RAS

module2/exo1/.gitignore

+toy_document_fr.html

module2/exo1/toy_document_fr.Rmd

----
-output:
-  html_document: default
-  pdf_document: default
----
 # À propos du calcul de pi
 
 _Arnaud Legrand_
-
 _25 juin 2018_
 
+
 ## En demandant à la lib maths
 
 Mon ordinateur m’indique que $\pi$ vaut _approximativement_

module2/exo1/toy_document_fr.html

@@ -166,8 +166,7 @@ pre code {
 
 <div id="à-propos-du-calcul-de-pi" class="section level1">
 <h1>À propos du calcul de pi</h1>
-<p><em>Arnaud Legrand</em></p>
-<p><em>25 juin 2018</em></p>
+<p><em>Arnaud Legrand</em> <em>25 juin 2018</em></p>
 <div id="en-demandant-à-la-lib-maths" class="section level2">
 <h2>En demandant à la lib maths</h2>
 <p>Mon ordinateur m’indique que <span class="math inline">\(\pi\)</span> vaut <em>approximativement</em></p>

module2/exo1/toy_document_fr.tex

+% Options for packages loaded elsewhere
+\PassOptionsToPackage{unicode}{hyperref}
+\PassOptionsToPackage{hyphens}{url}
+%
+\documentclass[
+]{article}
+\usepackage{amsmath,amssymb}
+\usepackage{lmodern}
+\usepackage{iftex}
+\ifPDFTeX
+  \usepackage[T1]{fontenc}
+  \usepackage[utf8]{inputenc}
+  \usepackage{textcomp} % provide euro and other symbols
+\else % if luatex or xetex
+  \usepackage{unicode-math}
+  \defaultfontfeatures{Scale=MatchLowercase}
+  \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
+\fi
+% Use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+\IfFileExists{microtype.sty}{% use microtype if available
+  \usepackage[]{microtype}
+  \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
+}{}
+\makeatletter
+\@ifundefined{KOMAClassName}{% if non-KOMA class
+  \IfFileExists{parskip.sty}{%
+    \usepackage{parskip}
+  }{% else
+    \setlength{\parindent}{0pt}
+    \setlength{\parskip}{6pt plus 2pt minus 1pt}}
+}{% if KOMA class
+  \KOMAoptions{parskip=half}}
+\makeatother
+\usepackage{xcolor}
+\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
+\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
+\hypersetup{
+  hidelinks,
+  pdfcreator={LaTeX via pandoc}}
+\urlstyle{same} % disable monospaced font for URLs
+\usepackage[margin=1in]{geometry}
+\usepackage{color}
+\usepackage{fancyvrb}
+\newcommand{\VerbBar}{|}
+\newcommand{\VERB}{\Verb[commandchars=\\\{\}]}
+\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
+% Add ',fontsize=\small' for more characters per line
+\usepackage{framed}
+\definecolor{shadecolor}{RGB}{248,248,248}
+\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}}
+\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}}
+\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
+\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}}
+\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
+\newcommand{\BuiltInTok}[1]{#1}
+\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
+\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}}
+\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
+\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
+\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}}
+\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}}
+\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
+\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
+\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}}
+\newcommand{\ExtensionTok}[1]{#1}
+\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
+\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
+\newcommand{\ImportTok}[1]{#1}
+\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
+\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}}
+\newcommand{\NormalTok}[1]{#1}
+\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}}
+\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}}
+\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}}
+\newcommand{\RegionMarkerTok}[1]{#1}
+\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
+\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
+\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
+\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
+\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
+\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
+\usepackage{graphicx}
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
+\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
+\makeatother
+% Scale images if necessary, so that they will not overflow the page
+% margins by default, and it is still possible to overwrite the defaults
+% using explicit options in \includegraphics[width, height, ...]{}
+\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
+% Set default figure placement to htbp
+\makeatletter
+\def\fps@figure{htbp}
+\makeatother
+\setlength{\emergencystretch}{3em} % prevent overfull lines
+\providecommand{\tightlist}{%
+  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
+\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
+\ifLuaTeX
+  \usepackage{selnolig}  % disable illegal ligatures
+\fi
+
+\author{}
+\date{\vspace{-2.5em}}
+
+\begin{document}
+
+\hypertarget{uxe0-propos-du-calcul-de-pi}{%
+\section{À propos du calcul de pi}\label{uxe0-propos-du-calcul-de-pi}}
+
+\emph{Arnaud Legrand}
+
+\emph{25 juin 2018}
+
+\hypertarget{en-demandant-uxe0-la-lib-maths}{%
+\subsection{En demandant à la lib
+maths}\label{en-demandant-uxe0-la-lib-maths}}
+
+Mon ordinateur m'indique que π vaut \emph{approximativement}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{pi}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 3.141593
+\end{verbatim}
+
+\hypertarget{en-utilisant-la-muxe9thode-des-aiguilles-de-buffon}{%
+\subsection{En utilisant la méthode des aiguilles de
+Buffon}\label{en-utilisant-la-muxe9thode-des-aiguilles-de-buffon}}
+
+Mais calculé avec la \textbf{méthode} des
+\href{https://fr.wikipedia.org/wiki/Aiguille_de_Buffon}{aiguilles de
+Buffon}, on obtiendrait comme \textbf{approximation} :
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\FunctionTok{set.seed}\NormalTok{(}\DecValTok{42}\NormalTok{)}
+\NormalTok{N }\OtherTok{=} \DecValTok{100000}
+\NormalTok{x }\OtherTok{=} \FunctionTok{runif}\NormalTok{(N)}
+\NormalTok{theta }\OtherTok{=}\NormalTok{ pi}\SpecialCharTok{/}\DecValTok{2}\SpecialCharTok{*}\FunctionTok{runif}\NormalTok{(N)}
+\DecValTok{2}\SpecialCharTok{/}\NormalTok{(}\FunctionTok{mean}\NormalTok{(x}\SpecialCharTok{+}\FunctionTok{sin}\NormalTok{(theta)}\SpecialCharTok{\textgreater{}}\DecValTok{1}\NormalTok{))}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 3.14327
+\end{verbatim}
+
+\hypertarget{avec-un-argument-fruxe9quentiel-de-surface}{%
+\subsection{Avec un argument ``fréquentiel'' de
+surface}\label{avec-un-argument-fruxe9quentiel-de-surface}}
+
+Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir
+d'appel à la fonction sinus se base sur le fait que si X∼U(0,1) et
+Y∼U(0,1) alors P{[}X2+Y2≤1{]}=π/4 (voir
+\href{https://fr.wikipedia.org/wiki/M\%C3\%A9thode_de_Monte-Carlo\#D\%C3\%A9termination_de_la_valeur_de_\%CF\%80}{méthode
+de Monte Carlo sur Wikipedia}). Le code suivant illustre ce fait:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\FunctionTok{set.seed}\NormalTok{(}\DecValTok{42}\NormalTok{)}
+\NormalTok{N }\OtherTok{=} \DecValTok{1000}
+\NormalTok{df }\OtherTok{=} \FunctionTok{data.frame}\NormalTok{(}\AttributeTok{X =} \FunctionTok{runif}\NormalTok{(N), }\AttributeTok{Y =} \FunctionTok{runif}\NormalTok{(N))}
+\NormalTok{df}\SpecialCharTok{$}\NormalTok{Accept }\OtherTok{=}\NormalTok{ (df}\SpecialCharTok{$}\NormalTok{X}\SpecialCharTok{**}\DecValTok{2} \SpecialCharTok{+}\NormalTok{ df}\SpecialCharTok{$}\NormalTok{Y}\SpecialCharTok{**}\DecValTok{2} \SpecialCharTok{\textless{}=}\DecValTok{1}\NormalTok{)}
+\FunctionTok{library}\NormalTok{(ggplot2)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## Warning: le package 'ggplot2' a été compilé avec la version R 4.3.3
+\end{verbatim}
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\FunctionTok{ggplot}\NormalTok{(df, }\FunctionTok{aes}\NormalTok{(}\AttributeTok{x=}\NormalTok{X,}\AttributeTok{y=}\NormalTok{Y,}\AttributeTok{color=}\NormalTok{Accept)) }\SpecialCharTok{+} \FunctionTok{geom\_point}\NormalTok{(}\AttributeTok{alpha=}\NormalTok{.}\DecValTok{2}\NormalTok{) }\SpecialCharTok{+} \FunctionTok{coord\_fixed}\NormalTok{() }\SpecialCharTok{+} \FunctionTok{theme\_bw}\NormalTok{()}
+\end{Highlighting}
+\end{Shaded}
+
+\includegraphics{toy_document_fr_files/figure-latex/unnamed-chunk-3-1.pdf}
+
+Il est alors aisé d'obtenir une approximation (pas terrible) de π en
+comptant combien de fois, en moyenne, X2+Y2 est inférieur à 1:
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\DecValTok{4}\SpecialCharTok{*}\FunctionTok{mean}\NormalTok{(df}\SpecialCharTok{$}\NormalTok{Accept)}
+\end{Highlighting}
+\end{Shaded}
+
+\begin{verbatim}
+## [1] 3.156
+\end{verbatim}
+
+\end{document}

mooc-rr.Rproj

+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX