Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Dynamical Systems
Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi
Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi
Mathematical Sciences Technical Reports (MSTR)
This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x2 − ny2 = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …