From d145b7402735ca2cc2c58ab570d3bf6c9dd19acf Mon Sep 17 00:00:00 2001 From: Guillaume Garnier Date: Thu, 26 Dec 2024 13:44:33 +0100 Subject: [PATCH] Modification papillon --- index.aux | 63 +++ index.fdb_latexmk | 316 ++++++++++++ index.fls | 550 +++++++++++++++++++++ index.log | 1160 +++++++++++++++++++++++++++++++++++++++++++++ index.out | 10 + index.pdf | Bin 0 -> 369875 bytes index.synctex.gz | Bin 0 -> 147590 bytes index.toc | 11 + src/bacteries.tex | 8 +- 9 files changed, 2114 insertions(+), 4 deletions(-) create mode 100644 index.aux create mode 100644 index.fdb_latexmk create mode 100644 index.fls create mode 100644 index.log create mode 100644 index.out create mode 100644 index.pdf create mode 100644 index.synctex.gz create mode 100644 index.toc diff --git a/index.aux b/index.aux new file mode 100644 index 0000000..941178c --- /dev/null +++ b/index.aux @@ -0,0 +1,63 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\@nameuse{bbl@beforestart} +\catcode `:\active +\catcode `;\active +\catcode `!\active +\catcode `?\active +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\babel@aux{french}{} +\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Préambule}}{1}{section*.1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Notations}}{1}{section*.3}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Un exemple de propagation, qui montre que le nombre 3 est réalisable. 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gradués}}{6}{section.3}% +\contentsline {section}{\tocsection {}{4}{Transformation de papillons}}{7}{section.4}% +\contentsline {section}{\tocsection {}{5}{Gerrymandering}}{8}{section.5}% +\contentsline {section}{\tocsection {}{6}{Le cauchemar de la ligne 20-25}}{9}{section.6}% +\contentsline {section}{\tocsection {}{7}{Le poids des graphes}}{11}{section.7}% +\contentsline {section}{\tocsection {}{8}{Points colorés sur un cercle}}{13}{section.8}% diff --git a/src/bacteries.tex b/src/bacteries.tex index e193b4b..25b429a 100644 --- a/src/bacteries.tex +++ b/src/bacteries.tex @@ -17,14 +17,14 @@ Est-il possible que l'un des papillons atteigne une taille arbitrairement grande Nous faisons désormais l'hypothèse que tous les papillons se transforment en même temps. -\q Chaque jour, chaque papillon se transforme en deux papillons: Le premier hérite de 80\% de l'envergure du parent, et le second de 120\%. -Soit $x \in [0, \infty[$. Quelle est la proportion de papillons ayant une taille supérieure à $x$ le $n$-ème jour ? Et la proportion de papillons ayant une taille inférieure à $x$ ? (\textit{On pourra commencer par regarder des valeurs particulières de $x$}) +\q Chaque jour, chaque papillon se transforme en deux papillons: Le premier hérite de 80\% de l'envergure du parent, et le second de 125\%. +Soit $x \in [0, \infty[$. Estimer la proportion de papillons ayant une taille supérieure à $x$ le $n$-ème jour ? Et la proportion de papillons ayant une taille inférieure à $x$ ? (\textit{On pourra commencer par regarder des valeurs particulières de $x$}) -\q Chaque jour, chaque papillon se transforme en deux papillons. Le premier hérite de 80\% de l'envergure de son parent, et le second de 120\% de l'envergure de son grand-parent. +\q Chaque jour, chaque papillon se transforme en deux papillons. Le premier hérite de 80\% de l'envergure de son parent, et le second de 125\% de l'envergure de son grand-parent. (Puisqu'il n'y a pas de grand parent à la première transformation, on supposera que le grand parent a la même envergure que le parent.) Soit $x \in [0, \infty[$. Quelle est la proportion de papillons ayant une taille strictement supérieure à $x$ le $n$-ème jour ? Et la proportion de papillons ayant une taille strictement inférieure à $x$ ? (\textit{On pourra commencer par regarder des valeurs particulières de $x$}) -\q Chaque jour, chaque papillon se transforme en deux papillons. La taille des nouveaux papillons est tirée aléatoirement selon une loi de probabilité. Peut-on retrouver cette loi de probabilité en observant assez longtemps l'évolution des papillons ? +\q Chaque jour, chaque papillon se transforme en deux papillons. La taille des nouveaux papillons est tirée aléatoirement selon une loi de probabilité continue. Peut-on retrouver cette loi de probabilité en observant assez longtemps l'évolution des papillons ? \q Proposer et étudier d'autres pistes de recherche.