1 \documentclass{article
}
8 \mplibcodeinherit{enable
} % pour permettre la mémoire entre les
9 % biginfig(i) produites
10 \newcommand{\lemniscate}[1]{% #1: l'angle en degres
19 carre = (
0,
0)--(
1,
0)--(
1,
1)--(
0,
1)--cycle;
22 pickup pencircle scaled
0.6pt;
23 drawarrow (
0,-s*u)--(
0,s*u);
24 drawarrow (-s*u,
0)--(s*u,
0);
25 path cercle,hori,verti;
28 cercle := fullcircle scaled (a);
29 pickup pencircle scaled
0.4pt;
30 draw cercle dashed evenly withcolor blue;
31 P:=(a/
2*cosd(
#1),a/
2*sind(
#1));
% chemin qui parcourt le cercle
32 Q:=(a/
2*cosd(
#1),
0);
%projection sur (Ox)
33 % projection de Q sur [O,P]
34 R = cosd(
#1)*cosd(
#1)*(a/
2*cosd(
#1),a/
2*sind(
#1));
35 % M sur [PQ] tel que QM = QR
49 if ((
#1>
0) and (
#1<
90)) or ((
#1>
180) and (
#1<
270)):
50 draw carre scaled
6 rotated (angle(Q-P)+
180) shifted Q;
51 draw carre scaled
6 rotated (angle(R-P)) shifted R;
53 if((
#1>=
90) and (
#1<
180)) or ((
#1>=
270) and (
#1<
360)):
54 draw carre scaled
6 rotated (angle(Q-P)+
180) shifted Q;
55 draw carre scaled
6 rotated (angle(R-P)+
180) shifted R;
58 draw O--P dashed evenly withcolor blue;
59 draw P--Q dashed evenly withcolor blue;
60 draw R--Q--M withcolor green;
62 label.lrt(btex $a$ etex, (a/
2,
0));
63 label.llft(btex $x$ etex, (s*u,
0));
64 label.llft(btex $y$ etex, (
0,s*u));
65 label(btex
\itshape Lemniscate
\par de Gerono etex, (-
0.7u,
1.15u));
66 label(btex $x^
4=a^
2(x^
2-y^
2)$ etex, (
0.7u,-
1.15u));
69 dotlabel.llft(btex $O$ etex, O);
70 dotlabel.urt(btex $M$ etex, M);
71 dotlabel.urt(btex $P$ etex, P);
72 dotlabel.urt(btex $Q$ etex, Q);
73 dotlabel.urt(btex $R$ etex, R);
75 pickup pencircle scaled
1pt;
76 draw lemn withcolor red;
78 clip currentpicture to (-s*u,-s*u)--(s*u,-s*u)--(s*u,s*u)--(-s*u,s*u)--cycle;
85 \begin{animateinline
}[poster=last, controls
]{24}
87 \multiframe{360}{i=
0+
1}{\lemniscate{\i}}
91 Le PDF produit est à télécharger dans la liste plus haut.