I kinda followed along with that trignonmetry. I dunno if I was imagining correctly, but I pictured a circle with two right triangles inside, sharing a hypotenuse. Triangle A has 16x the area that triangle B has, and with each collision, triangle B increases in size and triangle A decreases. After pi collisions, the areas of the trianlges are the same.

As we scale up, and the mass of the ball (area of the triangle relative to the other) increases hundred-fold, the number of collisions until we have equality, is pi increased ten-fold.

Fuck knows why, but it's cool.