The workings of a π Machine- Lecture # 144

Guest Speaker: Jim Ham To calculate π, take two identical balls. Put one near a wall and roll the other ball toward it. The first ball will hit the second, which will bounce off the wall and come back to hit the first ball. Click click click. Three collisions. The first digit of π is a three. This isn’t very convincing, of course, but the machine can be adjusted to show that π to two, three … digits is 3.1 and 3.14 …. The talk starts with the physics of this system in terms of conservation of momentum and energy which leads to a linear system of equations. The eigenvectors of the matrix for this system leads to a very nice explanation of why this produces the digits of π and the potential for the machine to break down. Questions? Contact John Grade at (608) 345-1519.