From f6bc01a992f4a9c3aee70945b8a380aca8c17c82 Mon Sep 17 00:00:00 2001
From: Meiling WU <a36b2a8227e6b46f4a4d564434a024e3@app-learninglab.inria.fr>
Date: Mon, 30 May 2022 09:46:51 +0000
Subject: [PATCH] Update toy_document_orgmode_R_fr

---
 module2/exo1/toy_document_orgmode_R_fr | 68 ++++++++++++++------------
 1 file changed, 37 insertions(+), 31 deletions(-)

diff --git a/module2/exo1/toy_document_orgmode_R_fr b/module2/exo1/toy_document_orgmode_R_fr
index b4f6f82..b368a47 100644
--- a/module2/exo1/toy_document_orgmode_R_fr
+++ b/module2/exo1/toy_document_orgmode_R_fr
@@ -1,53 +1,59 @@
----
-title: "À propos du calcul de pi"		
-auteur : EvaC
+title: "On the computation of pi"		
+auteur : Meiling WU
 output: html_notebook
----
-```{r setup, include=FALSE}
-knitr::opts_chunk$set(echo = TRUE)
-```
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
+#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
+#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
 
-## En demandant à la lib maths
-Mon ordinateur m'indique que $\pi$ vaut *approximativement* 
+#+PROPERTY: header-args  :session  :exports both
 
-```{r cars}
-pi 
-*3.141592653589793*
+* Asking the maths library	
+My computer tells me that $\pi$ is /approximatively/
 
-```
+#+begin_src R :results output :session *R* :exports both
+pi
+#+end_src
 
-## En utilisant la méthode des aiguilles de Buffon 
-Mais calculé avec le __méthode__ des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme __approximation__ :
+#+RESULTS:	
+: [1] 3.141593
 
-```{r}
+* Buffon's needle
+Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]], we get the *approximation*
+
+#+begin_src R :results output :session *R* :exports both	
 set.seed(42)
 N = 100000
 x = runif(N)
 theta = pi/2*runif(N)
 2/(mean(x+sin(theta)>1))
-_3.12891113892_
-```
+#+end_src
+
+#+RESULTS:
+: [1] 3.14327
 
-# 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
-$X \sim U(0,1)$ et 
-$Y \sim U(0,1)$ alors 
-$P[X^{2} + Y^{2} \leq 1]= \pi /4$ 
-(voir [méthode de Monte Carlo sur Wikipedia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80). Le code suivant illustre ce fait:
+* Using a surface fraction argument
+A method that is easier to understand and does not make use of the $\sin$ function is based on the fact that if $X\sim U(0,1)$ and $Y\sim U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). The following code uses this approach:
 
-```{r}
+#+begin_src R :results output graphics :file figure_pi_mc1.png :exports both :width 600 :height 400 :session *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()
-```
-
-Il est alors aisé d’obtenir une approximation (pas terrible) de $\pi$ en comptant combien de fois, en moyenne, $X^{2}+Y^{2}$ est inférieur à 1:
+#+end_src
 
+#+RESULTS:
+[[file:figure_pi_mc1.png]]
 
-```{r }
+It is then straightforward to obtain a (not really good) approximation to $\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1:
+#+begin_src R :results output :session *R* :exports both
 4*mean(df$Accept)
-3.1120000000000001
-```
+#+end_src
+
+
+#+RESULTS:
+: [1] 3.156
-- 
2.18.1