Le théorème de Pythagore ...

Fichier : pythagore1.mp


input constantes;
input geometriepoint;
beginfig(1);
  u:=5mm;
  affixe.B(u*(1,1))so;
  affixe.C(z.B shifted(u*(sqrt(89),0)))se;
  path cc;
  cc=cercledia(B,C);
  affixe.A(cc intersectionpoint cercle(C,8u))n;
  affixe.D(z.A rotatedabout(z.B,90))so;
  affixe.E(z.B rotatedabout(z.A,-90))no;
  affixe.G(z.C rotatedabout(z.A,90))n;
  affixe.F(z.A rotatedabout(z.C,-90))n;
  affixe.H(z.B rotatedabout(z.C,90))se;
  affixe.I(z.C rotatedabout(z.B,-90))so;
  affixe.O(1/2[z.A,z.F])no;
  affixe.K((z.A--z.G) intersectionpoint para(O,B,C,15));
  affixe.L((z.C--z.F) intersectionpoint para(O,B,C,15));
  affixe.M((z.A--z.C) intersectionpoint perpen(O,B,C,15));
  affixe.N((z.F--z.G) intersectionpoint perpen(O,B,C,15));
  picture piece[];
  draw hachure(60,0.5,1);
  clip currentpicture to (z.A--z.M--z.O--z.K--cycle);
  piece1=currentpicture;
  currentpicture:=nullpicture;
  draw hachure(30,0.5,1);
  clip currentpicture to (z.C--z.M--z.O--z.L--cycle);
  piece2=currentpicture;
  currentpicture:=nullpicture;
  draw hachure(60,0.5,2);
  clip currentpicture to (z.L--z.O--z.N--z.F--cycle);
  piece3=currentpicture;
  currentpicture:=nullpicture;
  draw hachure(120,0.5,2);
  clip currentpicture to (z.N--z.G--z.K--z.O--cycle);
  piece4=currentpicture;
  currentpicture:=nullpicture;
  draw hachure(60,0.5,0);
  clip currentpicture to (z.A--z.B--z.D--z.E--cycle);
  piece5=currentpicture;
  currentpicture:=nullpicture;
  for j=1 upto 5:
    draw piece[j];
  endfor;
  affixe.B(u*(1,1))so;
  affixe.C(z.B shifted(u*(sqrt(89),0)))se;
  path cc;
  cc=cercledia(B,C);
  affixe.A(cc intersectionpoint cercle(C,8u))n;
  affixe.D(z.A rotatedabout(z.B,90))so;
  affixe.E(z.B rotatedabout(z.A,-90))no;
  affixe.G(z.C rotatedabout(z.A,90))n;
  affixe.F(z.A rotatedabout(z.C,-90))n;
  affixe.H(z.B rotatedabout(z.C,90))se;
  affixe.I(z.C rotatedabout(z.B,-90))so;
  affixe.O(1/2[z.A,z.F])no;
  affixe.K((z.A--z.G) intersectionpoint para(O,B,C,15));
  affixe.L((z.C--z.F) intersectionpoint para(O,B,C,15));
  affixe.M((z.A--z.C) intersectionpoint perpen(O,B,C,15));
  affixe.N((z.F--z.G) intersectionpoint perpen(O,B,C,15));  
  draw triangle(A,B,C);
  draw codeperp(B,A,C,5);
  draw z.B--z.D--z.E--z.A;
  draw z.A--z.G--z.F--z.C;
  draw z.C--z.H--z.I--z.B;
  draw z.K--z.L;
  draw z.M--z.N;
  draw codeperp(N,O,L,5);  
endfig;
end

Fichier : pythagore5.mp


input constantes;
input geometriepoint;
beginfig(1);
affixe.A(u*(1,1))so;
affixe.B(u*(5,0))se;
affixe.C(8/5[z.B,z.A rotatedabout(z.B,-90)])n;
draw triangle(A,B,C);
draw codeperp(A,B,C,5);
endfig;
end

Fichier : pythagore2.mp


input constantes;
input geometriepoint;
beginfig(1);
u:=5mm;
affixe.R(u*(1,1))so;
affixe.S(u*(9,1))se;
affixe.T(u*(1,7))n;
draw triangle(R,S,T);
draw codeperp(S,R,T,5);
cotation(R,S,-2mm,-2mm,btex $8\,cm$ etex);
cotation(R,T,2mm,2mm,btex $6\,cm$ etex);
cotation(T,S,2mm,2mm,btex ? etex);
endfig;
end

Fichier : pythagore3.mp


input constantes;
input geometriepoint;
beginfig(1);
u:=5mm;
affixe.I(u*(1,1))so;
affixe.K(u*(9,1))se;
path cc;
cc=cercledia(I,K);
affixe.J(point(0.15*length cc) of cc)n;
draw triangle(I,J,K);
draw codeperp(I,J,K,5);
cotation(I,K,-2mm,-2mm,btex $9\,mm$ etex);
cotation(I,J,2mm,2mm,btex $5\,cm$ etex);
cotation(J,K,2mm,2mm,btex ? etex);
endfig;
end

Fichier : pythagore4.mp


input constantes;
input geometriepoint;
beginfig(1);
affixe.F(u*(1,1))so;
affixe.G(u*(8.5,1))se;
affixe.E(cercle(F,6cm) intersectionpoint cercle(G,2cm))n;
draw triangle(E,F,G);
cotation(F,E,2mm,2mm,btex $6\,cm$ etex);
cotation(E,G,2mm,2mm,btex $2\,cm$ etex);
cotation(F,G,-2mm,-2mm,btex $7,5\,cm$ etex);
endfig;
end