From 8663c42cd6f9f7d3479fc7db100cb9223fd769d6 Mon Sep 17 00:00:00 2001 From: Jamal KHAN Date: Mon, 14 Sep 2020 06:16:13 +0200 Subject: [PATCH] Fix formatting --- module2/exo1/toy_document_orgmode_R_en.org | 24 +++++++++++----------- 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/module2/exo1/toy_document_orgmode_R_en.org b/module2/exo1/toy_document_orgmode_R_en.org index f6a03b7..4a870e9 100644 --- a/module2/exo1/toy_document_orgmode_R_en.org +++ b/module2/exo1/toy_document_orgmode_R_en.org @@ -12,7 +12,7 @@ #+HTML_HEAD: * Asking the maths library -My computer tells me that \pi is approximattively +My computer tells me that $\pi$ is /approximatively/ #+begin_src R :results output :session *R* :exports both pi #+end_src @@ -20,9 +20,9 @@ pi #+RESULTS: : [1] 3.141593 -* Buffon;s needle -Applying the method of [[https://en.wikipedia.org/wiki/Buffon's_needle_problem][Buffon's needle]], we get the **approximation** -#+begin_src R :results output :session *R* :exports both +* Buffon's needle +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 x = runif(N) @@ -31,15 +31,15 @@ theta = pi/2*runif(N) #+end_src #+RESULTS: -: : [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: -#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R* +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) N = 1000 df = data.frame(X = runif(N), Y = runif(N)) @@ -49,10 +49,10 @@ ggplot(df, aes(x=X, y=Y, color=Accept)) + geom_point(alpha=.2) + coord_fixed() + #+end_src #+RESULTS: -[[file:/tmp/babel-9oTMJE/figure0FnJcH.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: +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