# The digits of Pi :: playing pool??; Quantum search ???? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [March 3, 2020, 10:55am UTC](https://boards.straightdope.com/t/the-digits-of-pi-playing-pool-quantum-search/848854 "2020-03-03T10:55:38Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [March 3, 2020, 10:55am UTC](https://boards.straightdope.com/t/the-digits-of-pi-playing-pool-quantum-search/848854/1 "2020-03-03T10:55:38Z")
We’ve had a lot of threads about the digits of pi. Do we have room for yet another one? Everybody knows you can calculate pi by dropping toothpicks on wood-planked floor, but I stumbled across webpages describing another physical experiment which yields pi. Indeed, it’s one of the simplest possible experiments in simple mechanics. Here’s the experiment: Line up three objects with masses ∞, 1, M. The object with mass ∞ is a rigid wall; (the 1 is 1 kilogram but units won’t matter). _M is the only variable in the experiment._ Initially all three objects are stationary, and you start by pushing object M toward object 1 (give M velocity 1, the units don’t matter). There’s no gravity, no friction; all collisions are elastic. Only one dimension (x) matters, y = z = dy = dz = 0 for all objects. Start the clock when M bumps into 1. What happens? _How many collisions in total will there be?_ When M is tiny, it will bounce back off of 1 as a first collision; and 1 will move slowly and eventually collide with the wall. TWO collisions total. When M = ⅓ the initial collision will give 1 a velocity of ½ and M a velocity of -½. This is the way to conserve both momentum . . . 1·½ - ⅓·½ = ⅓·1 and kinetic energy . . . 1·½[sup]2[/sup] + ⅓·½[sup]2[/sup] = ⅓·1[sup]2[/sup] After 1 bounces off the wall, it will have the same velocity as M. Or slightly more velocity if M is slightly more than ⅓. So if M=.3334 there will be THREE collisions compared with TWO for M \< .3333. Solve for M=1? A very elegant case has THREE collisions; M=1.0001 would yield FOUR collisions. Here are some more results: M = 10 –\> 10 collisions M = 100 –\> 31 collisions M = 1000 –\> 99 collisions M = 10000 –\> 314 collisions M = 100000 –\> 993 collisions M = 1000000 –\> 3141 collisions Notice anything? Here are some more examples: M = 100000000 –\> 31415 collisions M = 10000000000 –\> 314159 collisions M = 1000000000000 –\> 3141592 collisions M = 100000000000000 –\> 31415926 collisions The digits of pi! Although I do realize that “arithmetic is what it is”, I still found this astounding! [Here (pdf) is an elegant proof of this relationship “PLAYING POOL WITH π”.](https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf) [Here’s someone who thinks this experiment may help us understand quantum search! “Playing Pool with |ψ⟩: from Bouncing Billiards to Quantum Search”](https://arxiv.org/abs/1912.02207) ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 3, 2020, 11:31am UTC](https://boards.straightdope.com/t/the-digits-of-pi-playing-pool-quantum-search/848854/2 "2020-03-03T11:31:15Z")
Cool! Thanks for sharing that. Both the method of calculating pi, and the isomorphism with Grover’s search are pretty neat, plus the paper is a joy to read: > [@](#): > > Nevertheless, whatever the shortcomings of billiard balls as tools for calculating π, the results of this paper suggest a tool that is even worse. 😃 ---
**Author:** ![breezman](https://avatars.discourse-cdn.com/v4/letter/b/4491bb/32.png) [@breezman](https://boards.straightdope.com/u/breezman)\ **Post date:** [March 5, 2020, 1:12am UTC](https://boards.straightdope.com/t/the-digits-of-pi-playing-pool-quantum-search/848854/3 "2020-03-05T01:12:00Z")
3blue1brown did a great video on this a while back. [https://youtu.be/HEfHFsfGXjs](https://youtu.be/HEfHFsfGXjs) ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [March 5, 2020, 1:59am UTC](https://boards.straightdope.com/t/the-digits-of-pi-playing-pool-quantum-search/848854/4 "2020-03-05T01:59:45Z")
> [@breezman](#): > > 3blue1brown did a great video on this a while back. > > [https://youtu.be/HEfHFsfGXjs](https://youtu.be/HEfHFsfGXjs) As I was reading the OP, I knew I had seen this recently. ([3blue1brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw) is wonderful )