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5c13e2907b128387adfbf972d1b506b3
mooc-rr
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78ccd1a8
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78ccd1a8
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Dec 26, 2024
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5c13e2907b128387adfbf972d1b506b3
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# À propos du calcul de pi
_Arnaud Legrand_
_25 juin 2018_
## En demandant à la lib maths
Mon ordinateur m’indique que $\pi$ vaut _approximativement_
```{r}
pi
```
##En utilisant la méthode des aiguilles de Buffon
Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme _approximation_ :
```{r}
set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))
```
## Avec un argument “fréquentiel” de surface
Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction sinus se base sur le fait que si X∼U(0,1)
et Y∼U(0,1)
alors P[X2+Y2≤1]=π/4
(voir méthode de Monte Carlo sur Wikipedia). Le code suivant illustre ce fait:
\ No newline at end of file
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