |
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| The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel, fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its motion and its terminal position; the monodromy map sending the initial position to the terminal one arises. This mapping of a circle to a circle is a Moebius transformation, a remarkable fact that has various geometrical and dynamical consequences. Moebius transformations belong to one of the three types: elliptic, parabolic and hyperbolic. I shall outline a proof of a 100 years old conjecture: if the front wheel track is an oval with area at least Pi then the respective monodromy is hyperbolic. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 12 / 02 / 2008 |
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| Time: | 05:00pm - 06:00pm |
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