Fichier fg-v8_61-62.mp (figure 1) — Modifié le 4 Avril 2008 à 00 h 23

## Construction d'un pentagone

Le point G divise le segment [A,B] selon le nombre d'or. Quatre cercles de même rayon AB suffisent alors à déterminer les sommets d'un pentagone.
Source
``````

picture UnBeauPoint;
UnBeauPoint := image(
fill fullcircle scaled 3pt;
fill fullcircle scaled 2pt withcolor red+green;
);

vardef pointe expr p = draw UnBeauPoint shifted p; enddef;

pair A,B,G,P[];
path C[];

UnSurPhi = (sqrt(5) - 1) / 2;

beginfig(1);
A := origin;
B := right scaled 3cm;
G := UnSurPhi [A,B];

C1 := fullcircle scaled (2 abs(B-A)) shifted A;
C2 := C1 shifted (B - A);
C4 := C1 shifted (G - A);

P1 := G + B - A;

C5 := C1 shifted (P1 - A);

P2 := C1 intersectionpoint C5;
P4 := (reverse C1) intersectionpoint C4;
P5 := (reverse C2) intersectionpoint C5;

fill (A--P4--P5--P1--P2--cycle) withcolor (.9,.7,.65);
draw A--P4--P5--P1--P2--cycle;

draw A--P1;
draw C1;
draw C2;
draw C4;
draw C5;

draw P2--P4 dashed evenly
withcolor (0.2,0.3,0.6);

pointe A;
pointe B;
pointe G;
pointe P1;
pointe P2;
pointe P4;
pointe P5;

label.llft(btex \$A\$ etex, A);
label.llft(btex \$G\$ etex, G);
label.lrt(btex \$B\$ etex, B);
label.lrt(btex \$P_1\$ etex, P1);
label.top(btex \$P_2\$ etex, P2);
label.llft(btex \$P_4\$ etex, P4);
label.lrt(btex \$P_5\$ etex, P5);

endfig;

end``````