
 \partie{Principe de la méthode}
 \begin{minipage}{.65\linewidth}
   \begin{enumerate}
   \item Dans un plan muni d'un repère orthogonal, on considère un
     domaine $\mathscr{D}$, d'aire $\mathscr{A}$, autour duquel on
     considère un rectangle de dimensions, et donc d'aire
     $\mathscr{R}$, connues.
   \item On choisit aléatoirement $N$ points dans ce rectangle et on
     compte le nombre $n$ de points qui appartiennent à $\mathscr{D}$.
   \item Si le choix des points est suffisamment aléatoire, il semble
     assez naturel que l'aire de $\mathscr{D}$ est proportionnelle au
     nombre de points appartenant à $\mathscr{D}$.
   \end{enumerate}
 \end{minipage}\quad
 \begin{minipage}{.35\linewidth}
   \def \tb {\tiny$\bullet$}
   \begin{center}
     \begin{tikzpicture}[xscale=0.4, yscale=0.4]
       \draw (-4.5,0)--(6,0); \draw (0,-0.5)--(0,5.5); \draw[color=F1,
       thick] (-4,0.5)--(5.5,0.5)--(5.5,5)--(-4,5)--cycle; \draw[<->,
       thick, color=F1] (5.9,0.5)--(5.9,5) node[midway,right]{$l$};
       \draw[<->, thick, color=F1] (5.5,5.4)--(-4,5.4)
       node[midway,above]{$L$}; \draw[ultra thick, ->] (0,0)--(1.5,0);
       \draw[ultra thick, ->] (0,0)--(0,1.5); \draw[color=black]
       (0.75,0) node[below] {$\overrightarrow{i}$}; \draw[color=black]
       (0,0.75) node[left] {$\overrightarrow{j}$}; \draw[color=C1]
       (2,2) node {$\mathscr{D}$};
       \begin{scope}
         \draw[color=A1, thick] (-3,0.6) .. controls +(1,0) and
         +(-1,0) .. (0,1.8) .. controls +(1,0) and +(0.6,-4) .. (5,3)
         .. controls +(-0.3,2) and +(2.1,0.5) .. (0,4) .. controls
         +(-2.1,-0.5) and +(0,3) .. (-3,3) .. controls +(0,-1) and
         +(-1,0).. (-3,0.6); \fill[color=C1, opacity=0.2] (-3,0.6)
         .. controls +(1,0) and +(-1,0) .. (0,1.8) .. controls +(1,0)
         and +(0.6,-4) .. (5,3) .. controls +(-0.3,2) and +(2.1,0.5)
         .. (0,4) .. controls +(-2.1,-0.5) and +(0,3) .. (-3,3)
         .. controls +(0,-1) and +(-1,0).. (-3,0.6);
       \end{scope}
       \draw (-2.02,1.1) node {\tb}; \draw (-3.27,1.56) node {\tb};
       \draw (-3.55,3.27) node {\tb}; \draw (-3.17,4.38) node {\tb};
       \draw (-2.53,3.02) node {\tb}; \draw (-1.36,2.06) node {\tb};
       \draw (-1.62,3.57) node {\tb}; \draw (-0.95,4.14) node {\tb};
       \draw (-0.86,2.97) node {\tb}; \draw (-0.62,0.94) node {\tb};
       \draw (0.45,4.45) node {\tb}; \draw (0.86,3.48) node {\tb};
       \draw (0.54,2.44) node {\tb}; \draw (0.67,1.09) node {\tb};
       \draw (-1.54,4.58) node {\tb}; \draw (1.72,2.92) node {\tb};
       \draw (1.28,1.68) node {\tb}; \draw (2.33,1.12) node {\tb};
       \draw (2.32,2.54) node {\tb}; \draw (2.55,3.46) node {\tb};
       \draw (3.54,4.48) node {\tb}; \draw (3.6,3.47) node {\tb};
       \draw (2.97,1.95) node {\tb}; \draw (3.81,1.12) node {\tb};
       \draw (4.06,2.22) node {\tb}; \draw (4.64,3.15) node {\tb};
       \draw (4.98,3.4) node {\tb}; \draw (4.84,1.60) node {\tb};
       \draw (1.5,4) node {\tb};
     \end{tikzpicture}
   \end{center}
 \end{minipage}

  On pourra se reporter au chapitre Lois à densité, p. 30 pour une approche probabiliste de cette méthode.
 
