---
title: "À propos du calcul de pi"
author: "Céline MORO"
date: "2024-11-20"
output: html_document
---

##En demandant à la lib maths
pi
## [1] 3.141593

##En utilisant la méthode des aiguilles de Buffon
set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))
## [1] 3.14327

##Avec un argument “fréquentiel” de surface
set.seed(42)
N = 1000
df = data.frame(X = runif(N), Y = runif(N))
df$Accept = (df$X**2 + df$Y**2 <=1)
library(ggplot2)
ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()
4*mean(df$Accept)
## [1] 3.156