From ddbddbbe69453b699af935de1c07938309323579 Mon Sep 17 00:00:00 2001 From: Jamal KHAN Date: Mon, 14 Sep 2020 06:34:32 +0200 Subject: [PATCH] Fix formatting exo1 --- module2/exo1/toy_document_orgmode_R_en.org | 17 +++++++---------- 1 file changed, 7 insertions(+), 10 deletions(-) diff --git a/module2/exo1/toy_document_orgmode_R_en.org b/module2/exo1/toy_document_orgmode_R_en.org index 4a870e9..6a02df3 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 -- 2.18.1