The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
Bouncing Balls and Geometric Series, Robert Styer and Morgan Besson
First, let's explore the relationship between the heights of the bounces. Let hn be the height of the nth bounce. Our basic assumption is that R = hn + 1 / hn, the ratio of the heights of successive bounces, is a constant; R is called the elasticity coefficient. We can easily find a general pattern relating all the heights to the first height.