summaryrefslogtreecommitdiffstats
path: root/notes-mitro206.tex
diff options
context:
space:
mode:
authorDavid A. Madore <david+git@madore.org>2016-02-16 14:46:21 (GMT)
committerDavid A. Madore <david+git@madore.org>2016-02-16 14:46:21 (GMT)
commit362ce5d5dc7aa081696c0707d52111947a69c31a (patch)
tree5378f523c4329cd88d59d88953522287227e71cd /notes-mitro206.tex
parent19f2c053fe5485d4246568ce4a7b93ff324eabf6 (diff)
downloadmitro206-362ce5d5dc7aa081696c0707d52111947a69c31a.zip
mitro206-362ce5d5dc7aa081696c0707d52111947a69c31a.tar.gz
mitro206-362ce5d5dc7aa081696c0707d52111947a69c31a.tar.bz2
Illustration for Hercules-versus-Hydra game.
Diffstat (limited to 'notes-mitro206.tex')
-rw-r--r--notes-mitro206.tex63
1 files changed, 62 insertions, 1 deletions
diff --git a/notes-mitro206.tex b/notes-mitro206.tex
index f50a49d..11fd8c2 100644
--- a/notes-mitro206.tex
+++ b/notes-mitro206.tex
@@ -18,7 +18,7 @@
\usepackage{graphics}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
-\usetikzlibrary{matrix}
+\usetikzlibrary{matrix,calc}
%
\theoremstyle{definition}
\newtheorem{comcnt}{Tout}[subsection]
@@ -647,6 +647,67 @@ souhaite. Hercule gagne s'il réussit à décapiter le dernier nœud de
l'hydre ; l'hydre gagnerait si elle réussissait à survivre
indéfiniment.
+\begin{center}
+\begin{tikzpicture}[baseline=0]
+\draw[very thin] (-1.5,0) -- (1.5,0);
+\begin{scope}[every node/.style={circle,fill,inner sep=0.5mm}]
+\node (P0) at (0,0) {};
+\node (P1) at (0,1) {};
+\node (P2) at (-1,2) {};
+\node (P3) at (0,2) {};
+\node (P4) at (1,2) {};
+\node (P5) at (0.5,3) {};
+\node (P6) at (1.5,3) {};
+\end{scope}
+\begin{scope}[line width=1.5pt]
+\draw (P0) -- (P1);
+\draw (P1) -- (P2);
+\draw (P1) -- (P3);
+\draw (P1) -- (P4);
+\draw (P4) -- (P5);
+\draw (P4) -- (P6);
+\end{scope}
+\begin{scope}[line width=3pt,red]
+\draw ($(P6) + (-0.2,-0.2)$) -- ($(P6) + (0.2,0.2)$);
+\draw ($(P6) + (-0.2,0.2)$) -- ($(P6) + (0.2,-0.2)$);
+\end{scope}
+\node[anchor=west] at (P6) {$x$};
+\node[anchor=west] at (P4) {$y$};
+\node[anchor=west] at (P1) {$z$};
+\end{tikzpicture}
+devient
+\begin{tikzpicture}[baseline=0]
+\draw[very thin] (-1.5,0) -- (1.5,0);
+\begin{scope}[every node/.style={circle,fill,inner sep=0.5mm}]
+\node (P0) at (0,0) {};
+\node (P1) at (0,1) {};
+\node (P2) at (-1,2) {};
+\node (P3) at (0,2) {};
+\node (P4) at (0.8,2) {};
+\node (P5) at (0.6,3) {};
+\node (P4b) at (1.2,2) {};
+\node (P5b) at (1.2,3) {};
+\node (P4c) at (1.7,2) {};
+\node (P5c) at (1.7,3) {};
+\node (P4d) at (2.2,2) {};
+\node (P5d) at (2.2,3) {};
+\end{scope}
+\begin{scope}[line width=1.5pt]
+\draw (P0) -- (P1);
+\draw (P1) -- (P2);
+\draw (P1) -- (P3);
+\draw (P1) -- (P4);
+\draw (P4) -- (P5);
+\draw[blue] (P1) -- (P4b);
+\draw[blue] (P4b) -- (P5b);
+\draw[blue] (P1) -- (P4c);
+\draw[blue] (P4c) -- (P5c);
+\draw[blue] (P1) -- (P4d);
+\draw[blue] (P4d) -- (P5d);
+\end{scope}
+\end{tikzpicture}
+\end{center}
+
Ce jeu est particulier en ce que, mathématiquement, non seulement
Hercule possède une stratégie gagnante, mais en fait Hercule gagne
\emph{toujours}, quoi qu'il fasse et quoi que fasse l'hydre.