%input newcourbes;
%input couleur;
input geometriesyr16;
%input TEX;

verbatimtex
%&latex
\documentclass{article}
\usepackage[upright]{fourier}
\usepackage{preambule}
\begin{document}
etex












%% fig 1 carrés


u:=1.5cm;
figure(-1.5u,-3.5u,10u,3u)


pair A,B,C,D,E,F,G,H,I,J,K,L;

numeric a,b;

a:=2*u; b:=0.5*u;

A:=origin; J:=A shifted (a-b,0); I:=A shifted (a,0); H:=A shifted (a+b,0);
B:=A shifted (0,-a+b);K:=A shifted (a-b,-a+b); C:=A shifted (0,-a);D:=A shifted (0,-a-b);
L:=A shifted (a,-a);E:=A shifted (a,-a-b);F:=A shifted (a+b,-a-b);G:=A shifted (a+b,-a);


path p,q;
p:=polygone(B,K,J,H,F,D);
fillcolor:=jaune;
transparence p;
trace p withpen pencircle scaled 1.2bp withcolor red;
q:=chemin(B,A,J);
trace q withpen pencircle scaled 1.2bp withcolor red;
trace C--G withpen pencircle scaled 1.2bp withcolor red;
trace I--E withpen pencircle scaled 1.2bp withcolor red;

trace cotation(A,I,6mm,2mm,btex \footnotesize   $2x$ etex );
trace cotation(I,H,2mm,2mm,btex   \footnotesize  $y$ etex );
trace cotation(J,I,2mm,2mm,btex   \footnotesize  $y$ etex );

trace cotation(C,A,6mm,2mm,btex \footnotesize $2x$ etex );
trace cotation(C,B,2mm,2mm,btex   \footnotesize  $y$ etex );
trace cotation(D,C,2mm,2mm,btex  \footnotesize  $y$ etex );


fin;






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  CERCLES TRIGO
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%fig2
 
figure(0,0,6cm,6cm);
pair M,N,P,O;
path cc;

O:=(3cm,3cm);

drawarrow (3cm,0)--(3cm,6cm);drawarrow (0,3cm)--(6cm,3cm);

cc:=cercles(O,2cm);
trace grille(0.5) withcolor .5white;

trace cc withpen pencircle scaled 1.1bp withcolor 0.5white;

M:=pointarc(cc,135);
N:=pointarc(cc,210);
P:=pointarc(cc,120);

dotlabel.ulft(btex M etex,M );
dotlabel.top(btex P etex,P );
dotlabel.llft(btex N etex,N );
label.lrt(btex O etex,O );
label.bot(btex {\footnotesize $\cos\pa{\frac{2\pi}{3}}=-\frac{1}{2}$} etex,(2cm,3cm) );
label.rt(btex {\footnotesize $\sin\pa{-\frac{5\pi}{6}}=-\frac{1}{2}$} etex,(3cm,2cm) );

draw O--M dashed evenly;
draw P--(2cm,3cm) dashed evenly;
draw N--(3cm,2cm) dashed evenly;
fin;

%fig3




figure(0,0,6cm,6cm);
pair M,N,P,O;
path cc;

O:=(3cm,3cm);

drawarrow (3cm,0)--(3cm,6cm);drawarrow (0,3cm)--(6cm,3cm);

cc:=cercles(O,2cm);
trace grille(0.5) withcolor .5white;

trace cc withpen pencircle scaled 1.1bp withcolor 0.5white;


N:=pointarc(cc,240);
P:=pointarc(cc,120);

dotlabel.ulft(btex $\frac{2\pi}{3}$ etex,P );
dotlabel.llft(btex $\frac{4\pi}{3}$ etex,N );
%label.lrt(btex O etex,O );
dotlabel.lrt(btex {\footnotesize $-\frac{1}{2}$} etex,(2cm,3cm) );
%label.rt(btex {\footnotesize $\sin\pa{-\frac{5\pi}{6}}=-\frac{1}{2}$} etex,(3cm,2cm) );

draw N--P dashed evenly withpen pencircle scaled 1.2bp withcolor red;

fin;



%fig4

figure(0,0,6cm,6cm);
pair M,N,P,O;
path cc,aa;

O:=(3cm,3cm);

drawarrow (3cm,0)--(3cm,6cm);drawarrow (0,3cm)--(6cm,3cm);

cc:=cercles(O,2cm);
trace grille(0.5) withcolor .5white;

trace cc withpen pencircle scaled 1.1bp withcolor 0.5white;

M:=pointarc(cc,135);
N:=pointarc(cc,45);




fillcolor:=jaune;
aa:=M--arccercle(M,N,O)--cycle;
transparence aa;
trace arccercle(M,N,O)  withpen pencircle scaled 1.2bp withcolor orange;

dotlabel.ulft(btex $\frac{3\pi}{4}$ etex,M );
dotlabel.urt(btex $\frac{\pi}{4}$ etex,N );
dotlabel.urt(btex {\footnotesize $\frac{\sqrt{2}}{2}$} etex,(3cm,4.414cm) );
dotlabel.ulft(btex $\pi$ etex, (1cm,3cm) );
dotlabel.llft(btex $-\pi$ etex, (1cm,3cm) );

draw O--M dashed evenly;
draw O--N dashed evenly;
draw M--N withpen pencircle scaled 1.1bp withcolor orange dashed evenly;
fin;





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%        S I M I L I T U D E S avec geometriesyr16
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% fig 5
numeric u,k;
u:=1cm;k:=1.8;
figure(-1.5u,-3.5u,10u,3u)

pair A,B,C,A',B',C',O;
path t,tt;
O:=origin;
A=u*(2,-1.5); B=u*(3,-1); C=u*(2.2,1);
t:=polygone(A,B,C);
A':=A scaled k; B':=B scaled k; C':=C scaled k;
tt:=t scaled k;
trace t withpen pencircle scaled 1.3bp withcolor green;
trace tt withpen pencircle scaled 1.3bp withcolor blue;
trace segment (O,A') dashed evenly;
trace segment (O,B') dashed evenly;
trace segment (O,C') dashed evenly;
nomme.bot(A);
nomme.bot(A');
nomme.lft(O);
nomme.urt(B);
nomme.urt(B');
nomme.top(C);
nomme.top(C');


fillcolor:=jaune;
transparence t;
fillcolor:=ciel;
transparence tt;


fin;





%fig6

figure(-5u,-.5u,5u,5.5u)
pair A,B,O,M,M',C,S,S',D;
A=u*(4,0);B=u*(-4,0);O=origin;
marque_p:="plein";
path cc;
cc:= arccercle(A,B,O);
trace cc withpen pencircle scaled 1.3bp withcolor blue;

M:=pointarc(cc,60);D:=rotation(A,O,90);
M':=symetrie(M,O,D);
C:=projection(M,A,B);
C':=projection(M',A,B);
S:=projection(M,O,D);
trace chemin(C,M,M',C') dashed evenly;


trace Codeangle(A,O,M,2,btex $\theta$ etex);

marque_a:=40;
trace Codeangle(A,O,M',1,btex $\pi-\theta$ etex) withcolor orange;

trace droite(A,B)withpen pencircle scaled 1.3bp;
trace segment (O,M);
trace segment (O,M') withcolor orange;
trace segment (O,D)withpen pencircle scaled 1.3bp;

label.bot(btex $\cos(\theta)$ etex, C );


label.bot(btex $\cos(\pi-\theta)$ etex, C' ) withcolor orange;


label.urt(btex $\sin\theta$ etex, S );


label.ulft(btex $\sin(\pi-\theta)$ etex, S ) withcolor orange;
label.bot(btex 0 etex, O);

pointe(M);pointe(M');pointe(O);pointe(S);

fin;




%fig7
figure(-3u,-3u,5u,3u)
path cc;
cc:=cercle(origin,2cm); trace cc dashed evenly;

pair O,A,B,C,D,M;
O:=origin;A=u*(2.3,0);B:=symetrie(A,O);C:=rotation(A,O,-90);D:=rotation(A,O,90);M:=pointarc(cc,40);
drawarrow C--D; drawarrow B--A;
draw O--M withpen pencircle scaled 1.3bp;
label.urt(btex $\arg Z=\arg Z'$ etex,M);
label.rt(btex \fbox{$Z=Z'$ : similitude directe} etex, C);
fin;



%fig8

figure(-3u,-3u,5u,3u)
path cc;
cc:=cercle(origin,2cm); trace cc dashed evenly;

pair O,A,B,C,D,M,M';
O:=origin;A=u*(2.3,0);B:=symetrie(A,O);C:=rotation(A,O,-90);D:=rotation(A,O,90);M:=pointarc(cc,40);
M':=symetrie(M,O,A);
drawarrow C--D; drawarrow B--A;
draw O--M withpen pencircle scaled 1.3bp;draw O--M' withcolor orange withpen pencircle scaled 1.3bp;
label.rt(btex $\arg Z'=-\arg Z$ etex,M') withcolor orange;
label.rt(btex \fbox{$Z'=\bar{Z}$ : similitude indirecte}  etex, C);

fin;



%fig9


figure(-1.5u,-3.5u,10u,3u)

pair A,B,C,A',B',C',v,D,D';
path t,tt;
v:=(4u,u);
A=u*(2,-1.5); B=u*(3,-1); C=u*(2.2,1);
t:=polygone(A,B,C);
A':=A shifted v; B':=B shifted v; C':=C shifted v;
tt:=t shifted v;
trace t withpen pencircle scaled 1.3bp withcolor green;
trace tt withpen pencircle scaled 1.3bp withcolor blue;
drawarrow A--A' dashed evenly;
drawarrow B--B' dashed evenly;
drawarrow C--C' dashed evenly;
label.bot(btex $M$ etex, A);
label.bot(btex $M'$ etex,A');
label.urt(btex $N$ etex,B);
label.urt(btex $N'$ etex,B');
label.top(btex $P$ etex,C);
label.top(btex $P'$ etex,C');
D:=C shifted(0,u); D':=C' shifted(0,u); 
drawarrow D--D' withcolor orange;
label.top(btex $\overrightarrow{v}$ etex, 0.5[D,D']) withcolor orange;

fillcolor:=jaune;
transparence t;
fillcolor:=ciel;
transparence tt;
fin;







%fig10


figure(-1.5u,-3.5u,10u,4u)

pair A,B,C,A',B',C',D;
path T,tt;
numeric t;
t:=60;
A=u*(2,-1.5); B=u*(3,-1); C=u*(1.2,.5); D=u*(-1,0);
T:=polygone(A,B,C);
A':=A rotatedaround(D,t); B':=B rotatedaround(D,t); C':=C rotatedaround(D,t);
tt:=T rotatedaround(D,t);
trace T withpen pencircle scaled 1.3bp withcolor green;
trace tt withpen pencircle scaled 1.3bp withcolor blue;
draw D--A dashed evenly scaled 0.5;draw D--A' dashed evenly scaled 0.5;
draw D--B dashed withdots withpen pencircle scaled 1.5bp;draw D--B' dashed withdots withpen pencircle scaled 1.5bp;
draw D--C dashed evenly scaled 2;draw D--C' dashed evenly scaled 2;

trace codesegments(D,A,D,A',1);trace codesegments(D,B,D,B',2); trace codesegments(D,C,D,C',4);
label.bot(btex $M$ etex, A);
label.bot(btex $M'$ etex,A');
label.urt(btex $N$ etex,B);
label.urt(btex $N'$ etex,B');
label.top(btex $P$ etex,C);
label.top(btex $P'$ etex,C');


label.lft(btex $C$ etex, D);


fillcolor:=jaune;
transparence T;
fillcolor:=ciel;
transparence tt;

fin;





%fig11


figure(-1.5u,-3.5u,10u,3u)

pair A,B,C,A',B',C',v,D,D',I,J,K;
path t,tt;

A=u*(2,-1.5); B=u*(3,-1); C=u*(2.2,1);
t:=polygone(A,B,C);
D=u*(4.5,-2); D'=u*(4,3);
A':=A reflectedabout(D,D'); B':=B reflectedabout(D,D'); C':=C reflectedabout(D,D');
tt:=t reflectedabout(D,D');
I:=0.5[A,A'];J:=0.5[B,B'];K:=0.5[C,C'];
trace t withpen pencircle scaled 1.3bp withcolor green;
trace tt withpen pencircle scaled 1.3bp withcolor blue;
draw A--A' dashed evenly scaled 2;
draw B--B' dashed evenly scaled 0.5;
draw C--C' dashed withdots withpen pencircle scaled 1.5bp;
label.bot(btex $M$ etex, A);
label.bot(btex $M'$ etex,A');
label.urt(btex $N$ etex,B);
label.ulft(btex $N'$ etex,B');
label.top(btex $P$ etex,C);
label.top(btex $P'$ etex,C');
 
trace droite(D,D') withcolor orange;
label.urt(btex $\DR$ etex, D) withcolor orange;

trace codeperp(C',K,D,5);trace codeperp(B',J,D,5); trace codeperp(A',I,D,5);

trace codesegments(A',I,I,A,1);trace codesegments(C',K,K,C,2);trace codesegments(B',J,J,B,4);



fillcolor:=jaune;
transparence t;
fillcolor:=ciel;
transparence tt;
fin;





%fig12


figure(-1.5u,-3.5u,10u,3u)
pair C,E,M,M';


marque_p:="non";

C:=origin; E=u*(2,0); M=u*(4,1); M':=rotation(M,C,30);

drawarrow C--E;
drawarrow C--M withpen pencircle scaled 1.3bp;
drawarrow C--M' withpen pencircle scaled 1.3bp withcolor orange;

trace arccercle(M,M',C) dashed evenly withcolor orange;

marque_a:=30;
trace Codeangle(E,C,M,1,btex $\theta$ etex);

marque_a:=20;
trace Codeangle(M,C,M',2,btex $\alpha$ etex) withcolor orange;

nomme.rt(M);
nomme.rt(M');
nomme.lft(C);
label.bot(btex $\ve{e_1}$ etex, 0.5E);

fin;





%fig13






figure(-1.5u,-3.5u,10u,3u)

pair A,B,C,A',B',C',v,D,D',I,J,K;

A=u*(2,-2); B=u*(3,2);

D=u*(4.5,-3); D'=u*(4,2);
A':=A reflectedabout(D,D'); B':=B reflectedabout(D,D');

I:=0.5[A,A'];J:=0.5[B,B'];
draw A--I dashed evenly;
draw I--A' dashed evenly withcolor orange;
draw J--A' withcolor orange;
draw J--A;

label.bot(btex $M$ etex, A);
label.bot(btex $M'$ etex,A');
label.ulft(btex $E$ etex,J);

 
trace droite(D,D') withcolor blue withpen pencircle scaled 1.3bp;
label.urt(btex $\DR$ etex, D) withcolor blue;


trace codeperp(A',I,D,5);

trace codesegments(A',I,I,A,1);trace codesegments(A',J,J,A,2);



fin;











%fig14


figure(0,0,11u,5u)

trace grille(0.5);


marque_p:="plein";


pair A,B,C,D,E,J,I,O,h,v;

E=u*(1,0.5);
h=u*(4,0); v=u*(0,4);
O:=E shifted h;A:=O shifted h;
D:=E shifted v;C:=O shifted v;B:=A shifted v;
I:=0.5[D,C]; J:=0.5[O,C];
trace polygone(E,D,B,A)withpen pencircle scaled 1.3bp;;
draw C--O withpen pencircle scaled 1.3bp;;
nomme.bot(E);
nomme.bot(O);
nomme.bot(A);
nomme.rt(J);
nomme.top(B);
nomme.top(C);
nomme.top(I);
nomme.top(D);

fin;





%fig15 Bac Blanc





numeric u;
u:=1cm;
figure(-5u,-4u,5u,3u);
vardef pol(expr r,t) =
  (r*cos(t),r*sin(t))
enddef;

transform T;
(0,0) transformed T =(-u,2.732u);
(u,0) transformed T =(-2.732u,1.732u);
(0,u) transformed T =(0,u);

pair M[];

M[0]:=(0.433u,0.75u);
for k=0 upto 2 :
  M[k+1]:= M[k] transformed T;
endfor;


drawarrow (-5u,0)--(5u,0);
drawarrow (0,-4u)--(0,3u);



dotlabel.lrt(btex $M_0$ etex, M[0] );
dotlabel.lft(btex $M_1$ etex, M[1] );
dotlabel.rt(btex $M_2$ etex, M[2] );
dotlabel.bot(btex $M_3$ etex, M[3] );
dotlabel.ulft(btex $\Omega$ etex,(0,u) );

for i=0 upto 3 :
  draw (0,u)--M[i];
endfor;

draw (0,u)--(5u,u) withcolor orange withpen pencircle scaled 1.3bp;

fin;




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%   E S P A C e
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






pickup pencircle scaled 1.2bp;


typerepre:="persp";


% Figure 16 :
figure(-u,-u,7u,7u);%1
picture depart;
marque_p:="non";
pair A,B,C,D,E,F,G,H,M,N,P,I,J;
path r;
A=(0,0);
B=(4u,0);
C=(5.5u,1.5u);
D=C+A-B;
E=(0,4u);
F=E+B-A;
G=F+C-B;
H=G+D-C;
% Les points en plus :
N=A+.3*(E-A);
P=D+.25*(C-D)+.45*(H-D);

% Le cube :
depart=image(
  trace (-10u,-10u)--(-10u,10u)--(10u,10u);
trace B--F--E--A--B--C--G--H--E;
trace F--G;
trace A--D--C dashed evenly;
trace H--D dashed evenly;
nomme.llft(A);
nomme.lft(E);
nomme.lrt(F);
nomme.ulft(H);
nomme.urt(G);
nomme.rt(C);
nomme.lrt(B);
nomme.lft(D);
marque_p:="croix";
nomme.lft(N);
nomme.top(P););
trace depart;
fin;



%%%%%% 17 Fig tetra


figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
 label.llft(btex A etex,Projette(R))withcolor white;
 trace demidroite(B,A) withcolor white;
 path section, prolongesection, fond;
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
% trace demidroite(B,A);
% trace demidroite(M,P);
% trace demidroite(K,N);
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
% nomme.urt(K); 
 finespace;








%% fig 18 pyramide dans boite coloree




figureespace(-15u,-30u,30u,30u);
 Initialisation(5,25,30,700);
 color A,B,C,D,H,E,F,G;
trace Pave(A,B,C,D,H,E,F,G)(2/10,1/2,1/4);
fillcolor:=orange;
 transparence polygone(B,F,G,C);
 fillcolor:=0.8jaune;
 transparence polygone(E,F,G,H);
 fillcolor:=1.2jaune;
 transparence polygone(E,F,B,A) ;
 
 trace appelation(B,C,-2mm,btex 4 cm etex);
 trace appelation(G,C,2mm,btex 5 cm etex);
 trace appelation(H,G,2mm,btex 10 cm etex);
nomme.llft(A);
nomme.lft(E);
nomme.lrt(F);
nomme.ulft(H);
nomme.urt(G);
nomme.rt(C);
nomme.lrt(B);
nomme.lft(D);
finespace;





%fig19 coupe d'un tétraèdre

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R,L,J;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=(1/8,1/6,5/24);
 N=1/4[C,A];
 R=1/2[D,C];
 K=IntersectionDroite(N,R,A,D);
 J=IntersectionDroite(K,M,B,A);
 L=IntersectionDroite(K,M,B,D);
 
 path section, face, fond, prolongesection;
 fond=polygone(A,B,D);
 face=polygone(A,C,R,K);
 section=polygone(N,J,L,R);
 prolongesection=polygone(L,R,K);
 fillcolor:=jaune;
 transparence fond;
 fillcolor:=ciel;
 transparence face;
 fillcolor:=rouge;
 transparence section;
 fillcolor:=orange;
 transparence prolongesection;
 
 trace chemin(J,N,R) withcolor red withpen pencircle scaled 1.2bp ;
 trace segment(J,L)  withcolor red withpen pencircle scaled 1.2bp dashed evenly;
 trace segment(R,L)  withcolor red withpen pencircle scaled 1.2bp dashed evenly;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(A,D);
 trace demidroite(N,R);
 trace segment(K,J) dashed evenly;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.bot(R);
 nomme.ulft(J);
 nomme.urt(K);
 nomme.top(L);
 finespace;


























 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 %
 % I N T E R S E C T I O N    tétraèdre
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%fig20



figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
  label.top(btex A etex,Projette(L))withcolor white;
% trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=1.3orange;
 %transparence section;
% nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;



%fig21






 %2


figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
  label.top(btex A etex,Projette(L))withcolor white;
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section,fond;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=jaune;
 fond=polygone(D,C,L,E);
 transparence fond;
 %nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;




%fig22



 %3

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 label.top(btex A etex,Projette(L))withcolor white;
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=jaune;
 path fond;
 fond=polygone(D,C,L,E);
 transparence fond;
% transparence section;
% nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;



%fig23

 %4

 

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=jaune;
 path fond;
 fond=polygone(D,C,L,E);
 transparence fond;
% transparence section;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;







 %fig24

 %5


 

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 
 
% transparence section;
 fillcolor:=jaune;
 path face;
 face=polygone(F,G,B,A);
 transparence face;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;









%fig25



 

%6


 

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
fillcolor:=orange;
% transparence section;

 path fond;
 fond=polygone(F,E,L,G);
 transparence fond;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;









 %fig26

 %7

 
 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
% trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=orange;
 path fond;
 fond=polygone(D,A,B,C);
 transparence fond;
% transparence section;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;









%fig27

 
 %8


 
 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);

 fillcolor:=jaune;
 path fond;
 fond=polygone(F,E,D,A);
 transparence fond;
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
%  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 
 
% transparence section;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;




 %fig28


%9


 

 
 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
 fillcolor:=orange;
 fillcolor:=jaune;
 path fond;
 fond=polygone(G,B,C,H);
 transparence fond;
% transparence section;

  trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
 nomme.top(L);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;








 %fig29


%10

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M,N,O,P;
 trace Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K) dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;


 I-N=whatever*(J-K);
 F-N=whatever*(F-G);;
 A-P=whatever*(A-D);
 G-O=whatever*(G-H);
 N-O=whatever*(N-L);
 P-J=whatever*(N-O);
 P-I=whatever*(K-O);
 
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(L,H) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)  dashed evenly withcolor bleu withpen pencircle scaled 1.5bp;
  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;

 path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
fillcolor:=ciel;
 transparence section;
 nomme.top(L);nomme.top(O);nomme.top(N);nomme.bot(P);
 nomme.llft(A);
 nomme.bot(B);
 nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 finespace;










 %fig30


 %11

 
figureespace(-20u,-20u,20u,20u);
 Initialisation(5,30,35,200);
 color A,B,C,D,E,F,G,H,I,J,K, L,M,N,O,P;
 picture c;
 c:=Cube(A,B,C,D,E,F,G,H);
 I=1/3[F,A];
 J=2/3[D,C];
 K=1/4[H,C];
 L=IntersectionDroite(J,K,E,H);
 trace segment(J,K)  withcolor bleu withpen pencircle scaled 1.5bp;
 %trace segment(K,L) withcolor bleu withpen pencircle scaled 1.5bp;
 %trace segment(H,L) withcolor bleu withpen pencircle scaled 1.5bp;


 I-N=whatever*(J-K);
 F-N=whatever*(F-G);;
 A-P=whatever*(A-D);
 G-O=whatever*(G-H);
 N-O=whatever*(N-L);
 P-J=whatever*(N-O);
 P-I=whatever*(K-O);

 trace segment(J,K)  withcolor bleu withpen pencircle scaled 1.5bp;
 
 trace IntersectionPlanPlan(A,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(F,A) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(H,G,F,I,J,K) cutbefore segment(F,G) cutafter segment(O,H) withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,D,C,I,J,K) cutbefore segment(D,C) cutafter segment(D,A)   withcolor bleu withpen pencircle scaled 1.5bp;
 trace IntersectionPlanPlan(A,E,F,I,J,K) cutbefore segment(F,A) cutafter segment(D,A)   withcolor bleu withpen pencircle scaled 1.5bp;
  trace IntersectionPlanPlan(G,H,C,I,J,K) cutbefore segment(H,G) cutafter segment(H,C) withcolor bleu withpen pencircle scaled 1.5bp;
  label.llft(btex A etex,Projette(A))withcolor white;
  label.bot(btex B etex,Projette(B))withcolor white;
  label.rt(btex A etex,Projette(C))withcolor white;
  label.lrt(btex A etex,Projette(G))withcolor white;
  label.top(btex A etex,Projette(L))withcolor white;

  

  trace segment(F,I)   withpen pencircle ;
  trace segment(F,N)   withpen pencircle ;
  trace segment(F,E)   withpen pencircle ;
  trace segment(E,H)   withpen pencircle ;
  trace segment(H,O)   withpen pencircle ;
  trace segment(H,K)   withpen pencircle ;
  trace segment(E,D)   withpen pencircle  dashed evenly;
  trace segment(P,D)   withpen pencircle dashed evenly;
  trace segment(J,D)  withpen pencircle  dashed evenly;



  path section;
 section=buildcycle(IntersectionPlanPlan(H,G,F,I,J,K),IntersectionPlanPlan(A,G,F,I,J,K),IntersectionPlanPlan(A,E,F,I,J,K),IntersectionPlanPlan(A,D,C,I,J,K),segment(J,K),IntersectionPlanPlan(G,H,C,I,J,K));
fillcolor:=ciel;
 transparence section;
 %nomme.top(L);
 nomme.top(O);nomme.top(N);nomme.bot(P);
% nomme.llft(A);
% nomme.bot(B);
% nomme.rt(C);
 nomme.ulft(D);
 nomme.ulft(E);
 nomme.lft(F);
 %nomme.lrt(G);
 nomme.urt(H);
 marque_p:="plein";
 nomme.lft(I);
 nomme.top(J);
 nomme.lft(K);
 
 finespace;




















%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 %
 %
 %  I N T E R S  E C T I O N          T E T R A
 %
 %
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%fig31

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
 label.llft(btex A etex,Projette(R))withcolor white;
 trace demidroite(B,A) withcolor white;
 path section, prolongesection, fond;
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
% trace demidroite(B,A);
% trace demidroite(M,P);
% trace demidroite(K,N);
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
% nomme.urt(K); 
 finespace;



 

%fig32

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path section, prolongesection, fond;
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
% trace demidroite(M,P);
% trace demidroite(K,N);
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
% nomme.urt(K); 
 finespace;












%fig33

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path section, prolongesection, fond;
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P)withcolor red;
% trace demidroite(K,N);
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
% nomme.urt(K); 
 finespace;





%fig34

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path section, prolongesection, fond;
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=orange;
 transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P)withcolor red;
% trace demidroite(K,N);
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
 nomme.urt(K); 
 finespace;



%fig35

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path cote,section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=ciel;
% transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P) withcolor red;
 trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
 nomme.urt(K); 
 finespace;





%fig36

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path cote,section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=ciel;
 transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P) withcolor red;
 trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
% nomme.llft(R);
 nomme.urt(K); 
 finespace;







%fig37

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path cote,section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=polygone(N,P,M,R);
 fillcolor:=ciel;
 transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
% trace section withcolor red;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P) withcolor red;
 trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
 nomme.llft(R);
 nomme.urt(K); 
 finespace;


%fig38

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path cote,section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=chemin(R,N,P,M);
 fillcolor:=ciel;
% transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
% transparence section;
 
 trace section withcolor red;trace segment(R,M) withcolor red dashed evenly;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P) withcolor red;
 trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
 nomme.llft(R);
 nomme.urt(K); 
 finespace;



%fig39

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label.urt(btex A etex,Projette(K))withcolor white;
  label.llft(btex A etex,Projette(R))withcolor white;
 path cote,section, Section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=chemin(R,N,P,M);Section=polygone(R,N,P,M);
 fillcolor:=ciel;
% transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
 transparence prolongesection;
 fillcolor:=.9jaune;
 transparence Section;
 
 trace section withcolor red;trace segment(R,M) withcolor red dashed evenly;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
 trace demidroite(B,A);
 trace demidroite(M,P) withcolor red;
 trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
 nomme.llft(R);
 nomme.urt(K); 
 finespace;









 






%fig40

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label(btex  etex,projette(K))withcolor white;
 label.llft(btex  etex,projette(R))withcolor white;
 trace demidroite(B,A) withcolor white;
 trace demidroite(M,P) withcolor white;
 path cote,section, Section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,A,D);
 section=chemin(R,N,P,M);Section=polygone(R,N,P,M);
 fillcolor:=ciel;
 %transparence cote;
 fillcolor:=orange;
 transparence fond;
 fillcolor:=jaune;
 transparence prolongesection;
 fillcolor:=.9jaune;
 transparence Section;
 
 trace section withcolor red;trace segment(R,M) withcolor red dashed evenly;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
% trace demidroite(B,A);
% trace demidroite(M,P) withcolor red;
% trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
 nomme.llft(R);
 nomme.urt(K); 
 finespace;





%fig41

figureespace(-10u,-10u,10u,10u);
 Initialisation(5,35,40,400);
 color D,A,B,C,M,N,P,K,R;
 A=(0,0,1/2);
 B=(1/2,0,0);
 D=(0,1/2,0);
 C=(1/2,1/4,0);
 M=5/8[B,D];
 N=1/2[C,A];
 P=5/7[D,A];
 K=IntersectionDroite(M,P,A,B);
 R=IntersectionDroite(K,N,B,C);
 label(btex  etex,projette(K))withcolor white;
 label.llft(btex  etex,projette(R))withcolor white;
 trace demidroite(B,A) withcolor white;
 trace demidroite(M,P) withcolor white;
 path cote,section, Section, prolongesection, fond;
 cote=polygone(B,K,N,C);
 prolongesection=polygone(K,N,P);
 fond=polygone(B,K,P,D);
 section=chemin(R,N,P,M);Section=polygone(R,N,P,M);
 fillcolor:=ciel;
% transparence cote;
 fillcolor:=orange;
% transparence fond;
 fillcolor:=jaune;
% transparence prolongesection;
 fillcolor:=.9jaune;
 transparence Section;
 
 trace section withcolor red;trace segment(R,M) withcolor red dashed evenly;
 trace polygone(C,A,B);
 trace segment(A,D);
 trace chemin(A,C,D);% dashed evenly;
 trace segment(B,D)dashed evenly;
% trace demidroite(B,A);
% trace demidroite(M,P) withcolor red;
% trace segment(K,R) withcolor blue;
 nomme.top(A);
 nomme.lft(B);
 nomme.bot(C);
 nomme.rt(D);
 marque_p:="plein";
 nomme.urt(M);
 nomme.lft(N);
 nomme.urt(P);
 nomme.llft(R);
% nomme.urt(K); 
 finespace;













 





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
 %
 %
 %     V E C T E U R S 
 %
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%beginfig(42)

figure(-2cm,-1cm,20cm,5cm);
  pair a[],u,v;path p;
  a[1]:=origin;
  u:=(2cm,0); v:=(0.5cm,1cm);
  a[2]:=a[1] shifted u;
  a[3]:=a[2] shifted u;
  a[4]:=a[1] shifted v;
  a[5]:=a[2] shifted v;
  a[6]:=a[3] shifted v;
  a[7]:=a[4] shifted v;
  a[8]:=a[5] shifted v;
  a[9]:=a[6] shifted v;
 
 p:=polygone(a[1],a[2],a[5],a[4]);
 trace p;
 trace p shifted u;
 trace p shifted v;
 trace p shifted (u+v);

 drawarrow a[1]--a[2] withpen pencircle scaled 1.6bp withcolor 0.7white;

 drawarrow a[4]--a[5] withpen pencircle scaled 1.6bp;
 
 drawarrow a[8]--a[9] withpen pencircle scaled 1.6bp;

 label.bot(btex A etex,a[1]);
  label.bot(btex B etex,a[2]);
 label.bot(btex C etex,a[3]);
 label.lrt(btex D etex,a[4]);
 label.lrt(btex E etex,a[5]);
 label.lrt(btex F etex,a[6]);
 label.top(btex G etex,a[7]);
  label.top(btex H etex,a[8]);
 label.top(btex I etex,a[9]);
 label.top(btex $\ve{d}$ etex,.5(a[1]+a[2])) withcolor 0.6white;
label.top(btex $\ve{d}$ etex,.5(a[4]+a[5])) ;
 label.top(btex $\ve{d}$ etex,.5(a[8]+a[9])) ;

 
 


fin; 
%endfig;





%43

%beginfig(43);

  figure(-10cm,-5cm,12cm,10cm); 

%egalité de deux vecteurs et parallelogramme 
numeric u; 
pair t; 
u = 1cm; 
t=(1u,2u); 
transform T; 
T= identity shifted t; 
z0 = (0,0);z1 = z0 transformed T; 
z2=(3u,-1u);z3=z2 transformed T ; 
drawarrow z0--z1 withcolor 0.5white withpen pencircle scaled 1.6bp; 
drawarrow z2--z3 withcolor 0.5white withpen pencircle scaled 1.6bp; 
draw z0--z2 dashed evenly; 
draw z1--z3 dashed evenly; 
label.lft(btex $A$ etex, z0); 
label.top(btex $B$ etex, z1); 
label.lrt(btex $C$ etex, z2); 
label.rt(btex $D$ etex, z3); 
label.lft(btex $\ve{u}$ etex, .5(z0+z1));
label.rt(btex $\ve{u}$ etex, .5(z2+z3));

fin; 








%beginfig(44);
figure(-10cm,-5cm,12cm,10cm); 
%addition de deux vecteurs(Chasles 1) 
numeric u; 
pair t,r,g,d; 
u=1cm; 
t=(2u,1u); 
r=(3u,-2u);
g:=(-2u,u);
d:=(3u,2u);
transform T,R,G,D; 
T= identity shifted t; 
R= identity shifted r;
D= identity shifted d;
G= identity shifted g;

z0=(0,0);z1= z0 transformed T; 
z2=z1 transformed R;

drawarrow z0--z1 withcolor 0.6white; 
drawarrow z1--z2 withcolor 0.6white; 


drawarrow z0--z2 withcolor 0.4white withpen pencircle scaled 1.6bp; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.rt(btex $C$ etex, z2); 
label.top(btex $\ve{u}$ etex, 0.5[z0,z1]); 
label.top(btex $\ve{v}$ etex, 0.5[z1,z2]); 

label.bot(btex $\ve{u}+\ve{v}$ etex, 0.5[z0,z2]) withcolor 0.4white withpen pencircle scaled 1.6bp; 
endfig;





%beginfig(45); 

figure(-10cm,-5cm,12cm,10cm); 

%addition de deux vecteurs(Chasles) 
numeric u; 
pair t,r,g,d; 
u=1cm; 
t=(2u,1u); 
r=(3u,-2u);
g:=(-2u,u);
d:=(3u,2u);
transform T,R,G,D; 
T= identity shifted t; 
R= identity shifted r;
D= identity shifted d;
G= identity shifted g;

z0=(0,0);z1= z0 transformed T; 
z2=z1 transformed R;
z0g=z0 transformed G;
z1g=z1 transformed G;
z1d=z1 transformed D;
z2d=z2 transformed D;
drawarrow z0--z1 withcolor 0.6white; 
drawarrow z1--z2 withcolor 0.6white; 
drawarrow z0g--z1g withcolor 0.6white; 
drawarrow z1d--z2d withcolor 0.6white; 
draw z0--z0g dashed evenly;
draw z1--z1g dashed evenly;
draw z1--z1d dashed evenly;
draw z2--z2d dashed evenly;

drawarrow z0--z2 withcolor 0.4white withpen pencircle scaled 1.6bp; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.rt(btex $C$ etex, z2); 
label.top(btex $\ve{u}$ etex, 0.5[z0,z1]); 
label.top(btex $\ve{v}$ etex, 0.5[z1,z2]); 
label.top(btex $\ve{u}$ etex, 0.5[z0g,z1g]); 
label.top(btex $\ve{v}$ etex, 0.5[z1d,z2d]); 

label.bot(btex $\ve{u}+\ve{v}$ etex, 0.5[z0,z2]) withcolor 0.4white withpen pencircle scaled 1.6bp; 
endfig;



%beginfig(45);

figure(-10cm,-5cm,12cm,10cm); 

%figure(-5cm,-5cm,12cm,5cm); 

  
%addition de deux vecteurs(parallelogramme) 
numeric u; 
pair t,r,s; 
u=1cm; 
t=(2u,1u); 
r=(-2u,3u); 
transform T,R; 
T= identity shifted t; 
R= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R;z3=z1+z2;
drawarrow z0--z1 withcolor 0.6white; 
drawarrow z0--z2 withcolor 0.6white; 
drawarrow z0--z3 withcolor 0.4white withpen pencircle scaled 1.8bp; 
label.bot(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.top(btex $D$ etex, z2); 
label.top(btex $C$ etex, z3); 
label.bot(btex $\ve{u}$ etex, 0.5[z0,z1]); 
label.bot(btex $\ve{v}$ etex, 0.5[z0,z2]); 
label.lft(btex $\ve{u}+\ve{v}$ etex, 0.7[z0,z3]);

draw z2--z3 dashed evenly;
draw z1--z3 dashed evenly;
endfig; 






%beginfig(46)

figure(-10cm,-5cm,12cm,10cm); 


  drawarrow origin--(5cm,1cm);
  label.bot(btex $\ve{u}$ etex, (2.5cm,.5cm));
  drawarrow (5cm,2cm)--(0,1cm) withcolor 0.4white withpen pencircle scaled 1.8bp;
  label.top(btex $-\ve{u}$ etex, (2.5cm,1.5cm)) withcolor 0.4white withpen pencircle scaled 1.8bp;
endfig;




%beginfig(47); 

figure(-10cm,-5cm,12cm,10cm); 


numeric u,a,b; 
%multiples d'un vecteur 
pair t; 
u = 1cm; 
t=(1u,2u); 
transform T,R,S; 
T = identity shifted t; 
R = identity shifted 2t; 
S = identity shifted -1.5t; 
z0 = (0,0); z1= z0 transformed T; 
z2 = (-2.5u,0); z3 = z2 transformed R; 
z4 = (3u,3u); z5 = z4 transformed S; 
drawarrow z0--z1  withcolor 0.4white withpen pencircle scaled 1.8bp; 
drawarrow z2--z3 ; 
drawarrow z4--z5 ; 
label.rt(btex $\ve{u}$ etex, 0.5[z0,z1]) withcolor 0.4white withpen pencircle scaled 1.8bp; 
label.rt(btex $k\ve{u} \, (k>0)$ etex, 0.5[z2,z3]); 
label.rt(btex $k\ve{u} \, (k<0)$ etex, 0.5[z4,z5]); 
endfig; 
  







%beginfig(48); 
%colinearite de deux vecteurs et directions paralleles 


figure(-10cm,-5cm,12cm,10cm); 

numeric u; 
pair t,r; 
u=1cm; 
t=(2u,3u); 
r=(-1u,-1.5u); 
transform T,R; 
T= identity shifted t; 
R= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=(2u,2u);z3=z2 transformed R; 
drawarrow z0--z1; 
drawarrow z2--z3; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.rt(btex $D$ etex, z2); 
label.rt(btex $C$ etex, z3); 
label.top(btex $\ve{u}$ etex, 0.5[z0,z1]); 
label.bot(btex $\ve{v}$ etex, 0.5[z2,z3]); 
endfig; 










%beginfig(49); 
%coordonnées d'un vecteur 

figure(-10cm,-5cm,12cm,10cm); 

numeric u; 
pair i,j; 
u=0.7cm; 
 
i=(2u,0u); 
j=(0.2u,1u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0); 
z33= z0 shifted 4i;z4= z0 shifted -i; 
z5= z0 shifted 4j; z6= z0 shifted -j; 
 
draw z4--z33 withcolor blue; draw z6--z5 withcolor blue; 
z7= z0 shifted i;z8 = z0 shifted j; 
label.bot(btex $\ve{v}$ etex, 0.5[z0,z7]); 
label.lft(btex $\ve{v}$ etex, 0.5[z0,z8]); 
drawarrow z0--z7; 
drawarrow z0--z8; 
 
z1=(4u,1u); 
z2=z1 shifted 1.5i; 
z3=z2 shifted 2j; 
drawarrow z1--z2 dashed evenly withcolor green; 
drawarrow z2--z3 dashed evenly withcolor green; 
drawarrow z1--z3 withcolor red; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $x\ve{u}$ etex, 0.5[z1,z2]); 
label.rt(btex $y\ve{v}$ etex, 0.5[z2,z3]); 
label.top(btex $\ve{t}$ etex, 0.5[z1,z3]);

z9=z0 shifted 1.5i; 
z10=z0 shifted 2j; 
z11= z0 shifted 1.5i+2j; 
draw z9--z11 dashed evenly withcolor green; 
draw z10--z11 dashed evenly withcolor green; 
drawarrow z0--z11 withcolor red; 
label.top(btex $M(x;y)$ etex, z11); 
label.top(btex $\ve{t}$ etex, 0.5z11);
endfig; 








































%beginfig(50)  % parallélogramme


figure(-10cm,-5cm,12cm,10cm); 

  pair a,b,c,d,o;
  numeric u;
  path p;
  u:=1cm;
  a:=origin;
  b:=(4u,0);
  d:=(u,3u);
  c:=b+d;
  o:=.5c;
  p:=a--b--c--d--cycle;
  fill p withcolor .9white;
  trace p withpen pencircle scaled 1.8bp withcolor .4white;
  trace codesegments(a,o,o,c,2);
  trace codesegments(b,o,o,d,4);
  trace a--c;
  trace b--d;
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
   label.top(btex C etex,c);
   label.top(btex D etex,d);
   label.lft(btex O etex,o);
endfig;











%beginfig(51)% Exercice para similitude

figure(-10cm,-5cm,12cm,10cm);

  pair a,b,c,d,o,m,n,p,q;
  numeric u;
  path pp,r;
  u:=1cm;
  a:=origin;
  b:=(4u,0);
  d:=(u,3u);
  c:=b+d;
  o:=.5c;
  q=1.5[d,a];
  p=1.5[c,d];
  n=1.5[b,c];
  m=1.5[a,b];
  pp:=a--b--c--d--cycle;
  r:=m--n--p--q--cycle;
  fill r withcolor .9white;
  fill pp withcolor .8white;


  
  trace pp withpen pencircle scaled 1.8bp withcolor .4white;
  trace r withpen pencircle scaled 1.8bp withcolor .6white;
  trace codesegments(a,o,o,c,2);
  trace codesegments(b,o,o,d,4);
  trace Codelongueur(a,.5[a,b],.5[a,b],b,b,m,1);
  trace Codelongueur(b,.5[b,c],.5[b,c],c,c,n,5);
   trace Codelongueur(c,.5[c,d],.5[c,d],d,d,p,1);
    trace Codelongueur(d,.5[d,a],.5[d,a],a,a,q,5);

  
  trace a--c;
  trace b--d;
  trace b--m;
  trace c--n;
  trace d--p;
  trace a--q;
 
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
   label.top(btex C etex,c);
   label.top(btex D etex,d);
   label.lft(btex O etex,o);
   label.bot(btex Q etex,q);
  label.bot(btex M etex,m);
   label.top(btex N etex,n);
   label.top(btex P etex,p);
   dotlabel.bot(btex  etex,.5[a,b]);
   dotlabel.bot(btex  etex,.5[b,c]);
   dotlabel.bot(btex  etex,.5[c,d]);
   dotlabel.bot(btex  etex,.5[d,a]);
endfig;




%beginfig(52)  % parallélogramme

figure(-10cm,-5cm,12cm,10cm); 

  pair a,b,c,d,o;
  numeric u;
  path p;
  u:=1cm;
  a:=origin;
  b:=(4u,0);
  d:=(u,3u);
  c:=b+d;
  %o:=.5c;
  p:=a--b--c--d--cycle;
  fill p withcolor .9white;
  trace p withpen pencircle scaled 1.8bp withcolor .4white;
  %trace codesegments(a,o,o,c,2);
  %trace codesegments(b,o,o,d,4);
  %trace a--c;
  %trace b--d;
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
   label.top(btex C etex,c);
   label.top(btex D etex,d);
  % label.lft(btex O etex,o);
endfig;



%beginfig(53)  % parallélogramme main levée

figure(-10cm,-5cm,12cm,10cm); 

%figuremainlevee(-4cm,-5cm,12cm,5cm)

  pair a,b,c,d,i,e,f;
  numeric u;
  path p;
  u:=1cm;
  a:=origin;
  b:=(4u,0);
  d:=(u,3u);
  c:=b+d;
  i:=.5[a,b];
  e:=(2/3)[d,i];
  f:=.5[d,e];
 
  p:=a--b--c--d--cycle;
  fill p withcolor .9white;
   trace d--i;
  trace a--c;
  trace p withpen pencircle scaled 1.8bp withcolor .4white;
  %trace codesegments(a,o,o,c,2);
  trace Codelongueur(d,f,f,e,e,i,2);
  %trace a--c;
  %trace b--d;
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
   label.top(btex C etex,c);
   label.top(btex D etex,d);
   label.bot(btex I etex,i);
   label.lft(btex E etex,e);
   dotlabel.rt(btex  etex,f);
%finmainlevee;
endfig;







%beginfig(54)
%figure(-2cm,-2cm,7cm,7cm);

figure(-10cm,-5cm,12cm,10cm); 

  pair a,b,c,i,o,p,d;
  path t;
  t:=triangleqcq(b,a,c);
  i:=.5[a,c];
  o:=(-1cm,-4cm);
  2[b,i]=1[b,d];
  p-o=a+c-2b;
  trace t withpen pencircle scaled 1.8bp withcolor .4white;
  fill t withcolor .8white;
  trace codesegments(b,i,i,d,2);
  drawarrow o--p withpen pencircle scaled 1.6bp withcolor blue;
  drawarrow b--d withpen pencircle scaled 1.6bp withcolor blue;
  drawarrow d--p dashed evenly;
  drawarrow b--o dashed evenly;
  dotlabel.bot(btex O etex,o);
  dotlabel.bot(btex P etex,p);
  dotlabel.top(btex D etex,d);
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
  label.top(btex C etex,c);
  dotlabel.ulft(btex I etex,i);
  
endfig;





%beginfig(55)
figure(0cm,0cm,10cm,7cm)
numeric u;
u:=1cm;
  
  trace papierpointe;
  dotlabel.llft(btex A etex,(2u,2u));
  dotlabel.lrt(btex B etex,(6u,3u));
  dotlabel.llft(btex C etex,(3u,5u));
endfig;









%beginfig(56)  % parallélogramme encore

figure(-10cm,-5cm,12cm,10cm); 

  pair a,b,c,d,e,f;
  numeric u;
  path p;
  u:=1cm;
  a:=origin;
  b:=(4u,0);
  d:=(u,3u);
  c:=b+d;
  e:=.5[b,c];
  f:=.5[d,c];
  p:=a--b--c--d--cycle;
  fill p withcolor .9white;
  trace p withpen pencircle scaled 1.8bp withcolor .4white;
  trace codesegments(b,e,e,c,2);
  trace codesegments(d,f,f,c,4);
  %trace a--c;
  %trace b--d;
  label.bot(btex A etex,a);
  label.bot(btex B etex,b);
   label.top(btex C etex,c);
   label.top(btex D etex,d);
    dotlabel.rt(btex E etex,e);
   dotlabel.top(btex F etex,f);
  % label.lft(btex O etex,o);
endfig;












%beginfig(57)  % triangle 

figure(-10cm,-5cm,12cm,10cm); 

pair a,b,c,m[],n[],p[];
path t;

t:= triangleqcq(a,b,c);
trace t withpen pencircle scaled 1.8bp withcolor .4white ;
fill t withcolor .9white;


m[1]:=(1/3)[a,b];
m[2]:=(2/3)[a,b];
p[1]:=(1/3)[b,c];
p[2]:=(2/3)[b,c];
p[3]:=(4/3)[b,c];
n[1]:=(1/3)[c,a];
n[2]:=(2/3)[c,a];

trace p[3]--n[1]--m[1] dashed evenly;

trace c--p[3];


dotlabel.bot(btex M etex,m[1]);
dotlabel.bot(btex  etex,m[2]);
dotlabel.rt(btex  etex,p[1]);
dotlabel.rt(btex  etex,p[2]);
dotlabel.lft(btex N etex,n[1]);
dotlabel.lft(btex  etex,n[2]);
dotlabel.lft(btex P etex,p[3]);
label.bot(btex A etex,a);
label.bot(btex B etex,b);
label.top(btex C etex,c);
trace Codelongueur(a,m[1],m[1],m[2],m[2],b,2);
trace Codelongueur(b,p[1],p[1],p[2],p[2],c,c,p[3],4);
trace Codelongueur(c,n[1],n[1],n[2],n[2],a,3);

endfig;




%beginfig(58)  % triangle main levée 

figure(-10cm,-5cm,12cm,10cm); 


pair a,b,c,m[],n[],p[];
path t;

t:= triangleqcq(a,b,c);
trace t withpen pencircle scaled 1.8bp withcolor .4white;
fill t withcolor .9white;


m[1]:=(1/4)[a,b];
m[2]:=(2/4)[a,b];
m[3]:=(3/4)[a,b];
p[1]:=(1/6)[b,c];
p[2]:=(2/6)[b,c];
p[3]:=(3/6)[b,c];
p[4]:=(4/6)[b,c];
p[5]:=(5/6)[b,c];
n[1]:=(1/3)[c,a];
n[2]:=(2/3)[c,a];
n[3]:=(4/3)[c,a];

trace n[3]--m[1]--p[3];

trace a--n[3];


dotlabel.bot(btex P etex,m[1]);
dotlabel.bot(btex  etex,m[2]);
dotlabel.bot(btex  etex,m[3]);
dotlabel.rt(btex  etex,p[1]);
dotlabel.rt(btex  etex,p[2]);
dotlabel.urt(btex Q etex,p[3]);
dotlabel.rt(btex  etex,p[4]);
dotlabel.rt(btex  etex,p[5]);
dotlabel.lft(btex  etex,n[1]);
dotlabel.lft(btex  etex,n[2]);
dotlabel.lft(btex R etex,n[3]);
dotlabel.ulft(btex A etex,a);
dotlabel.bot(btex B etex,b);
dotlabel.top(btex C etex,c);
trace Codelongueur(a,m[1],m[1],m[2],m[2],m[3],m[3],b,2);
trace Codelongueur(b,p[1],p[1],p[2],p[2],p[3],p[3],p[4],p[4],p[5],p[5],c,4);
trace Codelongueur(c,n[1],n[1],n[2],n[2],a,a,n[3],3);

fin;













%fig59 triangle iso

 
figure(-8cm,-9cm,9cm,8cm);
pair A,B,C,D,E,O,Z;
path cc,dd;
O:=(0,0);
A:=(-2cm,-5cm); B:=(2cm,-5cm);Z:=2*B;
trace codesegments(O,A,O,B,2);
cc:= cercles(A,O); dd:= B--Z;
E:= cc intersectionpoint dd;

trace arccercle(E,O,A) withcolor orange dashed evenly;
trace A--O--B--cycle withcolor red;
trace B--E withcolor blue;

label.lft(btex A  etex,A );
label.rt(btex B etex,B );
label.top(btex O etex,O );
label.rt(btex E etex, E);
fin;

 


end