Fichier triangles-oa2009.mp (figure 8) — Modifié le 4 Octobre 2009 à 23 h 34

Triangles magiques

triangles-oa2009.mp (figure 8)
Figures associées à l'un des exercices des olympiades académiques de mathématiques (2009).
Source


verbatimtex
%&latex
\documentclass[12pt]{article}
\usepackage{fourier}
\begin{document}
etex

pair A,B,C;
A = origin;
B = (4cm,0);
C = B rotated 60;

pair P[];
P1 = A;
P2 = (1/3)[A,B];
P3 = (2/3)[A,B];
P4 = B;
P5 = (1/3)[B,C];
P6 = (2/3)[B,C];
P7 = C;
P8 = (1/3)[C,A];
P9 = (2/3)[C,A];

picture disque;
disque := image(
    fill fullcircle scaled 0.7cm 
	withcolor white;
    draw fullcircle scaled 0.7cm
	withpen pencircle scaled 1.5pt
	withcolor (0.7,0.5,0);
);

picture triangle;
triangle := image(
    draw A--B--C--cycle
	withpen pencircle scaled 1pt
	withcolor (0.2,0.1,0.5);
    for i:=1 upto 9: draw disque shifted P[i]; endfor;
);



beginfig(0);
    draw triangle;
endfig;


beginfig(1);
    draw triangle;
    label(btex 5 etex,P1);
    label(btex 3 etex,P2);
    label(btex 4 etex,P3);
    label(btex 8 etex,P4);
    label(btex 9 etex,P5);
    label(btex 1 etex,P6);
    label(btex 2 etex,P7);
    label(btex 7 etex,P8);
    label(btex 6 etex,P9);
endfig;


beginfig(2);
    draw triangle;
    label(btex 5 etex,P1);
    label(btex 6 etex,P2);
    label(btex 1 etex,P3);
    label(btex 8 etex,P4);
    label(btex 7 etex,P5);
    label(btex 3 etex,P6);
    label(btex 2 etex,P7);
    label(btex 9 etex,P8);
    label(btex 4 etex,P9);
endfig;


beginfig(3);
    draw triangle;
    label(btex 2 etex,P1);
    label(btex 5 etex,P2);
    label(btex 7 etex,P3);
    label(btex 3 etex,P4);
    label(btex 9 etex,P5);
    label(btex 4 etex,P6);
    label(btex 1 etex,P7);
    label(btex 8 etex,P8);
    label(btex 6 etex,P9);
endfig;


beginfig(4);
    draw triangle;
    label(btex 2 etex,P1);
    label(btex 9 etex,P2);
    label(btex 5 etex,P3);
    label(btex 3 etex,P4);
    label(btex 8 etex,P5);
    label(btex 1 etex,P6);
    label(btex 7 etex,P7);
    label(btex 4 etex,P8);
    label(btex 6 etex,P9);
endfig;


beginfig(5);
    draw triangle;
    label(btex 1 etex,P1);
    label(btex 9 etex,P2);
    label(btex 5 etex,P3);
    label(btex 4 etex,P4);
    label(btex 6 etex,P5);
    label(btex 2 etex,P6);
    label(btex 7 etex,P7);
    label(btex 3 etex,P8);
    label(btex 8 etex,P9);
endfig;


beginfig(6);
    draw triangle;
    label(btex 4 etex,P1);
    label(btex 8 etex,P2);
    label(btex 6 etex,P3);
    label(btex 1 etex,P4);
    label(btex 9 etex,P5);
    label(btex 2 etex,P6);
    label(btex 7 etex,P7);
    label(btex 3 etex,P8);
    label(btex 5 etex,P9);
endfig;


beginfig(7);
    draw triangle;
    label(btex 3 etex,P1);
    label(btex 8 etex,P2);
    label(btex 6 etex,P3);
    label(btex 2 etex,P4);
    label(btex 9 etex,P5);
    label(btex 1 etex,P6);
    label(btex 7 etex,P7);
    label(btex 4 etex,P8);
    label(btex 5 etex,P9);
endfig;


beginfig(8);
    draw triangle;
    label(btex $n_4$ etex,P1);
    label(btex $n_5$ etex,P2);
    label(btex $n_6$ etex,P3);
    label(btex $n_7$ etex,P4);
    label(btex $n_8$ etex,P5);
    label(btex $n_9$ etex,P6);
    label(btex $n_1$ etex,P7);
    label(btex $n_2$ etex,P8);
    label(btex $n_3$ etex,P9);
endfig;


beginfig(9);
    draw triangle;
    label(btex 5 etex,P1);
    label(btex $n_5$ etex,P2);
    label(btex $n_6$ etex,P3);
    label(btex 8 etex,P4);
    label(btex $n_8$ etex,P5);
    label(btex $n_9$ etex,P6);
    label(btex 2 etex,P7);
    label(btex $n_2$ etex,P8);
    label(btex $n_3$ etex,P9);
endfig;

end.