---
title: "À propos du calcul de pi"
author: "Arnaud Legrand"
date: "25 juin 2018"
output: html_document
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

pi

set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))


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)