Department of Mechanical Engineering, University of Colorado, Boulder, EUA.
Quinta-feira, 13 de novembro de 2014, 15:30
Following a brief review of the history of computing ?, we introduce the work of Galperin who contends that the successive digits of ? may be produced using a dynamical system. The system, presented under the guise of billiard balls, considers the rectilinear collisions of two point masses m and M=100Nm with each other and a wall. Mass m is initially placed between the wall and the oncoming mass M. For such initial conditions, Galperin’s method for determining the successive digits of ? at each value N is simply to count the total number of ball-ball and ball-wall collisions. Computations up to N=6 illustrate Galperin’s method for over three million collisions. General results concerning this dynamical system found while performing the computations will be presented, the most important of which is a discrete invariant of the motion.