PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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
Abstract:
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
Date:12 / 02 / 2008
Time:05:00pm - 06:00pm