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Your title -#+AUTHOR: Your name -#+DATE: Today's date +#+TITLE: On the computation of pi +#+AUTHOR: Jamal KHAN +#+DATE: 2020-09-13 #+LANGUAGE: en # #+PROPERTY: header-args :eval never-export @@ -11,97 +11,51 @@ #+HTML_HEAD: #+HTML_HEAD: -* Some explanations - -This is an org-mode document with code examples in R. Once opened in -Emacs, this document can easily be exported to HTML, PDF, and Office -formats. For more information on org-mode, see -https://orgmode.org/guide/. - -When you type the shortcut =C-c C-e h o=, this document will be -exported as HTML. All the code in it will be re-executed, and the -results will be retrieved and included into the exported document. If -you do not want to re-execute all code each time, you can delete the # -and the space before ~#+PROPERTY:~ in the header of this document. - -Like we showed in the video, R code is included as follows 1)) #+end_src #+RESULTS: -#+begin_example - mpg cyl disp hp - Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0 - 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5 - Median :19.20 Median :6.000 Median :196.3 Median :123.0 - Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7 - 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0 - Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0 - drat wt qsec vs - Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000 - 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000 - Median :3.695 Median :3.325 Median :17.71 Median :0.0000 - Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375 - 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000 - Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000 - am gear carb - Min. :0.0000 Min. :3.000 Min. :1.000 - 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000 - Median :0.0000 Median :4.000 Median :2.000 - Mean :0.4062 Mean :3.688 Mean :2.812 - 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000 - Max. :1.0000 Max. :5.000 Max. :8.000 -#+end_example - -Finally, an example for graphical output: -#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R* +: +: [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* +set.seed(42) +N = 1000 +df = data.frame(X = runif(N), Y = runif(N)) +df$Accept = (df$X**2 + df$Y**2 <=1) library(ggplot2) - -ggplot() + - geom_point(data=mtcars, mapping=aes(x=wt, y=mpg, color=factor(gear))) + - scale_x_continuous("Weight") + - scale_y_continuous("Milage") + - scale_color_discrete("Gear") + - theme_bw() - -ggsave('./cars.png', width=5, height=2.5, units="in", dpi=120) - +ggplot(df, aes(x=X, y=Y, color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw() #+end_src #+RESULTS: -[[file:./cars.png]] - -Note the parameter ~:exports results~, which indicates that the code -will not appear in the exported document. We recommend that in the -context of this MOOC, you always leave this parameter setting as -~:exports both~, because we want your analyses to be perfectly -transparent and reproducible. - -Watch out: the figure generated by the code block is /not/ stored in -the org document. It's a plain file, here named ~cars.png~. You have -to commit it explicitly if you want your analysis to be legible and -understandable on GitLab. +[[file:/tmp/babel-9oTMJE/figure0FnJcH.png]] -Finally, don't forget that we provide in the resource section of this -MOOC a configuration with a few keyboard shortcuts that allow you to -quickly create code blocks in R by typing ~