For more information about this meeting, contact Mary Anne Raymond.
|Title:||Tire tracks geometry, hatchet planimeter and Menzin's conjecture|
|Seminar:||Slow Pitch Seminar|
|Speaker:||Sergei Tabachnikov, Penn State|
|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
|Date:||12 / 02 / 2008|
|Time:||05:00pm - 06:00pm|