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[robve]

(03-14-2022 12:25 PM)Gerson W. Barbosa Wrote:  

(03-14-2022 11:44 AM)Dave Britten Wrote:  Personally I kind of like the absurdity of using the Monte Carlo method.

https://www.wikihow.com/Calculate-Pi-by-...n-Hot-Dogs

That’s literally the wurst method to compute \(\pi\), but it’s an interesting one nonetheless.

Worst means hot dog (or generally sausage) in Dutch. So yeah, definitely the worst way to compute \( \pi \) in Anglo-Dutch. I tried it, but after one throw the dogs grabbed the hot dogs. Not even one digit of \( \pi \). Comte de Buffon would not approve.

Perhaps the worst way to compute \( \pi \) is to exploit an interesting relationship between (co-)primes and \( \pi \). If we take \( n \) random integer pairs and determine the fraction \( R_n \) that are co-prime, then we have \( \pi \approx \sqrt{\frac{6}{R_n}} \) where \( \displaystyle \lim_{n\rightarrow\infty} \sqrt{\frac{6}{R_n}} = \pi \). It will take one million random pairs to get about 1 or 2 decimal places of \( \pi \) and 100,000,000 random pairs to get 5 decimal places.

- Rob