Update toy_document_en.Rmd

module2/exo1/toy_document_en.Rmd

@@ -5,6 +5,7 @@ Date: 28.06.2026
 output: html_document:
 ---
 
+# A propos de pi
 
 ```{r setup, include=FALSE} 
 knitr::opts_chunk$set(echo = TRUE)
@@ -12,22 +13,27 @@ knitr::opts_chunk$set(echo = TRUE)
 
 ```{r}	
 pi
+```
 
 
-
+```{r}
 set.seed(42)
 N = 100000
 x = runif(N)
 theta = pi/2*runif(N)
 2/(mean(x+sin(theta)>1))
+```
 
-
-
+```{r}
 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()
+```
+
 
-*mean(df$Accept)
\ No newline at end of file
+```{r}
+4*mean(df$Accept)
+```
\ No newline at end of file