final

module2/exo1/toy_document_en.Rmd

 ---
 title: "On the computation of pi"
-author: "*Arnaud Legrand*"
-date: "*25 juin 2018*"
+author: "Arnaud Legrand"
+date: "25 juin 2018"
 output: html_document
 ---
 
@@ -9,7 +9,7 @@ output: html_document
 knitr::opts_chunk$set(echo = TRUE)
 ```
 
-# Asking the maths libary
+## Asking the maths library
 My computer tells me that $\pi$ is *approximatively*
 
 ```{r}
@@ -17,7 +17,7 @@ pi
 ```
 
 ## Buffon's needle
-Applying the methond of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__)
+Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__)
 
 ```{r}
 set.seed(42)
@@ -27,7 +27,7 @@ theta = pi/2*runif(N)
 2/(mean(x+sin(theta)>1))
 ```
 
-## Using a surface fraction arugment
+## 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 ["Monte Carlo method" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:
 
 ```{r}

module2/exo1/toy_document_en.html

@@ -375,20 +375,21 @@ $(document).ready(function () {
 
 
 <h1 class="title toc-ignore">On the computation of pi</h1>
-<h4 class="author"><em>Arnaud Legrand</em></h4>
-<h4 class="date"><em>25 juin 2018</em></h4>
+<h4 class="author">Arnaud Legrand</h4>
+<h4 class="date">25 juin 2018</h4>
 
 </div>
 
 
-<div id="asking-the-maths-libary" class="section level1">
-<h1>Asking the maths libary</h1>
+<div id="asking-the-maths-library" class="section level2">
+<h2>Asking the maths library</h2>
 <p>My computer tells me that <span class="math inline">\(\pi\)</span> is <em>approximatively</em></p>
 <pre class="r"><code>pi</code></pre>
 <pre><code>## [1] 3.141593</code></pre>
+</div>
 <div id="buffons-needle" class="section level2">
 <h2>Buffon’s needle</h2>
-<p>Applying the methond of <a href="https://en.wikipedia.org/wiki/Buffon%27s_needle_problem">Buffon’s needle</a>, we get the <strong>approximation</strong>)</p>
+<p>Applying the method of <a href="https://en.wikipedia.org/wiki/Buffon%27s_needle_problem">Buffon’s needle</a>, we get the <strong>approximation</strong>)</p>
 <pre class="r"><code>set.seed(42)
 N = 100000
 x = runif(N)
@@ -396,8 +397,8 @@ theta = pi/2*runif(N)
 2/(mean(x+sin(theta)&gt;1))</code></pre>
 <pre><code>## [1] 3.14327</code></pre>
 </div>
-<div id="using-a-surface-fraction-arugment" class="section level2">
-<h2>Using a surface fraction arugment</h2>
+<div id="using-a-surface-fraction-argument" class="section level2">
+<h2>Using a surface fraction argument</h2>
 <p>A method that is easier to understand and does not make use of the <span class="math inline">\(\sin\)</span> function is based on the fact that if <span class="math inline">\(X\sim U(0,1)\)</span> and <span class="math inline">\(Y\sim U(0,1)\)</span>, then <span class="math inline">\(P[X^2+Y^2\leq 1] = \pi/4\)</span> (see <a href="https://en.wikipedia.org/wiki/Monte_Carlo_method">“Monte Carlo method” on Wikipedia</a>). The following code uses this approach:</p>
 <pre class="r"><code>set.seed(42)
 N = 1000
@@ -415,7 +416,6 @@ library(ggplot2)</code></pre>
 <pre class="r"><code>4*mean(df$Accept)</code></pre>
 <pre><code>## [1] 3.156</code></pre>
 </div>
-</div>