Commit 5b6036d8 authored by Jamal KHAN's avatar Jamal KHAN

Fix formatting exo1

parent 8a248461
...@@ -8,7 +8,7 @@ ...@@ -8,7 +8,7 @@
#+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/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
#+PROPERTY: header-args :session :exports both #+PROPERTY: header-args :session :exports both
* Asking the maths library * Asking the maths library
My computer tells me that $\pi$ is /approximatively/ My computer tells me that $\pi$ is /approximatively/
...@@ -35,7 +35,7 @@ theta = pi/2*runif(N) ...@@ -35,7 +35,7 @@ theta = pi/2*runif(N)
: [1] 3.14327 : [1] 3.14327
* Using a surface fraction argument * 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 $P[X^2+Y^2\leq 1] = \pi/4$ (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 $X\sim U(0,1)$ and $Y\sim U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (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* #+begin_src R :results output graphics :file figure_pi_mc1.png :exports both :width 600 :height 400 :session *R*
set.seed(42) set.seed(42)
...@@ -50,6 +50,7 @@ ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + t ...@@ -50,6 +50,7 @@ ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + t
[[file:figure_pi_mc1.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: 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 #+begin_src R :results output :session *R* :exports both
4*mean(df$Accept) 4*mean(df$Accept)
#+end_src #+end_src
......
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