Fix formatting

module2/exo1/toy_document_orgmode_R_en.org

@@ -12,7 +12,7 @@
 #+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
 
 * Asking the maths library
-My computer tells me that \pi is approximattively
+My computer tells me that $\pi$ is /approximatively/
 #+begin_src R :results output :session *R* :exports both
 pi
 #+end_src
@@ -20,9 +20,9 @@ pi
 #+RESULTS:
 : [1] 3.141593
 
-* Buffon;s needle
-Applying the method of [[https://en.wikipedia.org/wiki/Buffon's_needle_problem][Buffon's needle]], we get the **approximation**
-#+begin_src R :results output :session *R* :exports both
+* 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 results
 set.seed(42)
 N = 100000
 x = runif(N)
@@ -31,15 +31,15 @@ theta = pi/2*runif(N)
 #+end_src
 
 #+RESULTS:
-: 
 : [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:
-#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R* 
+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)
 N = 1000
 df = data.frame(X = runif(N), Y = runif(N))
@@ -49,10 +49,10 @@ ggplot(df, aes(x=X, y=Y, color=Accept)) + geom_point(alpha=.2) + coord_fixed() +
 #+end_src
 
 #+RESULTS:
-[[file:/tmp/babel-9oTMJE/figure0FnJcH.png]]
+[[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:
+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