From 5b6036d83569d65b5e7041bb0fc46ddf8781b02b Mon Sep 17 00:00:00 2001 From: Jamal KHAN Date: Mon, 14 Sep 2020 06:39:51 +0200 Subject: [PATCH] Fix formatting exo1 --- module2/exo1/toy_document_orgmode_R_en.org | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/module2/exo1/toy_document_orgmode_R_en.org b/module2/exo1/toy_document_orgmode_R_en.org index 0febcfe..1caa19b 100644 --- a/module2/exo1/toy_document_orgmode_R_en.org +++ b/module2/exo1/toy_document_orgmode_R_en.org @@ -8,7 +8,7 @@ #+HTML_HEAD: #+HTML_HEAD: -#+PROPERTY: header-args :session :exports both +#+PROPERTY: header-args :session :exports both * Asking the maths library My computer tells me that $\pi$ is /approximatively/ @@ -35,7 +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 $P[X^2+Y^2\leq 1] = \pi/4$ (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* set.seed(42) @@ -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]] 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 -- 2.18.1