# Definition of an exercise ruler & compass.
# syntax of the file.
# points:  each line defines a point.  x,y
# lines:   each line defines two points on a line.   x1,y1,x2,y2,type
#          type: 1 (segment), 2 (line), 3 (semiline direct), 4 (semiline inverse)
#	   type is facultative, defaulting to 1.
# circles: each line defines a circle. x,y,r,n
#	   where (x,y) is the center, r=radius,
#          n is the number of point for the center (if n>0).
# goal: each line defines an object. First item is the type of the object
# (point,line or circle), the rest are parameters (same as above).
# goal_text: text explaining the goal. (language-dependent)

title=Polygone rgulier de 17 cts

points=0,0\
0,-1

lines=0,0,0,-1,1

goal=line,0,-1,sin(pi*19/17),cos(pi*19/17),1\
line,sin(pi*19/17),cos(pi*19/17),sin(pi*21/17),cos(pi*21/17)\
line,sin(pi*21/17),cos(pi*21/17),sin(pi*23/17),cos(pi*23/17)\
line,sin(pi*23/17),cos(pi*23/17),sin(pi*25/17),cos(pi*25/17)\
line,sin(pi*25/17),cos(pi*25/17),sin(pi*27/17),cos(pi*27/17)\
line,sin(pi*27/17),cos(pi*27/17),sin(pi*29/17),cos(pi*29/17)\
line,sin(pi*29/17),cos(pi*29/17),sin(pi*31/17),cos(pi*31/17)\
line,sin(pi*31/17),cos(pi*31/17),sin(pi*33/17),cos(pi*33/17)\
line,sin(pi*33/17),cos(pi*33/17),sin(pi*35/17),cos(pi*35/17)\
line,sin(pi*35/17),cos(pi*35/17),sin(pi*37/17),cos(pi*37/17)\
line,sin(pi*37/17),cos(pi*37/17),sin(pi*39/17),cos(pi*39/17)\
line,sin(pi*39/17),cos(pi*39/17),sin(pi*41/17),cos(pi*41/17)\
line,sin(pi*41/17),cos(pi*41/17),sin(pi*43/17),cos(pi*43/17)\
line,sin(pi*43/17),cos(pi*43/17),sin(pi*45/17),cos(pi*45/17)\
line,sin(pi*45/17),cos(pi*45/17),sin(pi*47/17),cos(pi*47/17)\
line,sin(pi*47/17),cos(pi*47/17),sin(pi*49/17),cos(pi*49/17)\
line,sin(pi*49/17),cos(pi*49/17),0,-1
goal_text=construire le polygone rgulier de 17 cts de centre 1 et ayant un sommet en 2
hint=Gauss (1777-1855) est le premier  raliser la possibilit de construire\
un polygone rgulier de 17 cts avec rgle et compas,  l'age de 19. <p>Depuis,\
plusieurs constructions concrtes sont proposes par diffrentes personnes.\
Comme ces constructions sont toutes trop compliques pour une indication\
en phrases, nous nous contentons de donner une solution base sur la mthode\
de H. W. Richmond (Quarterly Journal of Mathematics 26, 1893, pp. 296-297;\
voir aussi H. E. Dudeney, Amusements in Mathematics (London 1917), p. 38),\
dcrite dans le livre ``Introduction to Geometry'' par H.-S.-M. Coxeter.\
<p>Vous pouvez suivre cette solution en cliquant sur le lien ``solution''\
dans la page de travail.

L'extrait du livre ci-dessous. <p><center>\
<img border=1 src=$module_dir/exo/17gon.gif></center>\

solution=nop#Cette construction de 155 tapes, due  H. W. Richmond, se trouve dans H.-S.-M. Coxeter, Introduction to Geometry, paragraphe 2.1.\
circle,1,2\
point,line,1,circle,1\
midper,2,3\
point,line,2,circle,1\
hide,point,3\
hide,point,5#Nous commenons par diviser segment 1-4 par 4 (point J dans Coxeter).\
middle,1,4\
middle,1,6#Point 7 est le point J dans Coxeter.\
hide,point,4\
hide,point,6\
segment,2,7#Maintenant on divise l'angle 1-7-2 par 4.\
circle,7,1\
point,line,3,circle,2\
hide,point,8\
circle,1,9\
circle,9,1\
point,circle,3,circle,4\
hide,point,10\
hide,circle,3\
hide,circle,4\
segment,7,11#Droite 4 est la bissectrice de l'angle 1-7-2. On continue. Zoomez pour voir plus clair.\
point,line,4,circle,2\
hide,point,11\
hide,point,12\
circle,1,13\
circle,13,1\
point,circle,5,circle,6\
line,7,15\
point,line,1,line,5#Point 16 est le point E dans Coxeter. On cache les objets intermdiaires.\
hide,circle,5\
hide,circle,6\
hide,circle,2\
hide,point,9\
hide,point,13\
hide,point,14\
hide,point,15\
hide,line,4#Maintenant la droite JF dans Coxeter, 45&deg; par rapport  JE (droite 5).\
circle,7,16\
point,line,5,circle,7\
midper,16,17\
point,line,6,circle,7\
circle,16,18\
circle,18,16\
point,circle,8,circle,9\
segment,7,21\
point,line,7,line,1#Point 22 est le point F dans Coxeter. On cache les objets qui ne servent plus.\
hide,circle,9\
hide,circle,8\
hide,point,21\
hide,point,20\
hide,point,19\
hide,point,18\
hide,point,17\
hide,circle,7\
hide,line,6#Ensuite la construction du point K dans Coxeter. Zoom global conseill.\
middle,2,22\
circle,23,2\
point,line,2,circle,10#Point 24 (25 aussi) est le point K dans Coxeter.\
hide,circle,10\
hide,point,23\
circle,16,25\
point,line,1,circle,11#Les points N<sub>3</sub> et N<sub>5</sub> dans Coxeter (26,27) sont sortis. Il suffit de tracer les lignes horizontales passant par eux.\
circle,27,1\
point,line,1,circle,12\
midper,1,28\
hide,circle,12\
hide,point,28\
circle,26,1\
point,line,1,circle,13\
midper,1,29\
hide,circle,13\
hide,point,29\
point,line,8,circle,1\
point,line,9,circle,1#Points 30,31,32,33 sont dj des sommets du polygone  construire. On continue pour marquer les autres sommets.\
midper,30,32\
point,line,10,circle,1\
hide,point,35\
circle,30,34\
point,circle,1,circle,14\
hide,circle,14\
circle,36,30\
point,circle,1,circle,15\
hide,circle,15\
circle,2,37\
point,circle,1,circle,16\
hide,circle,16\
circle,38,2\
point,circle,1,circle,17\
hide,circle,17\
circle,31,39\
point,circle,1,circle,18\
hide,circle,18\
circle,33,40\
point,circle,1,circle,19\
hide,circle,19\
circle,41,33\
point,circle,1,circle,20\
hide,circle,20\
circle,42,41\
point,circle,1,circle,21\
hide,circle,21\
circle,43,42\
point,circle,1,circle,22\
hide,circle,22\
circle,44,43\
point,circle,1,circle,23\
hide,circle,23\
circle,45,44\
point,circle,1,circle,24#Voici tous les sommets de ce polygone de 17 cts.\
hide,circle,24#Maintenant on trace les artes du polygone.\
segment,2,37\
segment,37,36\
segment,36,30\
segment,30,34\
segment,34,32\
segment,32,46\
segment,46,45\
segment,45,44\
segment,44,43\
segment,43,42\
segment,42,41\
segment,41,33\
segment,33,40\
segment,40,31\
segment,31,39\
segment,39,38\
segment,38,2#Voil la construction est termine. On continue pour cacher les objets intermdiaires.\
hide,line,10\
hide,circle,11\
hide,point,27\
hide,point,26\
hide,point,25\
hide,point,24\
hide,point,22\
hide,point,16\
hide,point,7\
hide,line,9\
hide,line,8\
hide,line,7\
hide,line,5\
hide,line,3\
hide,line,2\
hide,circle,1

