Fix formatting exo1

module2/exo1/toy_document_orgmode_R_en.org

 #+TITLE:  On the computation of pi
-#+AUTHOR: Jamal KHAN
-#+DATE: 2020-09-13
 #+LANGUAGE: en
-# #+PROPERTY: header-args :eval never-export
 
 #+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"/>
@@ -11,8 +8,11 @@
 #+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>
 
+#+PROPERTY: header-args :eval never-export
+
 * Asking the maths library
 My computer tells me that $\pi$ is /approximatively/
+
 #+begin_src R :results output :session *R* :exports both
 pi
 #+end_src
@@ -21,7 +21,8 @@ pi
 : [1] 3.141593
 
 * Buffon's needle
-Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]] we get the *approximation*
+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 results
 set.seed(42)
 N = 100000
@@ -34,10 +35,7 @@ theta = pi/2*runif(N)
 : [1] 3.14327
 
 * 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 $X\simU(0,1)$ and
-$Y\simU(0,1)$, then $P[X^2+Y^2 \le1]=\pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on
-Wikipedia]]). The following code uses this approach:
+A method that is easier to understand and does not make use of the $\sin$ function is based on the fact that if $X\simU(0,1)$ and $Y\simU(0,1)$, then $P[X^2+Y^2 \le1]=\pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). The following code uses this approach:
 
 #+begin_src R :results output graphics :file figure_pi_mc1.png :exports both :width 600 :height 400 :session *R* 
 set.seed(42)
@@ -51,8 +49,7 @@ ggplot(df, aes(x=X, y=Y, color=Accept)) + geom_point(alpha=.2) + coord_fixed() +
 #+RESULTS:
 [[file:figure_pi_mc1.png]]
 
-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:
+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)
 #+end_src