
Finding Pi from Random Numbers - Tomte
https://measureofdoubt.com/2018/07/22/finding-pi-from-random-numbers/
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hannasanarion
This is a classic statistics/machine learning exercise. It is also the topic
of my favorite scientific paper of all time:

[https://arxiv.org/abs/1404.1499](https://arxiv.org/abs/1404.1499)

> _A Ballistic Monte Carlo Approximation of π_

>> _We compute a Monte Carlo approximation of π using importance sampling with
shots coming out of a Mossberg 500 pump-action shotgun as the proposal
distribution._

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xucheng
There is another way to compute pi from random numbers while having nothing to
do with geometry. The probability of two random numbers being co-prime is
related to pi [1]. Notably, standupmaths did this once by hand [2].

[1]:
[https://en.wikipedia.org/wiki/Coprime_integers#Probability_o...](https://en.wikipedia.org/wiki/Coprime_integers#Probability_of_coprimality)

[2]: [https://youtu.be/RZBhSi_PwHU](https://youtu.be/RZBhSi_PwHU)

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liberte82
How do you do this with the need to use a ceiling? (Sorry, I didn't watch the
video).

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hcs
If you mean a highest integer, he didn't, he's using rolls of a pair of 100+
sided dice. It's an approximation, anyway.

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inlineint
There is also the classical Buffon's needle experiment:
[https://en.wikipedia.org/wiki/Buffon%27s_needle#Estimating_%...](https://en.wikipedia.org/wiki/Buffon%27s_needle#Estimating_%CF%80)

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nine_k
The article is not about the (trivial) way to compute pi by putting random
numbers in the square. It's about altering the way you compute your target
function to narrow down the confidence intervals, while still computing the
same value.

Definitely you can compute pi by scanning a uniform grid in a square and
checking how much ends up in the quarter-circle. But with these stats tricks
applied, mere 10k points give the author very good approximation, beating 22/7
30% of the time. Scanning a 100x100 grid will give a much coarser
approximation, I suppose.

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liberte82
I had to do this exercise in my undergrad, it's always stuck out as one of the
exercises I've remembered and found really interesting.

