Minor changes

module2/exo1/toy_document_en.Rmd

@@ -5,9 +5,13 @@ date: "23/7/2021"
 output: html_document
 ---
 
-## Asking the math library 
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE)
+```
+
+## Asking the math library
 
-My computer me that $\pi$ is *approximatively*
+My computer tells me that $\pi$ is *approximatively*
 
 ```{r}
 pi
@@ -27,7 +31,7 @@ theta = pi/2*runif(N)
 
 ## 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 $X∼U(0,1)$ and $Y∼U(0,1)$, then $P[X^2+Y^2 \le 1]=\pi/4$ (see ["Monte Carlo method" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code use 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 $X \sim U(0,1)$ and $Y \sim U(0,1)$, then $P[X^2+Y^2 \le 1]=\pi/4$ (see ["Monte Carlo method" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code use this approach:
 
 ```{r}
 set.seed(42)
@@ -37,7 +41,7 @@ df$Accept = (df$X**2 + df$Y**2 <=1)
 library(ggplot2)
 ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()
 ```
-It is therefore straightforward to obtain a (not really good) approximation to π by counting how many times, on average, $X^2+Y^2$ is smaller than 1 :
+It is therefore 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 :
 
 ```{r}
 4*mean(df$Accept)