# 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=Poligono regolare di 17 lati

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=costruire il poligono regolare di 17 lati di centro 1 e avente un vertice in 2
hint=Gauss (1777-1855)  stato il primo a rendersi conto della possibilit \
di costruire un poligono regolare di 17 lati con regola e compasso, all'et \
di 19 anni. \
<p>Successivamente, altre costruzioni concrete sono state proposte da \
diverse persone. \
Essendo tutte queste costruzioni troppo complicate per una indicazione a \
parole, ci contenteremo di dare una soluzione basata sul metodo di \
H. W. Richmond  (Quarterly Journal of Mathematics 26, 1893, pp. 296-297;\
voir aussi H. E. Dudeney, Amusements in Mathematics (London 1917), p. 38),\
descritta nel libro ``Introduction to Geometry'' par H.-S.-M. Coxeter.\
<p>Puoi seguire questa soluzione cliccando sul link ``soluzione'' \
nella pagina di lavoro.

L'estratto del libro citato. <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

