From 54a6f0b355ed5c86a074c439bec08cd34e6d59da Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 27 May 2021 12:10:30 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=201E=20et=201P=20sur=20l'=C3=A9chelle=20l?= =?UTF-8?q?og=20pour=20les=20TST?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/13_echelle_log/1E_echelle_log.pdf | Bin 0 -> 20788 bytes TST/13_echelle_log/1E_echelle_log.tex | 18 +++ TST/13_echelle_log/1P_ordre_grandeur.pdf | Bin 0 -> 59304 bytes TST/13_echelle_log/1P_ordre_grandeur.tex | 171 +++++++++++++++++++++++ TST/13_echelle_log/exercises.tex | 98 +++++++++++++ TST/13_echelle_log/index.rst | 10 +- 6 files changed, 296 insertions(+), 1 deletion(-) create mode 100644 TST/13_echelle_log/1E_echelle_log.pdf create mode 100644 TST/13_echelle_log/1E_echelle_log.tex create mode 100644 TST/13_echelle_log/1P_ordre_grandeur.pdf create mode 100644 TST/13_echelle_log/1P_ordre_grandeur.tex diff --git 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+\documentclass[11pt,xcolor=table]{classPres} + +\setlength\columnsep{0pt} + +\title{Ordre de grandeurs} +\date{Mai 2021} + +\begin{document} + +\begin{frame}{Regrouper le choses en fonction de leur taille} + \begin{multicols}{2} + \begin{itemize} + \item Un chat + \visible<2>{ + \begin{center} + $\approx 30cm$ + \end{center} + } + \item Un grain de sable + \visible<2>{ + \begin{center} + $\approx 0.5mm$ + \end{center} + } + \item Longueur de l'équateur + \visible<2>{ + \begin{center} + $\approx \np{40000}km$ + \end{center} + } + \item Un homme + \visible<2>{ + \begin{center} + $\approx 1,7m$ + \end{center} + } + \item Insecte + \visible<2>{ + \begin{center} + $\approx 1mm$ + \end{center} + } + \item Un marathon + \visible<2>{ + \begin{center} + $\approx 42km$ + \end{center} + } + \item Un virus + \visible<2>{ + \begin{center} + $\approx 10^{-8}m$ + \end{center} + } + \item L'altitude du mont blanc + \visible<2>{ + \begin{center} + $\approx \np{4810}m$ + \end{center} + } + \item La distance terre-lune + \visible<2>{ + \begin{center} + $\approx \np{384400}km$ + \end{center} + } + \item Diamètre d'un cheveux + \visible<2>{ + \begin{center} + $\approx 0,0001m$ + \end{center} + } + \end{itemize} + \end{multicols} +\end{frame} + +\begin{frame}{Placer ces choses sur un axe en fonction de leur taille} + \begin{multicols}{2} + \begin{itemize} + \item Un chat + \begin{center} + $\approx 30cm$ + \end{center} + \item Un grain de sable + \begin{center} + $\approx 0.5mm$ + \end{center} + \item Longueur de l'équateur + \begin{center} + $\approx \np{40000}km$ + \end{center} + \item Un homme + \begin{center} + $\approx 1,7m$ + \end{center} + \item Insecte + \begin{center} + $\approx 1mm$ + \end{center} + \item Un marathon + \begin{center} + $\approx 42km$ + \end{center} + \item Un virus + \begin{center} + $\approx 10^{-8}m$ + \end{center} + \item L'altitude du mont blanc + \begin{center} + $\approx \np{4810}m$ + \end{center} + \item La distance terre-lune + \begin{center} + $\approx \np{384400}km$ + \end{center} + \item Diamètre d'un cheveux + \begin{center} + $\approx 0,0001m$ + \end{center} + \end{itemize} + \end{multicols} +\end{frame} + +\begin{frame}{Échelle logarithmique} + Un chat + \begin{center} + $\approx 30cm = 0.3m \Rightarrow \log(0.3) = -0.5$ + \end{center} + Placer tous les éléments sur l'échelle logarithmique. + \begin{multicols}{2} + \begin{itemize} + \item Un grain de sable + \begin{center} + $\approx 0.5mm$ + \end{center} + \item Longueur de l'équateur + \begin{center} + $\approx \np{40000}km$ + \end{center} + \item Un homme + $\approx 1,7m$ + \item Insecte + $\approx 1mm$ + \item Un marathon + $\approx 42km$ + \item Un virus + $\approx 10^{-8}m$ + \item L'altitude du mont blanc + \begin{center} + $\approx \np{4810}m$ + \end{center} + \item La distance terre-lune + \begin{center} + $\approx \np{384400}km$ + \end{center} + \item Diamètre d'un cheveux + \begin{center} + $\approx 0,0001m$ + \end{center} + \end{itemize} + \end{multicols} +\end{frame} + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/TST/13_echelle_log/exercises.tex b/TST/13_echelle_log/exercises.tex index abf5aed..c5fd428 100644 --- a/TST/13_echelle_log/exercises.tex +++ b/TST/13_echelle_log/exercises.tex @@ -1,2 +1,100 @@ \collectexercises{banque} +\begin{exercise}[subtitle={Population mondiale}, step={1}, origin={Création}, topics={Fonction Logarithme}, tags={Analyse, logarithme}] + \begin{minipage}{0.4\linewidth} + Les données ci-contre sont données en milliards de personnes. + \begin{enumerate} + \item Représenter graphiquement ces données dans un repère avec l'année en abscisse et la population en ordonnée. + \item À l'aide du graphique, estimer la population en l'an 0 puis en 2000. + \item Représenter graphiquement ces données dans un repère avec l'année en abscisse et le logarithme de la population en ordonnée. + \item Refaire l'estimation. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.5\linewidth} + \begin{tabular}{|p{2cm}|p{2cm}|p{4.5cm}|} + \hline + Année & Population & logarithme de la population\\ + \hline + 0 & 0,206 & \\ + 400 & 0,206 & \\ + 1000 & 0,679 & \\ + 1800 & 1,125 & \\ + 1900 & 1,762 & \\ + 1910 & 1,750 & \\ + 1920 & 1,860 & \\ + 1930 & 2,07 & \\ + 1940 & 2,3 & \\ + 1950 & 2,5 & \\ + 2000 & 2,5 & \\ + \hline + \end{tabular} + \end{minipage} + + \begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=0.7] + \tkzInit[xmin=0,xmax=8,xstep=1, + ymin=0,ymax=6,ystep=1] + \tkzGrid + \tkzDrawY[label=Population, right=1pt] + \tkzDrawX[label=Année] + \end{tikzpicture} + \hfill + \begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=0.7] + \tkzInit[xmin=0,xmax=8,xstep=1, + ymin=0,ymax=6,ystep=1] + \tkzGrid + \tkzDrawY[label=Population, right=1pt] + \tkzDrawX[label=Année] + \end{tikzpicture} +\end{exercise} + +\begin{exercise}[subtitle={Intensité sonore}, step={1}, origin={Création}, topics={Fonction Logarithme}, tags={Analyse, logarithme}] + \begin{minipage}{0.5\linewidth} + Correspondance entre l’augmentation de l’énergie sonore et son équivalent de niveau sonore en décibels (dB) + \begin{enumerate} + \item Représenter graphiquement ces données dans un repère avec le niveau sonore en abscisse et l'énergie en ordonnée. + \item Estimer par combien faut-il multiplier l'énergie pour augmenter le niveau sonore de 15. De 30. + \item Représenter graphiquement ces données dans un repère avec le niveau sonore en abscisse et le logarithme de l'énergie en ordonnée. + \item Refaire l'estimation. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \begin{tabular}{|p{3.5cm}|p{3.5cm}|} + \hline + Augmentation du niveau sonore de & Multiplication de l'énérgie sonore par \\ + \hline + 3dB & 2 \\ + 5dB & 3 \\ + 6dB & 4 \\ + 7dB & 5 \\ + 8dB & 6 \\ + 9dB & 8 \\ + 10dB & 10 \\ + 15dB & \\ + 20dB & 100 \\ + 30dB & \\ + \hline + \end{tabular} + \end{minipage} + + \begin{tikzpicture}[baseline=(a.north), xscale=1.2, yscale=0.7] + \tkzInit[xmin=0,xmax=6,xstep=1, + ymin=0,ymax=6,ystep=1] + \tkzGrid + \tkzDrawY[label=Énergie, right=1pt] + \tkzDrawX[label=Niveau] + \end{tikzpicture} + \hfill + \begin{tikzpicture}[baseline=(a.north), xscale=1.2, yscale=0.7] + \tkzInit[xmin=0,xmax=6,xstep=1, + ymin=0,ymax=6,ystep=1] + \tkzGrid + \tkzDrawY[label=Énergie, right=1pt] + \tkzDrawX[label=Niveau] + \end{tikzpicture} + +\end{exercise} + + + \collectexercisesstop{banque} diff --git a/TST/13_echelle_log/index.rst b/TST/13_echelle_log/index.rst index 97abf26..9d9fcc6 100644 --- a/TST/13_echelle_log/index.rst +++ b/TST/13_echelle_log/index.rst @@ -2,7 +2,7 @@ ##################### :date: 2021-05-20 -:modified: 2021-05-20 +:modified: 2021-05-27 :authors: Benjamin Bertrand :tags: Fonctions inverse :category: TST @@ -15,8 +15,16 @@ Présentation sur les échelles log pour représenter des objets de tailles différentes. +.. image:: ./1P_ordre_grandeur.pdf + :height: 200px + :alt: Découverte de l'échelle logarithmique + Exercice: tracer 2 graphiques 1 échelle normale et un échelle log. +.. image:: ./1E_echelle_log.pdf + :height: 200px + :alt: Exercices sur la représentation dans une graphique log + Conclusion des exercices par un ajustement affine et transfo d'expression. Bilan: représentation graphiques