PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Matthew Katz, James Sellers, George Andrews.

Title:Periodic billiard paths and integer partitions
Seminar:Combinatorics/Partitions Seminar
Speaker:Andrew Baxter, PSU
Abstract:
Throw a ball on a polygonal billiard table and it will trace a path dictated by the laws of reflection. If the path loops back on itself after n bounces, we call it a period-n billiard path. For a given polygon, we are interested in counting all period-n billiard paths (up to a natural equivalence relation). We will focus on the cases of the rectangle, square, right isosceles triangle, and 30-60-90 triangle. In the course of doing this, we will run across a geometric interpretation of Euler's totient function and develop an intriguing connection with integer partitions which hints at a much richer structure than one would suspect.

Room Reservation Information

Room Number:MB106
Date:11 / 08 / 2011
Time:11:15am - 12:05pm