From 593b045d50bb3a7437073da92b232af18139a5ba Mon Sep 17 00:00:00 2001
From: e04f7876d60626fad04783b2a5fa00cd
 <e04f7876d60626fad04783b2a5fa00cd@app-learninglab.inria.fr>
Date: Wed, 9 Sep 2026 15:09:41 +0000
Subject: [PATCH] Update toy_document_en.Rmd

---
 module2/exo1/toy_document_en.Rmd | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/module2/exo1/toy_document_en.Rmd b/module2/exo1/toy_document_en.Rmd
index 61b2040..4064fc6 100644
--- a/module2/exo1/toy_document_en.Rmd
+++ b/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
-- 
2.18.1