Proceeded to changes following comparison with solution

module2/exo1/toy_document_orgmode_python_en.org

@@ -11,42 +11,36 @@
 #+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>
 
-* Table of Contents
+#+PROPERTY: header-args  :session  :exports both
 
-1. Asking the math libraryo
-2. * Buffon's needle
-3. Using a surface fraction argument
-
-* 1 Asking the math library
+* Asking the math library
 My computer tells me that $\pi$ is /approximatively/
 
-#+begin_src python :results output :exports both
-import math
-print(math.pi)
+#+begin_src python :results value :session *python* :exports both
+from math import *
+pi
 #+end_src
 
 #+RESULTS:
 : 3.141592653589793
 
-* 2 * Buffon's needle
-Applying the method of [[https://en.wikipedia.org/wiki/Buffon%27s_needle_problem][Buffon's needle]], we get the approximation
+* * Buffon's needle
+Applying the method of [[https://en.wikipedia.org/wiki/Buffon%27s_needle_problem][Buffon's needle]], we get the *approximation*
 
-#+begin_src python :results output :exports both
-import math
+#+begin_src python :results value :session *python* :exports both
 import numpy as np
 np.random.seed(seed=42)
 N = 10000
 x = np.random.uniform(size=N, low=0, high=1)
-theta = np.random.uniform(size=N, low=0, high=math.pi/2)
-print(2/(sum((x+np.sin(theta))>1)/N))
+theta = np.random.uniform(size=N, low=0, high=pi/2)
+2/(sum((x+np.sin(theta))>1)/N)
 #+end_src
 
 #+RESULTS:
 : 3.128911138923655
 
-* 3. 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
+* 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 ocde uses this approach:
 #+begin_src python :results output file :session :var matplot_lib_filename="C:/Users/Utilisateur/mooc-rr/module2/exo1/PictureRes.png" :exports results