A short one, just to get the ol’ bloggin’ fingers movin’ again’. It’s starting to get chilly outdoors and they’re simply covered in cobwebs!! Where did they come from? How did I get spider webs on my hands…..?

Last year, 3Blue1Brown produced a series of lovely videos (but really, they *all* are) on a strange little thing. An object is sent bouncing back and forth between a rigid wall and another moving object with a particular (integer!) mass ratio. If this ratio is a power of 100, the number of collisions will be some of the first digits of pi!! Isn’t that nuts.

Anyone who has taken a high school senior level physics class or above would recognize the need to implement two conservation laws: that of momentum (linear with velocities) and that of energy (quadratic with speeds). Someone with just a bit of programming experience should be able to set up a series of solutions for the speeds after successive collisions, until the “no-collide” condition is met: the two blocks are traveling in the same direction, away from the wall, and gaining distance between them.

Hey, I’ve got a bit of programming experience! I whipped this up to see if I could get the same results.

It looks like they’re doing it right! A fun little exercise. In the spirit of the original prompt I’ll let you find or figure out *why* it works for yourself. You can always watch Sanderson’s explanation video.

One hint I can give is it is a bit related to the Buffon’s needle technique of finding pi. This is a fun idea that understanding could open some avenues of thought for more difficult estimation problems. Check out the description and explanation on Numberphile:

OK ENJOY PI PLEASE AND THANKS PEACE OUT DUDERINOS