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upstart writes:

Submitted via IRC for chromas

For Pi Day, Calculate Pi Yourself Using Two Colliding Balls

This is at least my ninth year of writing about Pi Day—here is my post from 2010. Of course it's called Pi Day because the date, 3/14, is similar to the first three digits of pi (3.1415 …). At this point I've built up a whole library of fun things in honor of Pi Day.

Here is a new one. You can calculate the digits of pi using elastic collisions between two objects of different masses and a wall.

[...] There are two balls, A and B. Ball A has a larger mass and is initially moving. It collides with ball B such that ball B speeds up and ball A slows down just a little bit (this is a perfectly elastic collision). After this, ball B starts moving toward the wall and eventually bounces off it back toward ball A for another collision. This continues until ball A is moving away from the wall instead of toward it, and there are no longer any collisions.

Now for the pi part. If you know that the mass of ball A is 100 times greater than that of ball B, there will be 31 collisions. If the ratio of masses is 10,000 to 1, there will be 314 collisions. Yes, that is the first 3 digits of pi. If you had a mass ratio of 1 million to 1, you would get 3,141 collisions. (Remember the first few digits of pi are 3.1415 …) In general, if you want "d" digits of pi, then you need mass A divided by mass B to be 100 raised to the d-1 power.

This is not a very efficient method for calculating the digits of pi, but it seems to work. Here is a great video from 3Brown1Blue that explains this situation. [YouTube link] Also, here is an older video from Numberphile that also goes over this problem.

[What I want to know is which one is better: apple, raspberry, or apricot? --ed.]

Original Submission

1. "upstart" - https://soylentnews.org/~upstart/
2. "For Pi Day, Calculate Pi Yourself Using Two Colliding Balls" - https://www.wired.com/story/for-pi-day-calculate-pi-yourself-using-two-colliding-balls/
3. "here is my post from 2010" - https://www.wired.com/2010/03/on-the-8th-day-god-made-pi/
4. "built up" - https://www.wired.com/story/this-pi-day-calculate-the-value-of-pi-for-yourself/
5. "whole" - https://www.wired.com/2016/03/six-things-probably-didnt-know-pi/
6. "library" - https://www.wired.com/2017/03/lets-calculate-pi-raspberry-pi-celebrate-pi-day/
7. "fun things" - https://www.wired.com/2017/03/hey-can-find-pi-random-walk-heres/
8. "Pi Day" - https://www.wired.com/2014/03/calculating-pi-pi-day/
9. "YouTube link" - http://www.youtube.com/watch?v=HEfHFsfGXjs
10. "here is an older video from Numberphile" - https://www.youtube.com/watch?v=abv4Fz7oNr0
11. "Original Submission" - https://soylentnews.org/submit.pl?op=viewsub&subid=32358

printed from SoylentNews, For Pi Day, Calculate Pi Yourself Using Two Colliding Balls on 2024-04-16 10:02:06