Pi Proof

This model demonstrates the meaning of the mathematical symbol “pi”, the ratio between the diameter and the circumference (distance around the outside) of a circle. You start with the arrow pointing straight down at the zero on the horizontal scale, then roll the disk exactly one full turn to find the arrow pointing straight down again just past the 3 mark. Specifically, at the mark representing pi, or 3.141592…. The same scale is wrapped around the disk, so you can see how the marks for 1, 2, and 3 match up as the disk rolls along the track.

A set of very fine gear teeth on the disk and scale (like a rack-and-pinion gear) make sure that the marks on the disk never slip out of perfect alignment with the scale.