diff --git a/module2/exo1/toy_document_orgmode_R_en.org b/module2/exo1/toy_document_orgmode_R_en.org
index 4a870e97f3c67756af308b09ae515360d32ff218..6a02df3bd9edac8b13ac9d738e3cc9b69f2fe5d4 100644
--- a/module2/exo1/toy_document_orgmode_R_en.org
+++ b/module2/exo1/toy_document_orgmode_R_en.org
@@ -1,8 +1,5 @@
#+TITLE: On the computation of pi
-#+AUTHOR: Jamal KHAN
-#+DATE: 2020-09-13
#+LANGUAGE: en
-# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD:
#+HTML_HEAD:
@@ -11,8 +8,11 @@
#+HTML_HEAD:
#+HTML_HEAD:
+#+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